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NIST Technical Note 1438

Optical Radiation Measurement with Selected

Detectors and Matched Electronic Circuits

Between 200 nm and 20 /im

George P. Eppeldauer, Editor

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ional Institute of Standards and Technology

inology Administration, U.S. Department of Commerce
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NIST Technical Note 1438

Optical Radiation Measurement with Selected

Detectors and Matched Electronic Circuits

Between 200 nm and 20 jDim

George P. Eppeldauer, Editor

Optical Technology Division

Physics Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-8440

April 2001

U.S. Department of Commerce

Donald L. Evans, Secretary

Technology Administration

Dr. Karen H. Brown, Acting Under Secretary of Commerce for Technology

National Institute of Standards and Technology

Dr. Karen H. Brown, Acting Under Secretary of Commerce for Technology
Certain commercial entities, equipment, or materials may be identified in this document in order to describe an

experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose.

Front Cover:

Equivalent circuit of a photodiode current-meter. The feedback impedance, R and C, of an

operational amplifier, OA, converts the photocurrent Ip of photodiode P into a voltage V. R and C

together with the impedance of the photodiode, Rs and Cj, attenuate ^ to the OA input. The inverse

of this feedback attenuation is the (closed-loop) voltage gain for the OA input drift and noise. Single

circles illustrate voltage sources and double circles illustrate cun-ent sources. One signal (the

photocurrent) source and three noise sources are shown in the circuit. The product of the feedback

attenuation and the OA open-loop gain gives the loop gain that determines the uncertainty of the

photocurrent-to-voltage conversion at a given signal frequency. Design considerations and

performance evaluation of photodiode current-meters are discussed in Papers 1, 3 and 4 for Si

photodiodes, in Paper 5 for Si trap detectors, in Paper 6 for Ge and InGaAs photodiodes, and in

Paper 7 for InSb photodiodes.

National Institute of Standards

and Technology

Technical Note 1438

Natl. Inst. Stand. Technol.

Tech. Note 1438

117 pages (April 2001)

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Preface

Improved detector technology in the past decade opened a new era in the field of radiometric and

photometric calibrations. Now, cryogenic electrical substitution radiometers with 0.01 % optical power

measurement uncertainty are the primary standards of the field. New generation radiometers, built with high

electronic and radiometric performance detectors, became the transfer and working standards to propagate

the high accuracy from the primary standard to field level measurements. The importance of high quality

detector standards has greatly increased as a result of demands in a wide range of technical areas. Nowadays, lamp standards, traditionally calibrated against source standards, are calibrated against detector

standards to obtain improved calibration accuracy.

The purpose of this Technical Note is to summarize the results of the research and development work carried out at the Optical Sensor Group of the Optical Technology Division for constructing accurate and wide

dynamic range radiometers with high performance detectors for the 200 nm to 20 /im wavelength range. Linear and stable operation was required from these radiometers to achieve detector spectral responsivity

transfer with low uncertainty. Large area thermal, pyroelectric, photoconductive (PC), and photovoltaic

(PV) detectors were selected, applied, and characterized at different controlled temperatures between 4.2 K

and 300 K. The resistance of these detectors ranged from 15 Q. to 50 GQ, their capacitance ranged from

0.18 nF to 36 nF. The detector output-signal measuring electronic circuits had to be designed and

individually matched to the complex impedance of the selected detector to optimize radiometer performance.

The frequency dependent fundamental gain-equations of operational-amplifier photocurrent-meters have

been worked out and applied for a large number of different types of photodiodes operating in both dc and ac

signal measurement modes. The gain equations were utilized to achieve signal measurement uncertainties

between 0.1 % and 0.01 % . Drift and noise were minimized for the radiometer outputs to obtain high

signal-to-noise ratios even at high signal gains.

The NIST developed radiometer standards are the key components of several recently realized high accuracy

scales. These are the spectral power and irradiance responsivity scales on the Spectral Comparator Facilities (for the ultraviolet, visible, and infrared ranges), the spectral power, irradiance, and radiance responsivity

scales of the Spectral Irradiance and Radiance Responsivity Calibrations with Uniform Sources Facility

(SIRCUS), the detector-based illuminance (photometric) scale, and the spectral irradiance scale

(disseminated by lamps).

Related additional papers, describing the input geometry, electronic and radiometric characterizations, and

spectral responsivity calibrations of the transfer and working standard radiometers are not included here. These subjects are beyond the scope of this Technical Note.

George P Eppeldauer

Ph.D. Electronics Engineer

Radiometer and Calibration Development

Optical Sensors Group, Optical Technology Division

National Institute of Standards and Technology

100 Bureau Drive, Gaithersburg, MD 20899-8441

111

Table of Contents

Preface iii

Introduction to the papers vii

1. "Fourteen-decade photocurrent measurements with large-area silicon photodiodes at room

temperature," Applied Optics, Vol. 30, No.22. 3091-3099, 1991. G. Eppeldauer and J. E. Hardis 1

2. "Temperature Monitored/Controlled Silicon Photodiodes for Standardization," SPIE

Proceedings, Vol. 1479, 71-77, 1991. G. Eppeldauer 11

3. "Chopped Radiation Measurement With Large Area Si Photodiodes," Journal of Research of

the National Institute of Standards and Technology, Vol. 103, No. 2, 153-162, 1998. G. P. Eppeldauer 19

4. "Noise-optimized silicon radiometers," J. Res. Natl. Inst. Stand. Technol. Vol. 105, No. 209,

209-219, 2000. G. Eppeldauer 29

5. "Opto-mechanical and electronic design of a tunnel-trap Si-radiometer," to be published in

the J. Res. Natl. Inst. Stand. Technol. G. P. Eppeldauer and D. C. Lynch 41

6. "Electronic characteristics of Ge and InGaAs radiometers," SPIE, Proceedings, Vol. 3061-

97, 833-838, 1997. G. Eppeldauer 63

7. "InSb Working Standard Radiometers," Metrologia, Vol. 35, 485-490, 1998. G. P. Eppeldauer, A. L. Migdall, and L. M. Hanssen 69

8. "Domain-engineered pyroelectric radiometer," Applied Optics, Vol. 38, No. 34, 7047-7055,

1999. J. Lehman, G. Eppeldauer, J. A. Aust, and M. Racz 75

9. "A cryogenic silicon resistance bolometer for use as an infrared transfer standard detector,"

in Thermal Phenomena at Molecular and in Cryogenic Infrared Detectors, M. Kaviany, D.

A. Kaminski, A. Majumdar, P. E. Phelan, M. M. Yovanovich, and Z. M. Zhang, eds., book

H00908-1994 (American Society of Mechanical Engineers, New York), pp. 63-67. G.

Eppeldauer, A. L. Migdall, and C. L. Cromer 85

10. "Linear HgCdTe radiometer," SPIE Proceedings, Vol. 1110, 267-273, 1989. G. Eppeldauer

andL. Novak 91

11. "Photocurrent measurement of PC and PV HgCdTe detectors," to be published in the J. Res.

NIST. G. P. Eppeldauer and R. J. Martin 99

Introduction to the Papers

George P. Eppeldauer

Paper 1 "Fourteen-decade photocurrent measurements with large-area silicon photodiodes at room

temperature," Applied Optics, Vol. 30, No.22. 3091-3099, 1991. G. Eppeldauer and J. E. Hardis

The noise and drift characteristics of large area sihcon photodiode current meters are analyzed at low

(dc) frequencies in this paper. High shunt-resistance silicon photodiodes and operational amplifiers

with large feedback resistors were used to achieve high photocurrent sensitivity at room temperature.

Operational amplifiers with very low input-bias-current were selected to minimize 1// noise from the

amplifier. The dominant resistor noise was equalized to the 1// amplifier noise by decreasing the

electrical bandwidth to 1.25 mHz. The drift was also equalized to the noise floor by regulating the

temperature of the Si radiometer within +/- 0.02 °C of the operating 25 °C value. The equivalent

photocurrent of the measured noise floor was 10'^^ A at a measurement time of 400 s. This implies a

signal measurement range of 14 decades. When the bandwidth was increased to 0.3 Hz, the noise

increased and ranged between 0.6 fA and 1 fA.

Paper 2

"Temperature Monitored/Controlled Silicon Photodiodes for Standardization," SPIE

Proceedings, Vol. 1479, 71-77, 1991. G. Eppeldauer

The paper describes how to monitor or control the temperature of photodiodes to obtain improved

accuracy in photocurrent measurements. Temperature monitored detectors are easier to construct, but

they require more calibration data and analysis as well as additional steps to interpret the results of

measurements. Temperature regulated detectors make measurement taking simpler, with the expenses

of additional and more complex hardware. Design considerations and examples for both methods are described.

Paper 3

"Chopped Radiation Measurement With Large Area Si Photodiodes," Journal of Research of

the National Institute of Standards and Technology, Vol. 103, No. 2, 153-162, 1998. G. P.

Eppeldauer

The different frequency-dependent gains of photodiode current meters were analyzed in this paper.

The gain equations are needed to perform constant (flat) signal-gains up to a high enough roll-off

frequency, to understand and minimize the noise-boosting effect with increasing frequencies (this

caused the factor of 10 noise increase in Paper 1), and to achieve small uncertainties in the current-to- voltage conversions. The different gain characteristics were illustrated with Bode plots. The Bode

plots were made from the gain equations using spread-sheets. Computer simulators were not used.

Signal-gain dependent frequency compensations were applied to optimize dc and ac photocurrent

measurements with large area Si photodiodes.

Paper 4

"Noise-optimized silicon radiometers," J. Res. Natl. Inst. Stand. Technol. Vol. 105, No. 209,

209-219, 2000. G. Eppeldauer

This paper is an extension of Paper 3. In addition to the design considerations of the dynamic

(frequency dependent) characteristics of photodiode current meters, an experimentally verified noise

Vll
analysis is described. After optimizing the dynamic characteristics, the noise floor was minimized in an ac measurement mode using Si photodiodes of different shunt resistance and operational

amplifiers with low 1// voltage and current noise. An equivalent root-mean-square (rms)

photocurrent noise of 8 x

10"' A was performed at a 9 Hz chopping frequency and 30 s integration

time constant. The radiometers, optimized for ac measurements, were tested in a dc measurement

mode as well. Performances in ac and dc measurement modes were compared. In the ac mode, a ten times shorter (40 s) overall measurement time was needed than in the dc mode (described in Paper 1) to obtain the same 10""" A noise floor.

Paper 5

"Opto-mechanical and electronic design of a tunnel-trap Si-radiometer," to be published in the

J. Res. Natl. Inst. Stand. Technol. G. P. Eppeldauer and D. C. Lynch

The design methods described in Papers 3 and 4 were applied to a transmission-type light-trap silicon

detector. Six Si photodiodes of two different sizes, selected for equal shunt resistance, were

connected in parallel in this power/irradiance mode transfer standard. The capacitance and the

resultant shunt resistance of the device were measured and frequency compensations were applied in

the feedback network of the photocun^ent-to-voltage converter to optimize signal-, voltage-, and loopgain characteristics. The trap-radiometer can measure either dc or ac optical radiation with high

sensitivity. The noise-equivalent power of the optimized device was 47 fW in dc mode and 5.2 fW at 10 Hz chopping. The deviation from the cosine responsivity in irradiance mode was measured to be

equal to or less than 0.02 % within 5° FOV and 0.05 % at 8° FOV. Both the electronic and the

optical-mechanical design considerations are discussed in detail.

Paper 6

"Electronic characteristics of Ge and InGaAs radiometers," SPIE, Proceedings, Vol. 3061-97,

833-838, 1997. G. Eppeldauer

Equal size (5 mm diameter) Ge and InGaAs photodiodes were tested in NIST-developed radiometers

and compared for sensitivity and stability. The electronic characteristics of the radiometers were measured versus photodiode temperature with a bandwidth of 0.3 Hz. At -30°C, a limit-sensitivity of

22 fA and a dark-current stability of 0.2 pA/16 hours were achieved with the InGaAs radiometer,

which was three times better than the results obtained with the Ge radiometer. The frequency

dependent gain characteristics were calculated and compared for the two types of radiometer as well.

The 36 nF capacitance of the Ge photodiode caused a noise boosting effect (voltage-gain increase)

for frequencies higher than 0.3 Hz. Accordingly, the Ge radiometer was restricted for dc signal

measurements only. The 0.5 nF capacitance of the InGaAs photodiode did not produce any noise

boosting up to about 8 Hz. The 10"^ loop gain at 8 Hz resulted in a 0.01% (coverage factor k=l)

current-to-voltage conversion uncertainty. The InGaAs radiometer could measure an 80 Hz signal

with a relative uncertainty of 0.1 % (^=1).

Paper 7

"InSb Working Standard Radiometers," Metrologia, Vol. 35, 485-490, 1998. G. P. Eppeldauer,

A. L. Migdall, and L. M. Hanssen

Characterization of custom-made transfer standard InSb radiometers is described in this paper. The

InSb radiometers maintain the spectral radiant power and irradiance responsivity scales of NIST

between 2 fim and 5.4 /xm. The field-of-view of the 77 K detectors is limited to 17°. The InSb

detectors were selected for high shunt impedance to achieve high sensitivity. The transimpedance-,

Vlll
voltage-, and loop-gains of the current-to-voltage converters were optimized for optical radiation

chopped at 40 Hz. At the peak responsivity, the noise-equivalent-power (NEP) is 0.6 pW in an

electrical bandwidth of 0.3 Hz. The ratio of the dc ambient-background-current to the ac noiseequivalent-current is 10^. Spatial and angular responsivities, linearity, stability, and flashing were

also characterized.

Paper 8

"Domain-engineered pyroelectric radiometer," Applied Optics, Vol. 38, No. 34, 7047-7055,

1999. J. Lehman, G. Eppeldauer, J. A. Aust, and M. Racz

A domain-engineered pyroelectric transfer standard radiometer has been developed at NIST to extend

the spectral responsivity scale from the visible to the ultraviolet and near-infrared ranges. The domain

engineering consisted of inverting the spontaneous polarization over a 10 mm diameter area in the

center of a uniformly poled, 15.5 mm x 15.5 mm square, 0.25 mm thick LiNbOs plate. Gold black was used as the optical absorber on the detector surface, and an aperture was added to define the

optically sensitive detector area. The radiometer included a temperature monitor for the detector and

a current-to-voltage converter optimized for signal- and loop-gain. The results indicate that the

acoustic sensitivity was significantly reduced without loss of optical sensitivity. The detector noiseequivalent-power was not exceptionally low but was nearly constant for different acoustic

backgrounds. In addition, the detector's spatial response uniformity variation was less than 0.1 %

across the 7.5 mm diameter aperture, and reflectance measurements indicated that the gold black

coating was spectrally uniform, within 0.2 %, from 800 nm to 1800 nm. Other detailed evaluations of

the radiometer include detector responsivity as a function of temperature, electrical frequency

response, angular response, and field of view.

Paper 9

"A cryogenic silicon resistance bolometer for use as an infrared transfer standard detector," in

Thermal Phenomena at Molecular and in Cryogenic Infrared Detectors, M. Kaviany, D. A.

Kaminski, A. Majumdar, P. E. Phelan, M. M. Yovanovich, and Z. M. Zhang, eds., book

H00908-1994 (American Society of Mechanical Engineers, New York), pp. 63-67. G.

Eppeldauer, A. L. Migdall, and C. L. Cromer

A transfer standard cryogenic bolometer has been developed to maintain the NIST spectral power

responsivity scale between 2 /xm and 20 /xm. The resistance of the heavily doped Si sensor increased

six orders of magnitude when it was cooled down from room temperature to the 4.2 K operating

temperature. The computer controlled bolometer has high sensitivity, accuracy, stability and

dynamic range as well as a large detector area, fast time response and flat spectral response. The

design and testing of the silicon composite bolometer is described in this paper. This device has a dynamic range of 5 decades, a noise floor of 36 pW/Hz''^^, a nonlinearity of less than 1%, a spatial

response nonuniformity of about 0.3% and a constant frequency-dependent response out to about 100

Hz.

Paper 10

"Linear HgCdTe radiometer," SPIE Proceedings, Vol. 1110, 267-273, 1989. G. Eppeldauer and

L. Novak

The basic modes of electrical operation of photoconductive optical radiation detectors are analyzed in

this paper. The nonlinearity in voltage-mode measurements can be eliminated by using current-mode

measurements. A HgCdTe photoconductive radiometer has been designed, based on this analysis,

IX
which measures the current through a biased detector. A built-in calibrating capability in the circuits

of the radiometer makes it possible to eliminate the effects of a long-term drift in the bias voltage,

thereby achieving a lower uncertainty.

Paper 1

"Photocurrent measurement of PC and PV HgCdTe detectors," to be published in the J. Res.

NIST. G. P. Eppeldauer and R. J. Martin

Novel photocurrent meters for working standard photoconductive (PC) and photovoltaic (PV)

HgCdTe detectors have been developed to maintain the spectral responsivity scale of NIST in the

wavelength range of 5 /im to 20 jLtm. The linear PC mode preamplifier does not need any

compensating source to zero the effect of the detector bias current for the preamplifier output. The

impedance multiplication concept with a positive feedback buffer amplifier was analyzed and utilized

in a bootstrap transimpedance amplifer to measure photocurrent of a 200 Q. shunt resistance

photodiode with a maximum signal gain of 10^ V/A. In spite of the high performance lock-in used as

a second-stage signal-amplifier, the signal-to-noise ratio had to be optimized for the output of the

photocurrent preamplifiers. Noise and drift were equalized for the output of the PV mode

preamplifier. The signal gain errors were calculated to determine the signal frequency range where

photocurrent-to-voltage conversion can be performed with very low uncertainties. For the design of

both PC and PV detector preamplifiers, the most important gain equations are described.

Measurement results on signal ranges and noise performance are discussed.
a reprint from Applied Optics

Fourteen-decade photocurrent measurements with large-area

silicon photodiodes at room temperature

G. Eppeldauer and J. E. Hardis

Recent improvements in commercial silicon photodiodes and operational amplifiers permit electrical noise to be reduced to an equivalent of 0.1 fA of photocurrent when a measurement time of 400 s is used. This is equivalent to a photocurrent resulting from fewer than 800 photons/s, and it implies a dynamic range of 14

orders of magnitude for a detector circuit. We explain the circuit theory, paying particular attention to the measurement bandwidth, the causes of noise and drift, and the proper selection of circuit components. These

optical radiation detectors complement the primary radiometric standards. These detectors may replace

photomultiplier tubes that have been used traditionally and or that were too costly to be used. Key words: Bandwidth, dynamic range, noise, optical detection, photodiode, photonics, radiometry,

sensitivity.

I. Introduction

The improvements in commercial silicon photodiodes

and operational amplifiers over the past several years

permit a corresponding increase in the performance of

optical radiation measurements. Important electrical

properties of photodiodes and operational amplifiers

that affect high-sensitivity applications have been re- ported in the literature.^ A limiting factor is the 1//

noise ofthe operational amplifier, which is chosen to be an electrometer-grade device characterized by a high

input impedance and a low input bias current. Anoth- er limiting factor is the shunt resistance of the photodiode. This is the effective resistance that connects in

parallel to the photocurrent source and is the slope of

the diode's I-V curve at the operating point. For the

study in Ref. 1 photodiodes were not available with

shunt resistances >1.4 GQ. More recently, the shunt

resistances of the best silicon photodiodes have in- creased by an order of magnitude. Further, operational amplifiers have become available with an order

of magnitude less input noise. These developments

The authors are with the Radiometric Physics Division, National

Institute of Standards and Technology, Gaithersburg, Maryland

20899. Received 12 October 1990. 0003-6935/91/223091-09$05.00/0.

© 1991 Optical Society of America.

have made it necessary to reanalyze the behavior of

these devices in a complete measurement circuit. Our

goals in this study were to get optimum performance

and to extend the application of these detectors to

situations in which greater sensitivity would be re- quired.

There is a growing market for such solid-state detectors. One photodiode manufacturer offers an integrated silicon-photodiode and monolithic-operational-amplifier package with a specification of 5-fW noise

equivalent power (NEP) in the band of dc to 1 Hz at 750-nm peak response.^ The manufacturer uses a

small-surface-area (6.7 mm^) photodiode and a fixedgain amplifier of 10^° V/A. The product literature

compares this device with a photomultiplier tube

(R374 with an S-20 photocathode), as its NEP is less than the photomultiplier for wavelengths longer than

760 nm. An intended application of this product is in optical

communication, where greater detector sensitivity

permits longer ranges. However, there are a large

number of other applications in which silicon detectors

could replace large and expensive photomultiplier

tubes or inspire new, better, or less-expensive products. There is an increasing demand for high-sensitivity radiant-power measurements in such diverse fields as chemiluminescence and bioluminescence, radiometry, photometry, pyrometry, materials science (optical

density and surface-scatter measurements), astronomy (Earth- and space-based stellar radiometry), and

night vision. Silicon photodiodes offer the additional

advantages of higher stability, greater reliability, lin- earity over a greater dynamic range,^ and simpler operation.

1 August 1991 / Vol. 30, No. 22 / APPLIED OPTICS
The field of stellar radiometry illustrates an application for which high stability is as important as high

sensitivity. Searching for planets around stars depends on the observance of small decreases in starlight

(0.01% for terrestrial-sized planets) produced by the

transit of a planet across a stellar disk.^-^ To measure

a 10~^ change requires a signal-to-noise ratio of 10^ or

better and a correspondingly high stability.

The goals of high sensitivity, wide dynamic range,

stability, and linearity complement the silicon photodiode detectors that are used as self-calibrated, primary standards.^ These photodiodes are inversion-layer

silicon devices, which have a limited range of linear

operation.'''^ When they are combined in a light-trap

arrangement to eliminate reflectance losses,^ the range

of operation for highest acciu-acy is further limited to

less than a decade. The appropriate radiant power

level used in realizing primary standards is a few

tenths of a milliwatt, which typically requires a laser

light source. However most applications that use tra- ditional light sources and monochromators involve

much lower radiant power levels. The silicon photodiode detectors discussed in this paper could act as transfer standards and improve the overall dynamic

range of silicon-based radiometric standardization.

II. Circuit Theory

Consider the basic circuit of Fig. 1(a). The photodiode operates without a bias voltage, in the so-called

short-circuit arrangement.^*^ The output voltage

iVoxit) of the amplifier is proportional to the photocurrent from the diode, as determined by the feedback

transimpedance Rf. From the viewpoint of the photodiode, the amplifier and the feedback resistor appear

as an impedance ofRf/A across its terminals, where A is the open-loop gain of the amplifier. As A is of the

order of 10^, the short-circuit impedance across the

photodiode is very small compared with typical values

of the photodiode's shunt resistance, i?sh, even when R{

is of the order of 10^^ ft. Figure 1(b) emphasizes the aspects of this circuit

that contribute to the measurement noise. The amplifier contains two noise sources. The first is Vvn, input

voltage noise, which manifests itself as an effective

voltage fluctuation at the input terminal of the amplifier. VvN is the principal source of l/f noise. That is, it has equal power in each decade of the measurement

passband. The other is /in, input current noise, which

is caused by the fluctuation of the input bias current of

the amplifier, /in is a white noise, with a power proportional to the bandwidth.

Although ideal operational amplifiers are usually

modeled as having a high, if not infinite, input impedance (and nothing more), real ones are the source of a

small amount of current at the input pins. This input

bias current is of the order of 10~^2_xo-i3 a in good

devices and may occur with either polarity on a pieceby-piece basis, /in is caused by the shot noise of the

charge carriers of the input bias current. Current shot

noise has the well-known rms value of yj2eIAf, where e

is the charge of the electron and A/ is the frequency

Out

Fig. 1. Model circuit (a) components and (b) noise sources.

bandwidth of the measurement. In a typical operational amplifier with differential inputs, the current

fluctuations would be larger. We approximate /in as

(4e/BiasA/)i/2.ii

The effect of /in depends on the amplifier's source

impedance. In our case, the source resistance, Rso, is the parallel combination of /?sh and Rf [Rso — Rsh X Rt/

{Rsh + R{)]- The input current noise is reflected as an

input voltage on the amplifier of /in/?so. In manufacturers* specifications the claim "low noise" usually refers to Vyn- "Low input bias current"

implies low /in. Choosing which attribute is the most

important for a particular application depends on Rso,

the bandwidth of the measurement, and the temperature stability of the measuring circuit. This theme is a

major pvu-pose of this paper.

Figure 1(b) also illustrates two other noise sources of

concern. One is the voltage that is due to resistor

noise, Vrn, which is also known as Johnson noise or thermal noise. This noise is an inevitable conse- quence of charge carriers in resistors. Its rms value is {AkTRso^f)'-^^, where k is Boltzmann's constant and T

is the absolute temperature.^^ Like /in, Vrn is a white

noise.

The last noise that we consider, i?xN> is often called

excess noise, and it is due to resistance fluctuations. It

is excess in the sense that resistors can be noisier than

the Johnson noise formula predicts. This noise used

to be called current noise because it reqtiires a current

through the resistors to detect it. However, the current does not produce the noise, and the association was misleading. ^^ Good, low-noise component resistors may be obtained for Rf. For us the excess noise is due to the fluctuation of /2sh of the photodiode.

Excess noise includes the generation-recombination

noise of semiconductors, which corresponds to fluctuations in the number of charge carriers. ^'^ This can be a white noise also. However the various factors that

determine the I-V relationship of a diode^^ include the

APPLIED OPTICS / Vol. 30, No. 22 / 1 August 199 ?
mobility of the carriers as well as their number. Fluctuations of these other factors may cause 1// noise. ^^ When we fail to include excess noise in our circuit

model it does not mean that this noise is insignificant

or unimportant but only that it is unpredictable without a deeper knowledge of the inner workings of the

photodiode. It may also vary because of environmental conditions, such as exposure of the photodiode to hxunid air.^^ Nevertheless, the circuit's response to photocurrent does not depend on iJgh, nor then to fluctuations in Rsh- These fluctuations matter in that

they impose a noise voltage on the amplifier because of

the amplifier's /Bias- Each of the four noise sources produces an

independent, randomly varying voltage. The resistor noise Frn can be directly measured at the amplifier

output. The rms value of the total input noise voltage as seen by the amplifier is: FiN= [Fvn' +4e/Biasi?so V+ (4ias^XNn (la)

The sensitivity of the photocurrent measurement is limited by the total output noise voltage of the

amplifier:

^ON = [(^v ^in)' + 4kTR,,^f]"^ (lb)

where the closed loop voltage gain Ay is equal to (Rf+Rsh)/RshThis explains the critical importance of the photodiode shunt resistance in determining the ultimate sensitivity of the measuring circuit. To enable us to measure weak photocurrents, R{ must be made large.

However, when R{ > Rsh, increasing R{ increases Ay

significantly as well, implying an amplification of the

noise along with the amplification of the signal. Larger values of i2gh permit larger values of R{ to increase

ampUfication of the signal without undue noise.

III. Measuring Voltage Noise

Before selecting a type of operational amplifier to be

used for high-sensitivity applications, we independently measured the voltage noise of various candidates. Although bias current is often specified by the

manufacturer, voltage noise, particularly at low fre- quencies, is a more subtle attribute. In this context,

the noise is manifested as the scatter of repeated measurements of the amplifier's output offset voltage.

Output offset voltage is the nominal output value of

the amplifier when no signal is apphed and when the

source resistance is low (so that input bias current

effects are negligible). Like output voltage noise, it is usually proportional to Ay. The input offset voltage is the measured output offset voltage as reduced by this

factor, and we take it to be an intrinsic amplifier characteristic. For this purpose, adjustment need not be

made to reduce it. Figure 2 shows the circuit used for these measure- ments as well as others that are discussed below. The

circuit was enclosed in a lighttight and electrically

shielded package. The amplifiers were installed in a socket for ease of substitution. Component resistors were sometimes substituted for the photodiode to rep10k 90k 900k 9M

I i~T"C—i~H— ^"T"^——^~|

OUT

Fig. 2. Circuit details.

licate different source resistances. Both Rf and M

were selected with switches. Here, Mis a multipher, an extra gain that could be introduced by reducing the

feedback voltage through a resistive divider. This

feature is appropriate only when R{ is well above the 1- kn output impedance of the divider.

[Whereas Mmay be used for amplifying the output

from the detector, measurements showed that it does

not improve the signal-to-noise ratio. Note that,

while the signal gain is Af X Rf, the noise gain Av is MX

(Rf + i?sh)/i?sh- On the other hand, because the output

of the amplifier remains bounded by the supply voltage, the dynamic range of the circuit is reduced when M> 1 . Tlierefore the multiplication switch should be

eUminated in most circumstances.]

The output of the circuit was connected directly to a microcomputer-controlled digital voltmeter (DVM).

This multislope-type DVM integrated the output voltage for a selectable time period, a count of the power

line cycles. To produce longer integration times than

the DVM normally allowed, an external microcomputer averaged a sequence of repeated measurements.

Table I compares multiple samples of three tj^jes of

operational amplifier from the Burr Brown product

line. All are designed to be electrometer-type amplifiers, with a low input bias current. The OPA128LM

and OPA104CM amplifiers are categorized as ultralow

bias current devices. They are specified as having a

bias current below 75 fA, the lowest of the product line. The OPAlllBM amplifier has a higher bias current

(specified as 1 pA, maximum) but is described as having lower noise. Nevertheless the manufacturer provides no specifications about noise below 0. 1 Hz. Both

the OPA128LM and the OPAlllBM are newer generation products.

To measure the offset voltage and voltage noise of

1 August 1991 / Vol. 30. No. 22 / APPLIED OPTICS
Table I. Statistics of Amplifier Output Measurements Showing the Mean

(the Offset Voltage) and the Standari Deviation (the Voltage Nolse)^ OPA104CM OPA128LM OPAlllBM

Sample Mean Std Dev Mean Std Dev Mean Std Dev

1 -23.84 7.94 -146.68 0:4 144.83 0.21 2 -36.81 9.10 67.24 0.53 -30.57 0.09 3 39.07 3.05 -111.02 0.55 -21.65 0.05 4 -79.14 8.27 158.66 1.30 -5.52 0.11 5 -107.05 6.71 30.19 0.42 — —

" Values are quoted in millivolts, and the system gain A\j was 1000.

these candidate operational amplifiers, a l-ki2 resistor was substituted for the photodiode to make the cur- rent and resistor noises negligibly small. Rf was set to

1 Mfi, and M=l was used for an overall gain Ay of 10^. The DVM was set to integrate for 100 power line cycles (10 cycles repeated 10 times and digitally aver- aged within the DVM). This integration time of 1 .67 s would correspond to a measurement bandwidth for white noise of 0.3 Hz. One hundred of these readings were externally averaged, resulting in a single measurement of the output offset voltage. The measure- ment bandwidth for white noise in the latter case would be 1.25 mHz. The reason is explained in Appendix A. The offset voltage was measured a nominal 10 times

for each amplifier in this fashion, and the statistics of

these 10 measinrements are reported in Table I. The

columns labeled Mean contain the results of final aver- aging of the 10 values. The columns labeled Std Dev

contain the standard deviations of the 10 intermediate

averages. The standard deviations of all 1000 individual readings were similar, showing that this noise was

not much affected by the longer integration.

, This behavior is indicative of 1// noise. A measure- ment passband depends on two characteristic times.

The integration time of the individual data points

determines the high-frequency roUoff, since the higher-frequency components are averaged out. Similarly

the time spent making the repeated measurements

determines the low-frequency roiloff, because lowerfrequency components will not be noticed. That is, noise frequencies that act too slowly will not cause a

scatter in the data during the time that one watches for

it. Both roiloff frequencies are inversely proportional

to their characteristic times in roughly the same way.

For P quickly repeated measurements, the lower roll- off frequency is ^\/P of the higher.

For white noise with a large P, the measurement

bandwidth is essentiaUy determined by the upper roll- off frequency, as the difference between the lower roll- off and Hz (i.e., dc) is small. Usually the lower roiloff frequency is ignored, and the noise is predicted by the

integration time only. In contrast, 1// noise is more

sensitive to the lower roiloff frequency. The rms volt- age fluctuation owing to 1// noise goes as [log(/high/

/low)]^^^. the radicand being the number of decades in the noise passband. This equals [log(P)]^/2, a slowly

varying function of P. Whereas data scatter caused by

white noise depends mostly on the integration time,

data scatter caused by 1// noise depends mostly on the

number of (equally timed) data points, independent of

their integration time.

Here, if the noise were truly a 1// noise we would

expect the standard deviation of the 1000 individual

readings to be roughly \/3 times larger than that of the

10 intermediate averages. If it were a white noise

instead, the standard deviation of the 1 intermediate

averages would have been roughly V240 times smaller,

following the ratio of the bandwidths. Our data for

the various amplifiers showed that the noise decreased

by less than a factor of 2. Therefore, for simplicity in

the remainder of this paper, input voltage noise will be

treated as a constant, a characteristic of an amplifier,

and independent of integration time. This relies on

the slowly varying nature of [log(P)]^''2 ^nd says that

the data in Table I (P = 10) should be similar to the

results obtained when 10 < P < 30. The data in Table I show that the OPA128LM amplifier has an order of magnitude less voltage noise

than does the OPA104CM, the earlier generation amplifier having a consistently low noise level, used in our previous research. ^ However, on average the

OPAl28LMs' have approximately five times the voltage noise of the OPAlllBM's.

Table I also shows noise variation among individual

samples of OPA128LM amplifiers within a factor of 2

of the mean. This compares favorably with variations

in other makes and models of operational amplifiers

which, in our experience, can have noise levels that

vary among samples by an order of magnitude. For

most purposes this variation would not be significant,

and individual selection of these amplifiers for low Vvn

would not be necessary.

Also, please note that in product literature noise

voltage is often reported peak to peak, not rms. As a

rule of thumb, for 1000 measurements the peak-topeak value will be ^6.6 times larger than the rms one.^^

IV. Temperature Dependence and Drift

It is not enough to develop new photodiodes with

greater itsh to achieve greater measurement sensitivity.

Psh and Pf affect the noise level in Eq. (1) through their

combination, Pso- The current noise term is quadratic

in Pso, and the resistor noise term depends on it linearly. As current noise becomes the dominant noise when

Pso is large, care must be taken to use an amplifier with

a sufficiently low /Bias- Fortunately this is an easy

criterion to meet. However, the bias current poses a

greater problem because it changes with temperature.

This is an aspect of the problem called drift. In addition to random fluctuations (noise), there are

also changes in the amplifier output that appear on

inspection to be distinctively slower and often of larger

magnitude. We interpret these changes as being

caused by such things as the aging of the electronic

components and their temperature dependence. We

will elaborate on the latter effect for purposes of illus- tration and because it is the easiest source of drift to

control. Drift is particularly bothersome in this reAPPLIED OPTICS / Vol. 30, No. 22 / 1 August 1991 4
search because it may be confused with the low-frequency noise that we seek to compare.

As an example the manufacturer specifies that the

OPA128LM amplifier has a typical input offset voltage

Vo of ±140 nY (±500 /iV, maximum) and an input

offset voltage drift Vd of ±5 mV/°C. Its typical input

bias current Zsias is ±40 fA (at 25°C), and it grows

geometrically at a rate 7d of 6.7%/°C. (In light of the

above discussion about input bias current noise, since

the noise goes as the square root of the bias current the

noise grows geometrically 3.3%/'*C.) In addition, we

previously determined^ the decrease of the photodiode

shunt resistance with increasing temperature to be

'~11%/°C, which we call i^sD- A nominal Rsh is 5 Gfi. In the worst case, Rf is 100 Gfi, with a negligible temperature dependence of <500 parts in lO^/'C. These

values lead to an Ay of 21, which increases 11%/°C, and

an Rso of 4.8 Gfi, which decreases 11%/°C.

Referring again to Fig. 1, we see the effect of Vq and

/Bias on the output voltage, = -Av(Vo + /b (2)

For small temperature changes AT with these typical

component values, AVoffset/AT = 0.7 mV/°C for the

worst case alignment of the signs of Vd. ^o. and /Bias- In our experience, the value is closer to 1.2 mV/°C, still well within specification limits.

It will simplify matters to cast the temperature ef- fects in terms of a photociurrent change, A/offset, that

would yield an equivalent change in the magnitude of

the output voltage. Because the photocurrent gain is R(, /offset = V^Offset/^f. a^d

•^Offset ~ ^O'^so + ^Bias

A/offset = (Vd/R.o + VoRsd/Rso + /d^BUs)^^-

(3)

(4) AT refers to the small temperature changes that occur during the course of a sequence of measurements.

Similarly noise may be expressed as the photocurrent that would give an equivalent deviation to the

output voltage, on average:

/NoiBe=^ON/«f=V^IN/«so- (5) Of course, the detector-amplifier combination can- not effectively distinguish actual photocurrents smaller than these values. An appropriate design goal of

the circuit is to equalize the effects of noise and drift,

choosing an amplifier type that balances both problems for reasonable integration times and temperature

control.

V. Amplifier-Type Selection

Figure 3 predicts the performance of OPAlllBM and

OPA128LM amphfiers in this circuit. Drift and noise

are computed by using Eqs. (4) and (5), respectively,

and are shown as a function of source resistance i?so- The data for the typical amplifier characteristics are taken from the manufacturer's catalog, with the exception of VvN, for which we use the average of the values

in Table I. In the upper part of Fig. 3, ATis 0.1°C, and

A/ is 300 mHz. Both are easy to realize in an actual

100000 r- 0PA111BM

p PPA128LM

10000 ;_ =.,. 300 mHz /O.I °C

1000 v"'-. - \^'.., 5" 100

10

1

0.1 0.01

-^^iis...^^^ XX

c

o

^'°^'^'

oo

n

100000 r r c

10000 - ; 1.25 mHz/ 0.02 °C >3

0- LU

1000

100

10

1 X\

-

0.1 —1 1 1 1 1 L.\^^-

0.001 0.01 0.1 1 10 100 O.OOf 0.01 0.1 1 10 100 Source Resistance [GQ]

Fig. 3. Balancing noise and drift. The noise (solid curves) and

thermal drift (dotted curves) are expressed in terms of the photocurrent that would cause an equal change in amplifier output. The two

figures at the left show the expected performance of the OPAl 1 IBM

amplifier; those on the right show the performance of the

OPA128LM amplifier. The two top figures show easy specifications

for integration time and temperature stability; the bottom two show

tight specifications.

measurement. In the lower part of Fig. 3, AT is 0.02''C, and A/ is 1.25 mHz.

Figure 3 shows that when Rso > 1 Gfi the most severe

limit on sensitivity would be the drift caused by the

temperature fluctuations of an OPAlllBM amplifier.

That is, the drift of the OPAlllBM is much larger

than both the noise and the drift of the OPA128LM.

The last term of Eq. (4) is the culprit. For highsensitivity investigations (when Rso must be large), it is generally better to choose an amplifier with low-input

bias current (hence low bias current drift) than one

with low voltage noise. However when i?so < 300 Mfl,

the lower input offset voltage of the OPAlllBM would

provide the advantage. (Indeed in this situation it might be worthwhile to trim the amplifier to reduce

Vo.)

There is an additional aspect to the combinations of

A/ and AT shown in Fig. 3. Photodiodes specially

selected for high shunt resistance are available in the

range of 1-50 Gfl. In this range of source resistance,

the noise and the drift that would result from the use of an OPA128LM amplifier are roughly equal. At the

upper right of the figure, both A/ and AT constrain the

sensitivity of the detector electronics to '^1 fA. A

sensitivity of 0.1 fA requires reducing both A/ and AT

in tandem, as shown at the lower right, as well as a

larger Rsh- For the remainder of this paper we discuss results

obtained while using OPA128LM amplifiers. The use

of these amplifiers is consistent with the possibility of

having excess detector noise, which would also be proportional to the input bias current.

VI. Noise Characteristics of the Operational Amplifiers

Figure 4 shows noise measurements similar to those

described in Section III made on OPA128LM amplifi1 August 1991 / Vol. 30, No. 22 / APPLIED OPTICS
0.0001 0.001 0.01 10.0 100.0 Source Resistance [GQ]

Fig. 4. Noise measurements of OPA128LM amplifiers with differ- ent source resistances. The hatched areas at the left show the range

of the characteristic input voltage noises of the amplifier types

reported in Table I. The dashed line guides the eye toward the

voltage noise level of these particular amplifiers. This level of minimum noise cannot be much reduced by longer integration. The

solid lines are the Johnson noise of the source resistances for our two

integration times (300 mHz in open symbols and 1.25 mHz in filled symbols).

ers with various combinations of iJsh and Ri (both

component resistors) at room temperature in a thermally insulated (but not regulated) box. This test determines whether the electrical noise from the elec- tronics assembly is consistent with the predictions of

the previous sections. The square data points were

taken with one copy of the circuit, and the circular data

points with another. The format parallels Eq. (1). The DVM took 100 readings with integration times

of 1.67 s. For each collection of 100 readings, the

voltmeter reported their mean (measured in a bandwidth of 1.25 mHz) and their standard deviation (representing the noise in a bandwidth of 300 mHz). This

cycle was repeated at least 40 times; sometimes the

apparatus was run overnight and repeated the cycle

~140 times.

The open points in Fig. 4 represent the total input

noise [Eq. (1)] in a 300-mHz bandwidth. As before,

the input noise is the measured (output) noise divided

by A\. The output noise is taken to be the average of

the standard deviation reports from the voltmeter

(each covering 100 individual readings). The single

standard deviation of all the individual readings is not

used in order to reduce the effect of long-term drift. The filled points in Fig. 4 indicate the scatter of the means computed by the voltmeter. These points rep- resent the total input noise in a bandwidth of 1.25 mHz. Nominally 30 consecutive readings were con- sidered a group. However temperature-induced drift over the span of 30 measurements was a significant

problem at large values of Rso- To reduce the effect of

drift on the reported values, a least-squares fit was made to a line through the 30 consecutive values, and

the implied time-dependent background was subtracted from the raw data. In effect, the noise below 1.25

mHz is taken to be the rms value of the residuals after

the fit. The results of multiple sets of equal size were

averaged when enough data were available.

The fitting procedure had the side effect of raising

the low-frequency roUoff that affects the magnitude of

1// noise. It also narrowed the meaning of AT in Eq.

(4) to those temperature fluctuations that occurred on

the time scale of a few measurements but not so slowly

that they could be accounted for by background subtraction.

The resistor noise, as calculated at 300 K, is shown in

Fig. 4 for the two bandwidths of interest. The ranges

of voltage noises, as reported in Table I, are shown as shaded blocks at the left of the figure. This should be

taken as a rough guide to the reproducibility of this

experiment when other amplifiers of the same types

are used. In our case, the two amplifiers used have

very similar Vvn values. The dashed line represents an input voltage noise of 0.68 ^V. As expected for a

bias current of only 75 fA, there is no evidence of current noise (noise proportional to Rao) in this range

of Rso- The voltage noise (1// noise independent of

Rso) was remarkably consistent between the two bandwidths despite the different number of samples used

and the differences in the way the data were treated.

The results show that the construction and the packaging of the complete amplifier circuits have not creat- ed an electrical noise much beyond that expected. At

the longer integration time, the slight additional noise

may be due either to temperature fluctuations

>0.02°C or to excess noise in the component resistors.

Finally note that in the viewpoint of Fig. 4 at a source

resistance of 12 GQ, the effects of voltage noise and

resistor noise are equal in a measurement bandwidth

of 1.25 mHz. The sensitivity ofthe circuit could not be

readily improved there by simply integrating longer

(which reduces resistor noise). Indeed, the shunt re- sistance of each photodiode implies an integration

time that need not be exceeded.

VII. Photodiode Noise In this section we discuss noise measurements made

when Hamamatsu photodiodes were used in the cir- cuit. These diodes were specially manufactured and

then selected for the highest shunt resistances that

Hamamatsu could offer. The maximum Rsh requires

the highest fabrication skill of the photodiode vendor

and is limited by the number of crystal defects in the

starting material. The type S1226-8BQ photodiode is a PNN+ device; types S2386-8K and S2956-8BQ are made by P on N planar diffusion.

High-sensitivity applications suggest the use of

large-area photodiodes to intercept more optical radiation. However with increasing area the shunt resis- tance is reduced, and the jimction capacitance in- creases. To the extent that i^sh is due to leakage

around the junction, Rsh will scale inversely by the

square root of the diode's active area. To the extent

that Rsh is an effect of the P-N junction itself, i?sh will scale inversely with the active area. The diodes used

in this work all had active areas of 1/3 cm^.

APPLIED OPTICS / Vol. 30, No. 22 / 1 August 1991
Table II. Noise and Drift of Complete Detector-Amplifier Packages Cast In Terms of the Photocurrent that Would Cause the Same Change In Output

Limit Sensitivity (fA)

Photodiode A/ = 300 A/ = 1.25 Type Rsh (Gfi) Cj (nF) Circuit Copy mHz mHz

S1226-8BQ 6.5 1.3 A 0.66 ± 0.05 0.20 ±0.07

S2956-8BQ 50 4 A 1.0 ± 1.2 0.16 ±0.05

S1226-8BQ 8 1.3 B 0.61 ± 0.05 0.101 ± 0.021 S1226-8BQ 6.5 1.3 B 0.61 ± 0.05 0.102 ± 0.015 S2386-8K 20 3.2 B 0.83 ± 0.35 0.095 ± 0.020

We independently estimated the Rsh values of the

photodiodes using a Hewlett-Packard 4145A semiconductor parameter analyzer to measure and display

their I-V curves. Depending on the photodiode type,

the highest shunt resistances available were in the

range of 5-50 Gfi. These measurements have a toler- ance of ~20% because the 4145A is not designed for

such small currents. Additionally, these measure- ments are somewhat subjective, resulting from eyeball

fits of the data with a visual guide provided on the

screen of the analyzer.

When an actual photodiode is used in the circuit, the

shunt impedance consists of the shunt resistance and a

parallel junction capacitance. Because the shunt impedance is reduced at high frequencies, increased amplification of high-frequency noise will result. This

can be compensated by adding parallel capacitance to the feedback resistor. We note the typical junction

capacitance Cj of the various diodes. These data come

from the manufacturer's catalog.

To determine the noise inherent in five different

photodiodes, we used the procedure discussed in Section VI. The data are shown in Table II. Two differ- ent copies of the circuit were used. The B copy had a temperature monitor, which showed that the temperature was stable within O.Ol^C during a 400-s measure- ment cycle. The reported uncertainties are due to the

reproducibility of the measurements. They are the

statistical standard deviation (1 a) of > 100 repeated

measurements (consisting of 100 samples each) with

300-mHz bandwidth and 3 repeated measurements

(consisting of 30 samples each) with 1.25-mHz bandwidth.

Note that the noise in A/ = 300 mHz increases with

increasing Rsh contrary to the expected trend. The

scatter of the measurements increases as well. This is explained in part by noting that the RC time constants,

which are of the order of 10-200 s, are much larger than

the integration time of 1.6 s. The shunt impedance is reduced for noise frequencies within the detection

bandpass, giving them extra amplification. With

longer integration, the effect of junction capacitance is reduced.

The data show that noise-equivalent photocurrents

of 0.1 fA have been achieved. This implies a dynamic

range of 14 orders of magnitude for these devices since

Hamamatsu specifies a saturation current of ^lO mA.

(In practice, the OPA128LM amplifier can drive only 5

mA; a second-stage amplifier would be required for the

full dynamic range.)

VIII. Practical Considerations In practice, the effect of long-term drift is mitigated by

background subtraction. Each measurement should

consist of a cycle containing intervals when the detector is exposed and when it is blocked. These periods of

integration are separated by settling times, during

which the output from the amplifier is ignored. When

using the highest feedback resistor, 100 Gfi, we found

that 2 min of settling was required for equilibrium to be reached. (This was considerably slower than the

settling time for the 10-Gfi resistor, which was <1 s.) In our experience, the maximum R{ that was suitable

for the OPA128LM was 100 Gfi. For larger Rf the

amplifier became noticeably nonlinear.

A fixed R{ of 100 Gfi gives the circuit a dynamic

range of ~6 orders of magnitude. Note that 0.1 fA of

photocurrent corresponds to an output voltage of 10

mV, whereas the maximum output voltage is ~10 V,

determined by the power supply. For field work, voltmeters with resolutions of 0.1 mV are readily available.

With these, the minimum detectable photocurrent

would be 1.0 fA, and the dynamic range would be one

decade less. Rf values <100 Gfi might be appropriate

depending on the brightness of the source.

It is customary to discuss noise in terms of the NEP

incident upon a detector. Typical silicon photodiodes

have a peak response of 0.4-0.6 A/incident W at approximately X = 720 nm. Here the NEP corresponding to 0.1 fA would be ~6 fW Hz'^/^ (reflecting the 1- mHz bandwidth). 0.1 fA also corresponds to 780

photons/s for a diode with a typical external quantum

efficiency of 80%.

IX. Conclusion

For high-sensitivity applications, large-area (1/3 to 1 cm^) silicon photodiodes with high shimt resistance

(>2 Gfi) and little excess noise are the detectors of

choice. They are best used in combination with an

amplifier having the smallest possible input bias cur- rent because the high shunt resistance mitigates the

input voltage noise. With the high-quality components now available, electrical noise can be reduced to an equivalent of 0.1 fA of photocurrent by using an

integrated measurement time of 400 s. This is equivalent to a photocurrent caused by <800 photons/s, and

it implies a dynamic range of 14 orders of magnitude

for a detector circuit. We have successfully built such a detector-amplifier

package. While its NEP is comparable with that of

1 August 1991 / Vol. 30, No. 22 / APPLIED OPTICS
commercial offerings, the photodiode in our design has

five times the active area. Research continues at the National Institute of

Standards and Technology to establish better the optical properties, such as their linearity over the whole

dynamic range, of these detector circuits. Our goal is to package the circuits in a simple and practical manner and to calibrate them optically for distribution.

We believe that these detector-based transfer stan- dards will serve the needs of the radiometric community for traceability to the National Institute of Standards and Technology's primary standards, which

serve a more limited dynamic range. In addition, the

spectral response of the detector may be customized by

the addition of a colored filter for special appUcations,

such as in photometry.

Beyond their application in standards research, the

improved performance of the detectors now possible

should find them application in many areas of commercial interest. Of particular note is the band of

near-infrared wavelengths between 700 and 1000 nm,

where photomultiplier tubes are generally less effi- cient and require noisy photocathodes. However the

relative simplicity and lower cost of high-sensitivity,

silicon photodiode detectors might make them more

appropriate than photomultiplier tubes, even for visi- ble light, in many circumstances. We hope that as photodiode manufacturers become more aware of the

significance of a high shunt resistance, devices featuring this characteristic will become more widely avail- able.

Appendix A: Determining the IMeasurement Bandwidth

The magnitude of the white noise discussed in Section

II was dependent on the bandwidth of the measure- ment. Although it is commonly known that the bandwidth A/ is inversely proportional to the integration

time T of a system, the value of the proportionality

constant is the source of perpetual confusion.

Consider a signal, which need not be noisy, which we

shall call fit). In our case, this signal is the output

voltage of our amplifier circuit. By integration of this

signal we mean a transformation to another signal,

fit), which could be, for example, either of the following:

nt) = - I nt')dt' (Case I), (Al)

f'{t)=-l' exp\-^—^l/(t')dt' (Case II). (A2)

In each of these cases the integration, expressed as a convolution integral, is an averaging with a particular

weighting function. The first case is pure integration over a finite time interval. It is the continuous analog

to the practice of digitally averaging a certain number

of the most recent points. The second case is that of a simple, single-pole filter. Consider now the effect of these time-domain filters upon a signal fit) = e~'"^ After integration

nt)

\ lOOT )

fit) =

f , \ ) e-'"'. (Case II). \1 — tWT/

(A4)

The expressions in parentheses correspond to attenuations in the frequency domain due to the filters [Eqs.

(Al) and (A2)] in the time domain. Note that they

approach 1 for small w and that their magnitudes approach for large oj. They are perhaps best recognized

as the Fourier transformations of the weighting functions.

For a signal fit) that contains white noise, there is equal noise power in all intervals of w and in both

quadratiu-e phases. Therefore the attenuation in Eq.

(A3) or (A4) would have the same effect on white-noise

power as an equivalent frequency-domain attenuator

that is 1 over an interval Aw and elsewhere, where Aoj

is the integral of the squared magnitude of the (voltage) attenuation over all frequencies:

, 2[1 - COS(a)T)] J

-K Ao) = I —

;; do) = — (Case I), («t)^ r

Jo l + (< -da, = ^ (Case II).

(A5)

(A6)

As o) = 2wf, A/ = 1/(2t) in Case I, and A/ = 1/(4t) in

Case II. That is, the value of the proportionality constant depends on the details of what makes up the

integration time, r. Here the two different results

reflect the fact that it takes more high frequencies to represent an abrupt function of time than a gradual

one.There are, of course, many other low-pass filters that

commercial dc voltmeters might use. One does not

know a priori what the proportionality should be between A/ and l/r. In this research we used Hewlett-Packard Models

3456A and 3457A voltmeters. Their analog-to-digital converters use variations of the well-known dual-slope

technique. However for long integration times,

successive samples made with shorter integration

times are digitally averaged. The upramp portion of a

single analog-to-digital cycle consists of the integration described in Eq. (Al), with t = 0.167 s (10 power

line cycles). These are repeated N times, T = 0.4 s apart (for the 3457A; 0.34 s for the 3456A).

The bandwidth of this class of instrument is

Ao) =^ r f 2[1 - cos(a)T)] |

r [1 - cos(iVcoD] 1

Jo 1 (o>rf J iiV2[l - cos(«D]J

do). (A7)

(Case I), (A3)

This follows directly from the choice of a weighting

function [as in Eqs. (Al) and (A2)] that is a sequence of

N square pulses each with amplitude 1/JV. Equation

(Al) is the special case with N = 1, and the first factor

in the integrand of Eq. (A7) parallels the integrand in

Eq. (A5). Using the well-known property of Fourier

transforms that the transform of a convolution is the

product of the transforms of its constituents, we recognize the second factor in Eq. (A7) as the squared magnitude of the transform of a sequence of N delta functions (impulses).

We have confirmed the behavior of this expression

by numerical integration. In the low-iV limit iN < 30

APPLIED OPTICS / Vol. 30, No. 22 / 1 August 1991
for these r and T), A/ « 1/{2Nt). In the high-iV limit

{N > 1000 for these r and T), A/ ^ 1/{2NT).

In this paper a bandwidth of 0.3 Hz refers to a panel

setting on an HP 3457A of 100 power line cycles (1.67 s) of integration time. Internally the HP 3457A implements this as T = 0.167 and A'^ = 10. A bandwidth of

1.25 mHz refers to panel settings of 100 power line cycles repeated 100 times. While the integration time

is 166.7 s, as iV = 1000 in this case, the elapsed time of

400 s determines the bandwidth.

Incidentally, nothing in the preceding analysis is connected with the problem of detecting low noise

frequencies. When trying to measure the noise by

determining the scatter (standard deviation) of many

samples, noise at low frequencies is not resolvable from

the signal (the mean). Just as r provided a characteristic time that determined the upper bound of the

passband, the total time T spent making measure- ments provides the characteristic time for the lower

bound. The actual bandwidth when we are trying to measure white noise is (1 — Ct/T)A/, where C is a constant of order unity (and which depends on the

details of the measurements). Nevertheless A/ is still the bandwidth that reflects the statistical uncertainty

in a real signal that is due to the noise.

The authors thank Joel Fowler, Jon Geist, and Ed

Zalewski for the encouragement that started this project, Steve Southworth for sharing his valuable experi- ences in the use of these detector circuits, Tom Lara- son for the long hours spent measuring the noise, Alan

Migdall for many helpful discussions on the nature of

the noise, Raju Datla for a careful reading of the manuscript, and Al Parr, Klaus Mielenz, and Chris Kuyatt

for their assistance and support.

References and Notes

1. G. Eppeldauer, "Measurement of very low light intensities by

photovoltaic cells," in Eleventh International Symposium on Photon Detectors, Weimar (GDR), 19S4, Proc. 182 (IMEKO,

Budapest, 1984).

2. Data sheet of the HC210-3314 and HC212-3314, "Integrated

silicon photodiode and ampUfier for low light level detection,"

(Hamamatsu Corp., 1988).

3. W. Budde, "Multidecade linearity measurements on Si photodiodes," Appl. Opt. 18, 1555-1558 (1979).

4. W. J. Borucki, "Photometric precision needed for planetary

detection," in Proceedings of the Workshop on Improvements

to Photometry, San Diego, 1984, NASA Conf. Publ. CP-2350,

15-27 (1984); W. J. Borucki and A. L. Summers, "The photometric method of detecting other planetary systems," Icarus 58, 121-134 (1984).

5. G. Eppeldauer and A. R. Schaefer, "Application of PN and

avalanche silicon photodiodes to low-level optical radiation measurements," in Second Workshop on Improvements to Photometry, Gaithersburg, 1987, NASA Conf. Publ. CP-10015,

111-151 (1988).

6. E. F. Zalewski and J. Geist, "Silicon photodiode absolute spectral response self-calibration," Appl. Opt. 19, 1214-1216 (1980).

7. A. R. Schaefer, E. F. Zalewski, and J. Geist, "Silicon detector

nonlinearity and related effects," Appl. Opt. 22, 1232-1236

(1983).

8. J. L. Gardner and F. J. Wilkinson, "Response time and linearity of inversion layer siUcon photodiodes," Appl. Opt. 24, 1531-1534

(1985).

9. E. F. Zalewski and C. R. Duda, "Silicon photodiode device with

100% external quantum efficiency," Appl. Opt. 22, 2867-2873

(1983).

10. C. L. Wyatt, Radiometric System Design (Macmillan, New

York, 1987), Chap. 18. 11. A. Ambrozy, Electronic Noise (McGraw Hill, New York, 1982),

p. 190.

12. It is incorrect to say that the shunt resistance, defined as dV/dl

at the operating point, is the effective resistance for thermal

noise in the Johnson-Nyquist equation. However for the well- known exponential I-V relation of a junction diode, it is an

appropriate approximation when the diode current is much less than its reverse saturation current. That is the case in this research, where /s « 5 pA and / « 0.05 pA owing to the op-amp

input bias current. In general, the effective resistance (and hence the noise generated) wiU be less, approaching 1/2 dV/dl

when / » Is', see Eq. (19) in M. S. Gupta, "Thermal noise in nonlinear resistive devices and its circuit representation," Proc.

Inst. Electr. Eng. 70, 788-804 (1982).

13. K. M. van Vliet, "Classification of noise phenomena," in Sixth

International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 3-11

(1981).

14. R. MuUer, "Generation-recombination noise," in Noise in Physical Systems, Proceedings of the Fifth International Conference on Noise, Bad Nauheim (FRG), 1978 (Springer-Verlag,

New York, 1978).

15. S. M. Sze, The Physics of Semiconductor Devices, 2nd ed. (Wiley, New York, 1981), Chap. 2. 16. See, e.g., D. A. Bell, "The role of mobility in 1// noise" in Sixth

International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 169-172

(1981); R. P. Jindal and A. Van der Ziel, "A model for 1// mobility fluctuations in elemental semiconductors," ibid., 173-

177; B. K. Jones, "Excess conduction noise in silicon resistors,"

ibid., 206-209.

17. G. L. Pearson, H. C. Montgomery, and W. L. Feldmann, "Noise

in silicon p-n junction photocells," J. Appl. Phys. 27, 91-92

(1956).

18. Linear Products Databook (Analog Devices, Inc., 1988), pp. 2-9.

1 August 1991 / Vol. 30, No. 22 / APPLIED OPTICS

Temperature Monitored/Controlled Silicon Photodiodes

for Standardization

George Eppeldauer

Radiometric Physics Division

National Institute of Standards and Technology

Gaithersburg, MD 20899

ABSTRACT

Two alternative approaches to reducing errors in radiometers and photometers

caused by temperature variations involve temperature monitoring and temperature

control. In the first method, the measurement results are interpreted using the

temperature of the detector at the time of measurement. The other method is to

control the temperature of the detector to a constant value. Design

considerations and examples of both approaches are discussed.

INTRODUCTION

Radiometric standardization today depends in large part on silicon photodiodes.

However, the responsivity of these detectors-part icularly towards the red end

of the spectrum-depends on their temperature. While the temperature dependence

varies among device types, its existence is unavoidable, even among "good"

photodiodes.

In detector based photometry and colorimetry (including color temperature

measurement), photodiodes are combined with filters to alter their spectral

response. Such filters, as well, are affected by temperature changes.

Experience shows that the filters are often more temperature sensitive than the

detectors. At NIST, we often use detectors that are chosen for their high shunt

resistance (which leads to lower noise and a wider dynamic range) . We find that

the response varies less than 0.02%/°C, for small variations in temperature (not

larger than 2 °C) , between 400 and 650 nm. This figure increases to about

0.1%/ °C at 750 nm and to about 1.2%/°C at 1100 nm, which is consistent with the

manufacturer's product data. On the other hand, when the detector is fitted with

a V(X) filter for photometry, its broadband response varies by about 0.1%/ °C when

viewing a CIE Standard Illuminant A source [1].

Therefore, measurement accuracy depends in large part on taking temperatures into

account. It is essential to either maintain the detector at the temperature at

which it was calibrated, or else to measure the temperature of the detector as

it is calibrated and used, applying a correction factor to measured values. Both

approaches have their advantages.

Temperature regulated detectors, while simplest to interpret, are the more

complicated to construct. They naturally require more components and circuitry

to form the temperature control loop, and there are additional considerations

having to do with the optics. We will describe our recent design, later.

SPIE Vol. 1479 Surveillance Technologies (1 991) /

11
Temperature monitored detectors can have a simpler design, at the expense of more

work required to calibrate them as a function of temperature, and additional

steps are required to interpret the data.

2. TEMPERATURE-MONITORED RADIOMETERS AND PHOTOMETER

A typical temperature monitored detector in use at NIST has an AD590* temperature

sensor mounted in the front piece of its aluminum housing as shown in Fig. 1.

The photodiode, the filter package (if any), and a precision aperture (if

required) are in metal holders, allowing good thermal contact between them. The

remainder of the detector, in the housing, includes electronics associated with

the sensor and the photodiode. The signal from the sensor is provided along with

the signal from the photodiode, both of which require measurement with external

voltmeters.

In this type of design, where a temperature probe is dedicated to a particular

detector, the calibration of the temperature sensor is unimportant. Provided

that the sensor is stable over time, the optical response of the detector may

be consistently described with reference to it alone.

Calibration of temperature monitored detectors is necessarily more involved,

since the calibration needs to be made as a function of temperature, rather than

at a single temperature. Some simplification can be made if the detector can

be calibrated on a relative basis with good precision as a function of

temperature. Then, only one absolute calibration needs be made to fix the scale.

As a practical matter, such detectors are often used under circumstances where

the temperatures are bound within a narrow range, such as by the building

utilities in a laboratory. We find it is often sufficient to use a linear

approximation to the temperature dependence, and to express the temperature

dependence factor as a percent change per degree change.

3. TEMPERATURE CONTROL OF RADIOMETERS AND PHOTOMETERS

The simplest temperature regulators use resistive heating to set a temperature

above the ambient value. (Ref. [2] provides an example.) However, optical

detectors are sometimes used in sealed, light-tight boxes that may contain other

heat-dissipating equipment, such as lamps and positioning motors. Because the

ambient temperature may sometimes be too high, we recently designed and built

temperature stabilized detectors that use thermoelectric coolers. They can

either heat or cool depending on the sign of the drive current. An ILX-Lightwave

LDT-5910* controller provides the temperature regulation.

With visible light, the temperature of silicon photodiodes need not be lowered

to reduce noise, however, providing a stable temperature avoids problems of drift

[3], It is our practice to regulate the temperature to approximately 20 °C,

where room temperature varies between 20 and 24 °C. We find that we can control

the temperature to within 0.1 °C without much difficulty. But, just as in the

temperature monitored case, the method depends on the long term stability of the

temperature sensor.

/ SPIE Vol 1479 Surveillance Technologies (1 991

)

12
When the detector is cooled below the ambient temperature, condensation of water

from the air becomes a problem. This requires that the cooled components be

sealed from outside air. Additionally, there is a close connection between this

problem and a problem associated with measuring laser light. Parallel optical

surfaces form resonant cavities, which can have a noticeable effect on the

transmittance of narrow bandwidth light. Among the parallel surfaces that should

be eliminated are those of the protective window of the photodiode. However,

removing the window subjects the photodiode to humidity variations, which can

change its quantum efficiency. Both problems are resolved by hermetically

sealing the windowless photodiode and other cooled components in a region with

a wedged entrance window, slightly tilted with respect to the plane of the

photodiode.

Fig. 2 shows the design of a temperature-controlled silicon radiometer based on

these principles. A large area (1 cm ) silicon photodiode is inserted into two

pin-sockets pressed into a black plastic disc. When the photodiode is installed,

its underside rests on a temperature-controlled copper plate. The thermoelectric

cooler is placed between the copper plate and a mesa on the aluminum cover plate.

The cover plate closes the cylindrical housing for the electronics and also

serves to dissipate the heat of the thermoelectric cooler. The black plastic

disc has a rectangular center cut-out which fits over the mesa. The disk and

the copper plate are held by three nylon screws, which provide support to, and

thermal insulation from, the cover plate. This arrangement provides some

flexibility in accommodating different photodiode pin lengths. The pins,

insulated by teflon tubing, straddle the copper plate and the thermoelectric

cooler.

The temperature sensor is a thermistor, positioned in a side hole in the copper

plate. There is also a threaded hole in the copper plate which allows an electrical connection to be made to the shielding junction. The wires of the

thermoelectric cooler, the thermistor, and the shielding lead go through holes

in the black plastic disk and the aluminum cover plate.

This hole in the cover plate and two other holes for the photodiode leads are

sealed with silicone caulk of low outgas rate and high insulation resistance.

An 0-ring provides the seal between the cover plate and a cap. A window is

formed in the top of the cap by using a wedged, fused silica beamsplitter. It

is mounted and sealed using an epoxy of low outgas rate.

This design can be adapted for use as a photometer. Instead of the copper plate,

a copper mount could be used as shown in Fig. 2(b). The spectrally correcting

filters with a precision aperture are also placed inside the copper mount, above

the silicon photodiode.

The circuit diagram of the temperature controlled detector is shown in Fig. 3.

The most important requirement for the temperature controlling circuit and its

associated components is its separation from the high sensitivity optical

radiation measuring circuit. This requires careful shielding and grounding.

The electrical common for the light measuring circuit and that for the

temperature controlling circuit must be separated. Additionally, components

composing a shield are tied together, separately. The copper plate, S, between

the photodiode, P, and the thermoelectric cooler, TE, was connected to the shield

junction, as was the aluminum housing. This improved the output AC ripple

SPIE Vol. 1479 Surveillance Technologies (1991) /

13
voltage by a factor of two. One lead of the thermoelectric cooler was covered

by a braid, which was also attached to the shield junction. The other lead was

connected to the shield junction directly. As a result, we observed little or

no excess noise in the photocurrent circuit as a result of operating the

thermoelectric cooler.

It should be noted that in the discussion of temperature effects in Ref. [3],

pertaining to the drift of the output signal, the temperature fluctuations of

the amplifier caused a greater effect than the temperature fluctuations of the

photodiode. Since this design does not temperature-regulate the amplifier, the

discussion of drift in Ref. [3] applies almost unchanged.

SUMMARY

Both temperature-monitored and temperature-regulated detectors are tractable

approaches to improve the accuracy of radiometric measurements.

Temperature-monitored detectors are easier to construct, but they require more

calibration data and analysis as well as additional steps to interpret the

results of measurements. Temperature-regulated detectors make measurement taking

simpler, with the expenses of additional and more complex hardware.

ACKNOWLEDGEMENTS

The author would like to extend thanks to Chris Cromer and Tom Larason for their

participation in the temperature dependent spectral response measurement of

photodiodes, to Hong Sun for temperature dependent broadband response

measurements of photometers, and to Jonathan Hardis for help in preparing this

manuscript.

*Certain commercial products are identified in order to more completely describe

this work. Such identification does not imply endorsement or recommendation by

the National Institute of Standards and Technology, nor does it imply that these

items are the best available for the purpose.

REFERENCES

1. G. Andor: Temperature dependence of high accuracy photometer heads, Appl.

Opt. 28, 4733-4, 1989.

2. E. F. Zalewski: NHS Measurement Services: The NBS Photodetector Spectral

Response Calibration Transfer Program, NBS Special Publication 250-17,

March, 1988, p. 7.

3. G. Eppeldauer and J. E. Hardis: Fourteen decade photocurrent measurements

with large area silicon photodiodes at room temperature. Submitted to

Applied Optics, September, 1990.

/ SPIE Vol. 1479 Surveillance Technologies (f 991)

14
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(a)

RETAINING RING

APERATURE HOLDER

FILTER HOLDER

COPPER MOUNT

PHOTODIODE PINS

WEDGED WINDOW

NYLON SCREW

COPPER PLATE

0-RING

COVER PLATE

THREADED HOLE FOR

ELECTRICAL SHIELDING

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THERMISTOR

PHOTODIODE PIN PLUG

HOUSING FOR ELECTRONICS

BLACK PLASTIC DISK

APERTURE

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PACKAGE

RING

PHOTODIODE

Figure 2. (a) Temperature controlled silicon radiometer. The silicon photodiode is not

shown for clarity but would be placed on top of copper plate, (b) Cross-section of a

copper mount containing silicon photodiode, filters and aperature that would be placed

directly on thermo-electric cooler in the temperature controlled photometer.

/ SPiE Vol. 1479 Surveillance Technologies (1 991

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SPIE Vol. 1479 Surveillance Technologies (1 991) /

17

Volume 103, Number 2, March-April 1998 Journal of Research of the National Listitute of Standards and Technology

[J. Res. Natl. Inst. Stand. Technol. 103, 153 (1998)]

Chopped Radiation Measurements With

Large Area Si Photodiodes

Volume 103 Number 2 March-April 1998

George Eppeldauer

National Institute of Standards and

Technology,

Gaithersburg, MD 20899-0001

Frequency dependent response characteristics of photocurrent meters using large

area, radiometric quality Si photodiodes

have been analyzed. The current responsivity, the voltage noise and drift amplification, and the gain and bandwidth of the photocurrent-measuring analog control loop were calculated. The photodiodes were

selected for high shunt resistance. The ef- fect of the photodiode junction capaci- tance on the response characteristics was

also analyzed. As a result of photocurrent gain dependent frequency compensations, the noise boosting effect was minimized at the output of the current meter. The loop gain and bandwidth were maximized. High-accuracy photocurrent measurements can be achieved using the described procedures for both dc and modulated optical radiation.

Key words: Bode plot; chopped light; detector, frequency dependence; gain; measurement; optical radiation; photocurrent; photodiode; radiometer, responsivity; siliAccepted: December 17, 1997

1. Introduction

In many applications, the signal of optical radiation

varies rapidly. Also, the optical radiation can be modulated or chopped. In these applications, the frequency

dependent signal and noise gains of a photocurrent meter are to be optimized. In order to maximize the perfor- mance of the current meters for different photodiodes,

their frequency dependent current-to-voltage (tran- sinapedance) and voltage gains will be determined and

the control loop gain and bandwidth will be optimized

for the signal frequencies at all signal-gain ranges. The dc and low-frequency characteristics of low-photocurrent measuring circuits of large area silicon photodiodes were analyzed earlier [1,2,3]. It was shown that for high sensitivity photocurrent measurements, high

feedback resistors and high shunt resistance photodiodes

are required. The high source resistance (parallel combination of the feedback and shunt resistances) requires

current measuring operational amplifiers with low input

bias currents. Such devices are the ultra low bias current

Field Effect Transistor (FET) or the dielectrically iso- lated FET operational amplifiers. The high source resis- tance produces high thermal (Johnson) voltage noise,

and the FET input stage of the operational amplifier has

a large 1// voltage noise. These dominant voltage noise sources were equalized when a measurement time of

400 s was used. Drifts and noise were equalized by

regulating the device temperature [4] with an instability smaller than +/— 0.02 °C. The photodiodes were se- lected for a shunt resistance close to 10 GH in order to keep the voltage amplification close to unity. The equivalent photocurrent of the equalized noise and drift was

0.1 fA with an electrical bandwidth of 1.25 mHz. This

implies a dynamic range of 14 orders of magnitude

(lO''') for a silicon photodiode current meter. The time

19
Volume 103, Number 2, March-April 1998 Journal of Research of the National Listitute of Standards and Technology

constants (shunt resistance times junction capacitance)

of the tested silicon photodiodes varied between 10 s and 200 s. When the bandwidth was increased to 300

mHz, the output noise of the photocurrent-measuring

circuit increased significantly. The sensitivity decrease

for the large-time-constant photodiodes was about a factor of 10. This was an indication of a frequency dependent noise boosting effect in the noise amplification of

the current meter. The optical radiation first is converted into an electri- cal signal by the photodiode itself; then, the electrical signal of the photodiode is measured. In radiometric

applications, current measuring preamplifiers are connected to the photodiode. The internal speed of the photodiode depends on the time needed to convert the accumulated charge into current. The photodiode inter- nal conversion time is determined by the diffusion time

of carriers generated outside the depletion layer and the

carrier transit time in the depletion layer [5]. The maximum frequency at which modern silicon photodiodes

will produce current is somewhere in the 2 GHz range

[6], depending on the area of the detector and the type

of silicon material used. It is important to keep the

internal capacitance of the photodiode low because this capacitance will produce an additional time constant in conjunction with the load resistance. This time constant T works like a low-pass filter for the current of the photodiode. The junction capacitance is proportional to the active area and inversely proportional to the square

or cube root of the width of the depletion layer. The

depletion layer width is proportional to the product of

the resistivity of the material and the reverse voltage [5]

(if it is applied to the diode). The silicon bulk resistivity can be specified from 1 O cm to 10000 Cl cm [6]. The

higher the resistivity, the lower the junction capacitance

of the photodiode.

Most frequently, the photodiode rise time is reported

instead of its 3 dB response roll-off frequency. The rise time is the time required for the output signal of the photodiode to change from 10 % to 90 %. For different types of large area silicon photodiodes the rise time is between 1 jjls and 7 |xs when a 1 kfl load resistor and

zero biasing voltage are applied [5]. An average junction

capacitance for large area silicon photodiodes is about

1 nF. This gives a t= 1 |jls time constant with the 1 kft

load resistor at test. This is equivalent to a 3 dB signal response roll-off frequency of 160 kHz. Caution is necessary when the modulation frequency of the measured

optical radiation is close to or higher than the 3 dB

frequency. At those high frequencies the modulated optical signal can be damped because of the amplitude

roll-off, resulting in a changing ac photocurrent re- sponse versus frequency. In these cases, ac to dc photocurrent conversions, realized by low pass filters, give

higher accuracy than ac signal measurements. This idea was successfully utilized in mode-locked laser measurements using two different kinds of large area silicon photodiodes [7]. The laser pulse width was 5 ps, the

repetition rate was 100 MHz, and the averaged (dc)

photocurrent was measured. The responses of the

photodiodes were equal for both pulsed and cw laser measurements. The type of the load resistor or preamplifier connected to the terminals of the photodiode plays an important role in the response time of the overall optical

radiation measurement. If the photodiode current is converted into a voltage through a single load resistor the

dominating time constant will be the product of the

photodiode capacitance and the load resistance. In order

to measure the short circuit current, which is proportional to the detected optical power, the load resistor has

to be much smaller than the photodiode resistance. Instead of a small load resistor, a current-to-voltage converting analog control loop can be used as a preamplifier

[8]. A current meter like this has a low input impedance

and a high current-to-voltage gain. However, the magnitude of the complex input impedance varies with fre- quency. This impedance is connected in parallel with the

photodiode junction capacitance. The transformation of

the feedback impedance to the input of the current meter

and the frequency dependent diode current-to-voltage response will be determined below.

The advantage of ac signal measurements is that the measuring circuit can be made selective for the signal

frequency. This way a narrow measurement bandwidth

can be chosen close to the elbow of the preamplifier's

1// noise range where the 1// noise is small. The shunt resistance and the junction capacitance of

different large area Si photodiodes can change significantly. It is important to understand the effect of the photodiode impedance on the optical radiation measuring analog control loop when high sensitivity and fast operations are expected. The analog control loop will produce a high accuracy current-to-voltage conversion

only if the loop gain and bandwidth are high enough at

the signal frequencies. Also, the current measuring

analog control loop, coupled to the output of the photodiode, is the first stage of the measuring circuit. The first stage dominates the signal-to-noise ratio for the output

of the measuring circuit. It is important to keep the first stage amplification for the dominant voltage noise low

within the electrical bandwidth of the measurement. The electronic circuits in the second stage, such as a

lock-in amplifier or a digital voltmeter, cannot restore

the established signal-to-noise ratio caused by the lack

of optimization in the first stage. In the present work, the previously described dc and

low frequency analysis of large area and wide dynamic

20
Volume 103, Number 2, March-April 1998 Journal of Research of the National Institute of Standards and Technology

range Si photodiode current meters is extended to higher

signal frequencies. The purpose of this paper is to show

how to maximize the performance of photocurrent meters for different photodiodes at different signal frequencies.

2. Photodiode Current Measuring Circuit

In order to achieve linear operation in a wide dynamic

signal range, the short-circuit current of the photodiode

has to be measured. The simplified scheme of widely

used short-circuit current meters is shown in Fig. 1.

Fig. 1. Simplified circuit diagram of a photocurrent meter. The

dashed line represents the photodiode P, and R and C are the feedback components of the operational amplifier OA.

The photocurrent /p of the photodiode P is measured

by a current-to-voltage converter. The current-to-voltage

conversion is realized by an operational amplifier OA. P

has a shunt resistance Rs and a junction capacitance Cj

which together produce the photodiode impedance Zj. /p

is converted into a voltage V through the feedback

impedance of the OA. The feedback impedance Z is the

parallel coimection of the feedback resistor R and its parallel capacitance C. The OA input voltage '/[ is small

because of the large OA open loop gain, A. As the maximum of V is 10 V, and A is about 10^, Vi is equal

or smaller than 10 jjlV. This very small voltage drop on P produces a small load resistance i?i for the photodiode':

i?,-

R

Determination of Ri is only sufficient for dc or low

frequencies. It is the input impedance Zi of the cunent

meter that determines the time constant r of the photodiode short-circuit current measurement at higher fre- quencies:

„_Z_/? 1

' A A{l+jo)CR)

1 -+j(oAC

(1)

The rewritten (popular) form of Eq. (1) shows that the

input impedance of the current meter can be calculated

as the parallel connection of the down-transformed

feedback resistor and the up-transformed feedback ca- pacitor of the OA:

(z,)- = (?)- + (

1 jcoAC y

Cj will be increased significantly by the parallel connected, up-transformed feedback capacitor AC. If R/A «Rs, the measurement time constant is

(Q + AC)R ^' A

(2)

As an example, AC = 2 p,F if C = 2 pF and A= 10*. For

/f = 10^ fi, the input resistance will be /?i = 10^ (1. AC » Cj for Cj = 1 nF; dierefore, r = /?C = 2 ms. Z and

the impedance of the photodiode Zd create a feedback

network from the OA output to the OA input. The

voltage attenuation of the feedback network is /3. For accurate dc and/or ac photocurrent measurements, the photodiodes have to be selected for shunt

resistance and junction capacitance; and the other passive components of the feedback network are to be cal- culated. Thereafter, an OA has to be selected which

satisfies the noise, drift, input current, and speed (bandwidth) requirements.

2.1 Drift and Noise Amplincation

The OA input voltage-noise, which is the principal source of 1// noise, and input offset-voltage with its drift

[1,2,3], are am_plified to the OA output by the closed loop voltage gain A\, of the photocurrent measuring

analog control loop [9,10]:

Av =

1 1

1 + G /3 1 + G"

(3)

where the loop gain is G =A^. According to Eq. (3), if G » 1, the feedback network determines A^,. The feed- back attenuation is:

,.f =.

z- Ay Z(j + Z

(4)

where (Zd)" ' = (i?s)" ' + joj Cj and Z~ '=/?"' + >C

Therefore,

21
Volume 103, Number 2, March-April 1998 Journal of Research of the National Institute of Standards and Technology

/3 =

/?s(l +jo)RC)

Rs(l+j(oRC)+Ril+j(oRsq)

Rs(l +j(oRC)

Rs + R +MR RsC + RRs Cj)

*

With

/3o =

/?s Rs + R'

the feedback attenuation can be written as:

1 +j(oRC

iS = ^o

1 +ja)

RRsC + RRsC,

R + Rs

(5)

The dc (or very low frequency) voltage amplification of

the photocurrent measuring circuit is the reciprocal of

Rs Rs

(6)

The frequency dependent closed loop voltage gain can

be written as the reciprocal of jS in Eq. (5):

Av Rs + R

R',

- . RRsC + RRsQ

1 + ](0 ;;; ^ R + Rs

1 +j(oRC (7)

where the integrating time constant is Ti = RC. The dif- ferentiating time constant is

T2 RRsC + RRsCj R Rs (^^ . r\ /-8^ R + Rs ~R + Rs^

''' ^^

Ti is calculated from the product of two factors. One

factor is the resultant resistance of the parallel connected

R and ^s- The other factor is the sum of C and Cj [10]. For fast operation, C has to be small. However, C has a minimum value of 1 pF to 2 pF, because of the stray capacitance parallel to R . For all large area photodiodes,

Cj » C when the external C is not connected parallel to R . In this case, the frequency dependent voltage amplification of the measuring circuit can be written as:

+ JU}

Av = i4v

RRsQ

R + Rs

1 +j(oRC '

If R » Rs the voltage amplification is:

(9)

1 +j(oRC Av'" = A (10)

In this case, the differentiating time constant in the numerator is determined exclusively by the impedance of

the photodiode. If Rs»R, then

'-'"''"T^- (")

In Eq. (3),

A=Ao 1

1 H-ywTi'

(12)

where t\ is the integrating time constant of the OA. A^ is the dc open loop gain of the OA.

2.2 Frequency Dependent Signal Response

The frequency dependent current-to-voltage response

of the photocurrent measuring circuit can be calculated

as well. With the Norton to Thevenin source conversion

formula [11] the photocurrent /p can be converted into

V,:

V, = /p

1 \+ja>RsCj (13)

As a next step, Vj is amplified by the OA. The voltage

amplification here [9] is equal to the ratio of Z to Z^:

y_

V,

R_ 1 +j(oRsC,

Rs \+jcoRC (14)

When Eq. (1 3) is substituted into Eq. (14) the photocurrent-to-voltage conversion [13,14] >1, which is frequently

called the transimpedance gain, can be written as:

/p 1 +j(oRC (15)

Equation (15) shows that the dc signal gain (or re- sponse), which is the ratio of the output voltage V to the

input photocurrent /p is equal to R . The frequency dependent signal response is determined by the integrating

time constant, t, = RC, of the feedback impedance. This

time constant and the OA input-impedance-determined

time constant r, in Eq. (2), are the same: t=ti = RC

.

Equation (1.5) also describes the gain for the input current noise of the circuit. Because Eq. (15) does not show

the frequency dependent contribution of the OA to the

signal response, the equation works only if Ti<ri.

22
Volume 103, Number 2, March-April 1998 Journal of Research of the National Institute of Standards and Technology

Otherwise, the OA frequency dependent response can

give an unwanted limitation for the signal response.

Similarly to Eq. (3),

/p"^l+G-' (16)

The current-to-voltage conversion, R , which is the sig- nal gain, will be accurate only if G » 1 at the signal

frequency. This is a very important design requirement

for the analog control loop.

3. Response Functions of Silicon

Photodiode Current Meters

Gain versus frequency curves adequately describe the dynamic characteristics of analog control loops. Most

frequently the responsivity (gain) products of the indi- vidual components of the open loop are shown on a log

amplitude scale versus log frequency. These characteristics can be constructed quickly and fairly accurately by

approximating the curves by piecewise linear regions.

The construction rules are easy. E.g., a constant in the gain equation gives a horizontal line. 1 +ju>t in the denominator gives a roll-off. Roll-off points are also

called "poles". The slope of the roll-off is — 20 dB per decade. 1 + jar in the numerator, gives a roll-on. A

roll-on point is also called "zero". The slope of the roll-on is 20 dB per decade. The interconnected straight- line characteristics realized this way are called idealized Bode plots [12].

3.1 Voltage Gain Plot of a Si Photodiode Current

Meter

The frequency dependent voltage amplification of a photodiode short circuit current meter is described by

Eq. (7). Tne shape of this function will be illustrated

first on the widely used silicon photodiode, Hamamatsu

Model S1226-8BQ'. This photodiode has an active area of 1/3 cm^. The photodiode was purchased with a se- lected Rs = 6.5 Gft. The junction capacitance is typically Cj = 1.3 nP. This photodiode was tested earlier [3] and a noise floor of 0. 1 fA was measured with an electrical bandwidth of 1 .25 mHz. When the bandwidth was

increased to 0.3 Hz, the noise floor increased to 0.6 fA. The feedback resistor was R = 10" fi and the estimated

' Certain commercial equipment, instruments, or materials are identi- fied in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

stray capacitance was C = 2 pF. The 3 dB open-loop

roll-off frequency of the OPA128LM operational amplifier used is/ = 3 Hz. This OA was chosen for low input

current (40 fA) and a peak-to-peak current noise of 2.3 fA. This selection was necessary to keep the effect of the OA input current small on the very high source resis- tance (parallel connected R and R^). The dc open-loop

gain of the operational amplifier is 110 dB.

A time constant of t\ = RC = 0.2 s gives a signal

roll-off frequency of /i = 0.8 Hz. From tz = 8 s, the

roll-on frequency is fi = 0.02 Hz. The roll-off and roll- on slopes are — 20 dB per decade and 20 dB per decade,

respectively. Avo= 16.4 from Eq. (6). In Fig. 2, log Ay

versus log frequency is shown, together with the fre- quency dependent open loop gain of OA. The figure

shows that the voltage amplification increases by 1.5 decade when the frequency increases from 0.02 Hz to 0.8 Hz. The photocurrent measuring electrical bandwidth can be limited by a low-pass filter or integrating

DVM connected to the output of the photocurrent meter.

If this out-of-loop limiting bandwidth is smaller than

0.02 Hz, the noise boosting effect of the photocurrent

measuring circuit will be rejected. In this case, the measurement will be slow. However, when the measurement

bandwidth is 0.3 Hz, as before [3], or larger, the OA

input voltage noise components will be amplified in the 0.02 Hz to 0.8 Hz frequency range.

100

CQ— 60 c

_ h

20

^oAo^o

A -^2 ^1

Ay V

A

/ J I sL.

lO ,a6

/[Hz]

Fig. 2. Closed-loop voltage gain (solid lines) of a Hamamatsu S 1 226- 8BQ silicon photodiode current meter. /?s = 6.5 Gfl, Cj = 1.3 nF, R = lO" fi, and C = 2 pF. The dashed line shows the open loop gain of the OPA 128LM operational amplifier without any feedback.

The shape of the area between the OA open loop gain curve and the Ay voltage amplification curve gives infor- mation about the dynamic chaiacteristics of the photocurrent measuring analog control loop. The information about the loop performance can be made more clear and more understandable if this area is illustrated by the Bode plot of the loop gain.

23
Volume 103, Number 2, March-April 1998 Journal of Research of the National Institute of Standards and Technology

3.2 Loop Gain Plot of a Si Photodiode Current

Meter

The frequency dependent loop gain of the open

analog control loop can be written from Eqs. (5) and

(12):

G = /4oiSo

1 1 +j(oRC

1 +ja)T, ,. RRsC + RRsQ'

''"' rTrs

' (17)

where RC = ti is the integrating time constant in Eq. (7) (noise voltage gain). Here T| is a differentiating time

constant. Similarly, Xa of Eq. (8) was a differentiating

time constant in the noise voltage gain equation. In Eq.

(17), T2 is an integrating time constant. The OA time

constant, t,, is always an integrating type time constant. Figure 3 shows the Bode plot [12] of the open photocurrent measuring control loop, where j8o = 0.06, as calculated from Eqs. (4) and (5) with ^ = 10" O.

Ao Po = 18000. The solid curve shows the dynamic characteristics of the analog control loop. The curve inter- cepts the frequency axis with a slope of — 20 dB per decade showing that the phase shift (phase lag) in the open loop at this frequency is not more than — 90°. This

phase shift corresponds to one integrating time constant. This - 90° phase shift, together with the - 180° phase

shift of the negative feedback, results in a maximum

phase shift of — 270°. Since this phase shift is less than — 360°, oscillations will not occur. Also, the loop gain,

G = .4/3, is equal to or larger than 1000 (60 dB) from

Hz to about the 3 dB roll-off frequency of the signal response curve. The large G in the low frequency inter- val gives a high current-to-voltage conversion accuracy. The dashed photocurrent-to-voltage response curve, which is described by Eq. (15), was matched at its 3 dB

point to the loop gain function.

00 1j

-oi3o\

-

60

a 1 mt *; \

-

20 - h

'

1 \1 /iVV

/ Vv 1

i I10-"I loO 102 104

60

- 20

/[Hz]

Fig. 3. Loop gain plot of the Hamamatsu S1226-8BQ Si photodiode

current meter. /?s = 6.5 Gfl, q = 1 .3 nF, « = lO" H, and C = 2 pF. The solid curve shows the gain of the open control loop. The dashed

curve shows the curi'ent response function as matched at its 3 dB

£-oil-cff point to tht loop gain function.

The overall electrical bandwidth of photocurrent

measurements greatly depends on R. This is true for both the signal response in Eq. (15) and the loop bandwidth described by Eq. (17). The speed of the above

analyzed high sensitivity photocurrent meter is slow because of the very large R . The speed can be increased

by decreasing R . However, smaller R decreases the photocurrent responsivity. Figure 4 shows the voltage gain

curves of the Hamamatsu S1226-8BQ silicon photodiode current meter. The noise boosting effect does not

disappear with decreasing R. Decreasing R shifts the

noise boosting interval to higher frequencies. Small

feedback resistors are used when the photocurrent is large. In these cases, the noise boosting effect is less of

a problem.

R=]o'^Q.

Fig. 4. Closed-loop voltage gain characteristics of the Hamamatsu

St226-8BQ Si photodiode current meter when the feedback resistors are changed from lO" Cl to lO" ft. Rs = 6.5 Gfl, Q = 1.3 nP, and C =

2 pp. The dashed line shows the open loop gain of the OB\ 128LM

operational amplifier, without any feedback.

Decreasing R will increase both the loop bandwidth

and the low frequency loop gain. Figure 5 shows the

different loop gain plots of the Hamamatsu S1226-8BQ

silicon photodiode circuit when R changes from 10" O,

to 10" n. Similarly to Fig. 3, /i </! for all feedback

resistors when C = 2 pF = constant. When R decreases,

both the roll-off frequency, /2, and the roll-on frequency,

/i, increase. With decreasing /?,/:, which is equal to the

signal 3 dB roll-off point, shifts towards the frequency

axis. At /? = 10^ n, /i reaches the log / axis. At this frequency, the phase lag in the open loop is — 135°. t; and T2 integrating time constants shift — 180°, and Ti differentiating time constant gives a phase lead of + 45°.

If y? is further decreased, the phase shift at high frequencies (close to the unity gain cut-off frequency) can reach - 180°, resulting in oscillations in the closed loop. In

order to increase stability and accuracy, /i has to be

decreased by increasing Ti. In our previous experimental

circuits [1,2,3], when R was 10* fl or smaller, r, was

increased using external capacitors, parallel connected

24
Volume 103, Number 2, March-April 1998 Journal of Research of the National Institute of Standards and Technology

e)

1^

80 ">\\V ^\Sv\v\

' R=l0^^i^\y.

A\ \ X^^R^io^a

40

- ^V\\\ R=io^n

, , ,\ 1 1 1 1^ I 10-2 10^ 10^ /[Hz]

10^

100

a 60 c

- n

20

^oP, o^o

'Fo /2=/l ^ L

/" \

mAJ I I L

10-2 jqO 10^ 10^ /[Hz]

10^

Fig. 6. Frequency compensated closed-loop voltage gain of the Hamamatsu S1226-8BQ Si photodiode current meter. /?s = 6.5 GO,

Cj= 1.3 nF, /?= 10" n, and C=80 pF. The dashed line shows the open loop gain of the OPA 128LM of)erational amplifier, without any

feedback.

Fig. 5. Loop gain characteristics of the Hamamatsu S1226-8BQ

photodiode current meter when the feedback resistors are changed from 10" n to 10* fi. ^s = 6.5 Gfi, Cj = 1.3 nF, and C = 2 pF (stray). No external capacitors are connected parallel to the feedback resistors. The open circles show the 3 dB roll-off points of the photocurrent

response. They are matched to the loop gain curves for each R

to the feedback resistors. Changing the feedback

impedance by tuning the external parallel capacitor [15] can fundamentally modify the frequency dependent

characteristics of the photocurrent meter.

3.3 Frequency Compensation of Current Meters

The noise boosting effect can be eliminated if ti = tj. This compensation can be done easily by connecting an

external capacitor of 78 pF parallel to /? = 10" fl. The sum of the 78 pF and the 2 pF stray capacitance will give

the neceso.ary C = 80 pF to achieve the frequency compensation. In this case, T| will be 8 s. After the compensation, the shape of the solid curve. Ay, m Fig. 2 will change to a straight line, as shown in Fig. 6. The improved noise amplification will be Ay = Avo for all fre- quencies within the loop.

If the compensation is made for all feedback resistors, the shape of the loop gain curves of Fig. 5 will be

different. In each compensation, Ti canceled tj, therefore, T; became the only integrating time constant in the loop. Figure 7 shows the compensated loop gain curves

for different feedback resistors. The loop bandwidth in- creased significantly because of the compensation.

Without frequency compensation the loop gains were

high enough only for dc and \o\v signal frequencies. For

feedback resistors between 10'° £l and lO'' (), the loop

dynamic characteristics are very similar. There are no

100 '\o\\' d

20

-a be

10-

1 1

10*-

1

/[Hz]

10^V10^ 10*^

Fig. 7. Compensated loop gain characteristics of the Hamamatsu

S1226-8BQ Si photocurrent meter. /?s = 6.5 Gfl and Cj = 1.3 nF. The

feedback impedances are changed: a) /?= lO" fi, C=80 pF; b) R= 10'" n, C = 510 pF; c) /? = lO' O, C= 1.1 nF; d) /? = 10* O to

lO'' €t and C = 1.3 nF. The open circles show the 3 dB roll-off points of the photocurrent response functions. They are matched to the loop

gain curves for all feedback resistors, after compensation.

oscillation problems because the phase shift is less than — 90° even at high loop frequencies. The 3 dB roll-off points of the photocurrent response function of Eq. (15)

are also shown for the different feedback impedances. For all feedback resistors, the compensated signal 3 dB

points limit the speed of the photocurrent meter. The

loop gains at the signal 3 dB points are always larger than 100. If a minimum loop gain of 1000 is required to achieve a 0.1 % relative standard uncertainty in photocurrent measurements, the signal frequency at the lowest signal gain of /? = 1 0* H has to be limited to about 1 kHz. In the case of a wide dynamic signal range, this frequency limitation is not a problem, because the signal

frequency limit is much lower at high signal gains. The

25
Volume 103, Number 2, March-April 1998 Journal of Research of the National Institute of Standards and Technology

very low input current OPA128LM operational amplifier

seemed to be the best selection for this very high sensitivity but very slow photocurrent meter. The frequency compensation made the signal re- sponse of the current meter slower. This can be a problem when R is high. E.g., for /? = 10" n, the t, = 8 s integrating time constant of the signal response requires

about a 1 min wait for the digital voltmeter (DVM) to measure the signal accurately at the output of the current

meter. The long waiting time before each DVM measurement is also necessary because of the roughly 2 min

settling time of the OPA128LM operational amplifier

when operated with this large feedback resistor. The

measured settling time of the above discussed silicon photodiode current meter is shown in Fig. 8. The figure

shows the output signal change of the meter after the

shutter is closed. The duration of one measured point on

the figure was determined by the integration time of the DVM, which was equal to the time of one power line cycle. This corresponds to an electrical bandwidth of 30

Hz [3]. A 16.2 s time constant was obtained from the curve fit to the measured data when an 7? = 10" fl feedback resistor was used. No external feedback capacitor was applied in this measurement. When R = 10'° Cl was selected, the settling time constant became shorter than the duration of one power line cycle.

As shown in Fig. 4, the dc voltage noise amplification

decreased almost a decade when R was reduced from

10" n to 10'° n. At the same time, the photocurrent

response also decreased by a factor of 10. Decreasing R

results in a smaller source resistance noise for the input

of the OA. As a result of the similar signal and noise

changes, the signal-to-noise ratio for the output of the

current meter is similar for these two signal gain selections. Based on the above settling time and signal to noise

ratio measurements, we conclude that /? = 10'° fl pro- duces a faster measurement than /? = 10" O with similar

photocurrent limit sensitivity.

3.4 Chopped Radiation Measurement

When dc or low frequency operation in a photocurrent measuring circuit is too slow to satisfy a certain

measurement speed requirement, different photodiode

and operational amplifier selections are needed.

The frequency dependent photocurrent-to-voltage

conversion is described by Eq. (15). The RC time constant of the feedback impedance determines the bandwidth of the signal measurement. This time constant has

to be small enough to keep the 3 dB signal roll-off frequency a decade higher than the frequency of the

signal to be measured. E.g., with C = 2 pF, ^ can not be

larger than 10' fi to use a chopping frequency of 8 Hz.

In this case Ti = 2 ms and /i = 80 Hz. Because the

voltage amplification can not be smaller than unity, for R < 10' n the photodiode shunt resistance should not be

larger than 10' fl. Also, if the junction capacitance is

s

c

u

0) Q

J 1 I L I

I I _! 1 I I I I I 1 JL« 100 200 300 400

Time [s]

Fig. 8. The measured settling time of the Hamamatsu S 1 226-8BQ silicon photocurrent meter when /? = 1 0" fl. The time constant from the fit is 16.2 s.

26
Volume 103, Number 2, March-April 1998 Journal of Research of the National Institute of Standards and Technology

low enough, the/2 roll-on frequency of the voltage gain curve of Eq. (7) can be selected higher than the signal

(chopping) frequency. A possible detector choice is the Hamamatsu S5226-8BQ silicon photodiode. This

device has an active area of 1/3 cm^. The shunt resis- tance is 1 GD, and the junction capacitance is 430 pF.

Figure 9 shows the voltage gain curves for the Hamamatsu S5226-8BQ silicon photodiode when used with

the OPA627BM low noise and wide band operational

amplifier. Partial frequency compensations were per- formed for all of those R where fz < 80 Hz. In these

cases, the signal 3 dB points were tuned to 80 Hz. For

those R where /2 > 80 Hz, full frequency compensations were obtained. Frequencies /i were decreased to be

equal to /a. For each fully compensated gain (R = 10^ H,

10^ fi, and 10'' fl), the sum of the stray and external capacitances was 432 pF. The signal 3 dB roll-off points

are matched to the voltage gain functions for each R and

are shown with open circles. The noise boosting effect disappeared after full compensations and decreased for

partial compensations. If a chopping frequency of 8 Hz

is selected and /? = 10* H is used as a maximum feed- back resistor, the noise amplification will be practically

unity.

10-2 iqO ]q2 10^

/[Hz]

10^

Fig. 9. Closed-loop voltage gains (solid curves) of a Hamamatsu

S5226-8BQ Si photodiode ac current meter. Rs= \ GCl and Cj = 430

pF. The dashed curve shows the open loop gain of the OPA627BM

operational amplifier, without any feedback. Partial frequency compensations were made at 80 Hz: a) /? = lO' fi and C = 2 pF; b) /? = 10*

ft and C = 20 pF; and c) /? = 10' n and C = 200 pF. Full compensations are shovi/n by d) where /? = lO' fl to lO" O and C = 432 pF. The

3 dB roll-off points of the signal response curves are matched to the voltage gain curves and are shown with open circles.

The OA selection criteria for rapidly changing optical radiation is different than the earlier discussed very slow

signal measurements. In the presently discussed ac measurement, the source resistance (parallel connection of R

and /?s) was selected to be smaller than in the previously

discussed dc and low frequency measurements. Consequently, the input bias current of the OA does not have

to be extremely low. However, low noise, fast settling

time, and fast operation are important OA requirements.

The OPA627BM dielectrically isolated OA satisfies these expectations. This operational amplifier has lownoise, equal to bipolar-input amplifiers, larger bandwidth than that of FET input operational amplifiers, and

the minimum slew rate is 40 V/|xs.

The loop gain characteristics of the optimized ac sili- con photodiode current meter for the different feedback

impedances are shown in Fig. 10. The signal 3 dB roll- off points are matched to the loop gain curves and are shown again with open circles. The loop gain is higher

than 300 at each signal 3 dB roll-off points for all R

selections. Because of the large loop gains at signal

frequencies smaller than the 3 dB point, the analog control loop errors are small and the implementation of Eq.

(16) is accurate. E.g., G> 10^ for signal frequencies

smaller than 40 Hz.

1^

100 /^^^ - <-^^'; c1

60 - N y

20

-

, , ,\

:^^ 10" 10^ 10^

/[Hz]

10^ 10^

Fig. 10. Loop gain curves of an ac photocurrent meter using a Hama

matsu S5226-8BQ Si photodiode. /?s = 1 Gfl and C, = 430 pF. OPA627BM operational amplifier is used. Partial frequency compensations are made at 80 Hz: a) /? = lO' H and C = 2 pF; h) R = \0' CI and C = 20 pF; and c) R = lO' fl and C - 200 pF. Full compensations

are shown by d) where /? = 10* n to lO** fi and C = 432 pF. The signal

3 dB roll-off points are matched to the loop gain curves and are shown

with open circles.

If the radiation is chopped, a lock-in amplifier is usually connected to the output of the current meter. The

lock-in, which is synchronized with the radiation chopper, performs a phase sensitive rectification of its input

signal. The low-pass filter, coupled to the output of the

lock-in, smooths the signal. The filter should be properly designed to take fast enough readings when the

optical radiation changes. Usually, active filters (e.g., Bessel) are used to optimize filter characteristics [9]. If a very small bandwidth is realized by the low-pass filter (for an improved signal to noise ratio), the measurement

will be very slow.

27
Volume 103, Number 2, March-April 1998 Journal of Research of the National Institute of Standcirds and Technology

4. Conclusions

In addition to signal range and sensitivity, speed can

be an important issue in photodiode short circuit current measurements. In order to calculate the frequency de- pendent signal and noise gains of different photodiode

current meters, a detailed analysis of the photocurrent

measuring analog control loops has been described.

First, the most important gain equations were deter- mined and then the current-to-voltage gain Ai, voltage

gain Av, and loop gain G were optimized for the signal

frequencies. Both the active and passive components of

photodiode current measuring circuits can be deter- mined using the described method. Photodiodes can be

selected for shunt resistance and junction capacitance

according to the sensitivity and speed requirements of a measurement. The feedback impedances for the selected operational amplifier can be matched to the impedance of the selected photodiode. As a result of

component selections and frequency compensations, the

signal-to-noise ratios can be optimized for the outputs of

the photocurrent meters, and improved loop gains can be

achieved for reasonably wide frequency ranges. Because

of improved loop gain and bandwidth, the accuracy of

the photocurrent-to-voltage conversion is increased for higher signal frequencies. As a result of photodiode

circuit optimization, the signal roll-off of large area

silicon photodiode light meters can be increased to 80 Hz even at a signal gain of 10' V/A.

[9] P. Horowitz and W. Hill, The Art of Electronics, Cambridge

University Press, Cambridge (1987) pp. 127, 94, 153.

[10] Product Data Book of Burr-Brown, Burr-Brown Corporation, Tucson, AZ (1984) pp. 1-38.

[11] R. L. Boylestad, Introductory Circuit Analysis, 6th Edition,

Merrill Publishing Company, Columbus, OH (1990) p. 719.

[12] J. W. Nilsson, Electric Circuits, Third Edition, Addison-Wesley

Publishing Company, Reading, MA (1990) pp. 639-648.

[13] Transimpedance Applications, Fall 1 994, Burr-Brown Applications Seminar.

[14] G. H. Rieke, Detection of Light: from the Ultraviolet to the

Submillimeter, Cambridge University Press, Cambridge, GB

(1994) p. 143. [15] J. G. Graeme, Photodiode Amplifiers, McGraw-Hill, New York,

NY (1996) p. 42.

About the author: George Eppeldauer is a Ph.D. Electronics Engineer in the Optical Technology Division of

the NIST Physics Laboratory. The National Institute of

Standards and Technology is an agency ofthe Technology Administration, U.S. Department of Commerce.

5. References

[1] G. Eppeldauer, Measurement of very low light intensities by

photovoltaic cells, in Eleventh International Symposium on

Photon Detectors, Weimar (GDR), 1984, Proc. 182, IMEKO,

Budapest (1984).

[2] G. Eppeldauer and A. R. Schaefer, Application of PN and

avalanche silicon photodiodes to low-level optical radiation rncasurcments in Second Workshop on Ir^nrovenicnts to Photometry. Gaithersburg, 1987, NASA Conf. Publ. CP-10015, 1 1 1-

151 (1988).

[3] G. Eppeldauer and J. Hardis, Fourteen-decade photocurrent measurements with large-area silicon photodiodes at room temperature, Appl. Opt. 30 (22), 3091-3099 (1991).

[4] G. Eppeldauer, Temperature monitored/controlled silicon photodiodes for standardization, in Surveillance Technologies,

S. Gowrinathai;, R. J. Mataloni, and S. J. Schwartz, eds., Proc.

Soc. Photo-Opt. Instrum. Eng. 1479, 71-77 (1991).

[5] Photodiodes, Hamamatsu Cat. No. KPD 0001 £05, (Hamamatsu

Corporation, Hamamatsu City, Japan, 1996), 8, 16-19.

[6] Y. Tamari, Custom silicon photodiodes offer design flexibility, Laser Focus World 33 (1), 123-126 (1997).

[7] T. R. Gentile and C. L. Cromer, Mode-locked lasers for high-ac- curacy radiometry, Metrologia 32 (6), 585-587 (1996).

[8] G. Eppeldauer, Some problems of photocurrent measurement of

photovoltaic cells, Appl. Opt. 12 (2), 408-409 (1973).

28
Volume 105, Number 2, March-April 2000 Journal of Research of the National Institute of Standards and Technology

[J. Res. Natl. Inst. Stand. Technol. 105, 209 (2000)]

Noise-Optimized Silicon Radiometers

Volume 105 Number 2 March-April 2000

George P. Eppeldauer

National Institute of Standards and

Technology,

Gaithersburg, MD 20899-8441

george.eppeldauer@nist.gov

This paper describes a new, experimentally

verified, noise analysis and the design

considerations of the dynamic characteristics of silicon radiometers. Transimpedance

gain, loop gain, and voltage gain were opti- mized versus frequency for photodiode

current meters measuring ac and dc optical

radiation. Silicon radiometers with im- proved dynamic characteristics were built and tested. The frequency-dependent

photocurrent gains were measured. The

noise floor was optimized in an ac measurement mode using photodiodes of differ- ent shunt resistance and operational amplifiers with low 1// voltage and current

noise. In the dark (without any signal), the noise floor of the optimized silicon ra- diometers was dominated by the Johnson

noise of the source resistance. The Johnson

noise was decreased and equalized to the amplified 1// input noise at a 9 Hz chopping frequency and 30 s integration time

constant, resulting in an equivalent rootmean-square (rms) photocurrent noise of

8 X 10"" A. The lowest noise floor of

5 X 10"" A, equal to a noise equivalent power (NEP) of 1.4 X 10"'* W at the 730

run peak responsivity, was obtained at a 100 s integration time constant. The ra- diometers, optimized for ac measurements, were tested in a dc measurement mode as well. Performances in ac and dc measurement modes were compared. In the

ac mode, a ten times shorter (40 s) overall measurement time was needed than in the dc mode (400 s) to obtain the same 10"" A noise floor.

Key words: chopped radiation; gain; noise; photocurrent; radiometer; sensitivity; sili- con photodiodes.

Accepted: January 13, 2000

Available online: http://www.nist.gov/jres

1. Introduction

Low-noise photocurrent measurements are needed for the detection of weak optical radiation [1]. Silicon photodiodes are well known for their excellent optical

and electronic characteristics, and for their high sensitivity and stability [2, 3]. The noise and drift characteristics of silicon photodiode current meters were analyzed earlier at low (dc)

frequencies [4]. High shunt resistance silicon photodiodes and operational amplifiers with large feedback resistors were used to achieve high photocurrent sensitivity. Operational amplifiers with very low input-bias

current were used to minimize 1/fnoise from the amplifier. The dominant Johnson noise was equalized to the

1// amplifier noise by decreasing the electrical bandwidth to 1.25 mHz. The drift was also equalized to the noise floor by regulating the temperature of the Si ra- diometer within ± 0.02 °C of the operating 25 °C value

[5]. The root-mean-square (rms) equivalent photocurrent of the measured noise floor was 10"'* A. The time

of the measurement was 400 s. When the bandwidth was

increased to 300 mHz, the noise increased and ranged

between 0.6 fA and 1 fA. The factor of 10 noise increase

29
Volume 105, Number 2, March-April 2000

Journal of Research of the National Institute of Standards and Technology

was measured for the photodiode with the largest time

constant (shunt resistance times junction capacitance).

This output noise increase was due to a frequency-dependent noise-boosting effect in the voltage gain of the photocurrent meter. The dynamic (ac) characteristics of photodiode current meters were analyzed in transimpedance amphfier

applications [6,7,8]. The fundamental gain equations were summarized recently [9] to optimize signal (tran- simpedance) gain, voltage gain, and loop gain versus

frequency. The gain equations can be used to optimize

both low-frequency (dc) and modulated/chopped (ac) photocurrent meters. The feedback impedances of the

selected operational amplifiers were matched to the impedance of the selected silicon photodiode in the an- alyzed ac photocurrent meters. The signal roll-off point

of large-area silicon photodiode current meters could be

increased to 80 Hz even at a signal gain of 10' V/A. The

suggested siUcon radiometer converts the optical radiation signal (chopped with 8 Hz) into an ac voltage signal

which has negligible amplitude distortion and signal

phase shift. The optimization of the frequency-dependent (three) gains was extended to Ge, InGaAs [10], and

InSb [11] photodiodes as well. Optimization of the dynamic (frequency-dependent)

characteristics of silicon radiometers will not necessarily optimize the sensitivity of the meters. The fundamental gains and the noise floor have to be optimized

together to get the best performance. This paper shows

the proper method of analysis for performing this task in the ac measurement mode. The design considerations

for both the dynamic characteristics and the noise per- formances are experimentally verified. Also, the perfor- mances of ac and dc silicon radiometers are compared.

2. Gain Equations of Photodiode Current

The equivalent circuit of photocurrent-to-voltage converters is shown in Fig. 1. The photocurrent /? from

photodiode P is converted into a voltage V at the output

of the operational amplifier OA. i?s is the shunt resis- tance and Cj is the junction capacitance of P. R is the feedback resistance and C is the feedback capacitance of

the OA. The photocurrent-to-voltage conversion can be

described by the transimpedance gain [9]:

Ai = ^ = R

1

7p l+ia)RC' (1)

Equation (1) shows that the dc signal gain (at w = 0), which is the ratio of the output voltage V to the input

photocurrent If, is equal to R . The frequency-dependent

Fig. 1. Equivalent circuit of photodiode radiometers. The dashed line

represents photodiode P. R and C are the feedback components of the

operational amplifier OA.

signal response is determined by the integrating time

constant ti = RC of the feedback impedance. Equation

(1) also describes the gain for the input current noise /in

of the circuit. Because Eq. (1) does not show the fre- quency dependent contribution of OA to the signal response, the equation works only if the roll-off time

constant of the OA open-loop gain Ti < ti. Otherwise,

the OA frequency-dependent response gives an unwanted limitation for the signal response.

Similarly to Eq. (1),

/p-'^l + G-'

(2)

where G is the loop gain. The photocurrent-to-voltage

conversion R , which is the signal gain, will be accurate

only if G» 1 at the signal frequency. This is a very

important design requirement for the analog control

loop.

The loop gain, which is the product of the OA open

loop gain A and the feedback attenuation /3, can be

written as

G = Ao/So

1 1 + j O) Ti

1 + ja> Tj 1 + JW T2

' (3)

where Aq is the dc open loop gain and /3o = Rs/{Rs + R).

The quantity t; = RC was the integrating time constant

in Eq. (1). Here, in Eq. (3), Ti is a differentiating time

constant. The integrating time constant tj here is the

product of the parallel resistances and the parallel capacitances:

R Rs C + R Rs Cj R Rs m . r'\ rA\

'' = rVr, = rVr^^^^^^- ^^^

T, is always an additional integrating type time constant.

30
Volume 105, Number 2, March-April 2000 Journal of Research of the National Institute of Standards and Technology

The closed loop voltage gain, which is the reciprocal

of /3[12], determines the amplification for the input

voltage noise Vvn:

Av = Avo

1 +jfe)T2

1 +j<yTi

(5)

where

Avo =

Rs + R

Rs

(6)

is the dc voltage gain.

In contrast to Eq. (3), ti is an integrating and T2 is a

differentiating time constant in Eq. (5). Vrn is the John- son (resistor) noise. This "white" noise shows up di- rectly at the OA output (without any amplification). The

current noise /in is caused by the fluctuation of the OA

input current. Both /in and Vvn have "white" and l/f noise components superimposed on each other. The photocurrent /p produces a shot noise /pn which

is not shown in Fig. 1. The current /pn is converted to the OA output similarly to /p. This current noise component is (lelpAf)^'^, where e is the elementary electron charge, 1.60 X 10"'' C, /p is the photocurrent, and A/is the electrical bandwidth. A 10"''*A photocurrent pro- duces an rms current noise of /pn = 7.1 X 10"'^ A at A/= 16 mHz, which corresponds to an integration time

constant of 10 s. At the OA output, the signal-produced voltage V has

to always be much larger than the superimposed total noise voltage originating from the above four noise

components.

3. Design of Dynamic Characteristics

A test silicon radiometer was built that satisfies the

three gain requirements discussed above with high photocurrent and loop gains and low voltage-gain at the

signal frequencies.

According to the suggestion in our previous work [9], the Hamamatsu Model S5226-8BQ' 1/3 cm^ area photodiode was selected and tested with /?s = 2.2 Gfl and

Cj = 410 pF. The large shunt resistance kept Ay low. The small junction capacitance tuned the /2 = 1/{2'ttt2)

Certain commercial equipment, instruments, or materials are identi- fied in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of

Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

roll-up point in the voltage-gain curve to high frequencies, resulting in decreased noise-boosting effect. The

Burr-Brown OPAl 1 IBM operational amplifier was se- lected because of its high dc open loop gain (Aq = 10^) and low l/f noise. The dynamic characteristics below

were designed with typical manufacturer's data regarding C], Ao, and the 3 dB roll-off frequency of the OA

open-loop gain.

The largest feedback resistor used in these tests was R= 10'° ft. In order to obtain a high enough signal

roll-off frequency /i = 1/(2itti) at this signal gain, a

small stray capacitance of Cs = 1.25 pF was realized. The overall feedback capacitance was C = Cs + Cf, where Q was the externally connected feedback capacitor. Cf was selected for all gains (except R= 10'° fl) to obtain a signal roll-off frequency of at least 10 times the chopping frequency.

Figure 2 shows Cf, /i, and f^ versus R for the test radiometer. The/i and/2 curves were calculated from tj and T2 of Sec. 2. As is shown in Eq. (4), fz depends on

C. A change in Cf will modify the starting value of/2. Cf was selected for all signal gains to obtain a high

enough / for chopping frequencies between 7 Hz and

10 Hz. The frequency /i was decreased by increasing Cf

in all signal gains (other than the highest) to tune/ close

to/2 as much as possible. This requirement is important

for minimizing noise voltage amplification and maximizing loop gain for the signal frequencies. At the same

time, / had to be high enough to keep the signal bandwidth of the radiometer broad enough for all signal-gain

selections. This is an important requirement to avoid

distortion of the signal shape and to make the signalphase-shift negligibly small. At full-frequency compensation, where Ti = T2, the differentiating time constant

cancels (compensates) the integrating time constant. This way, the loop gain can be increased and the voltage

gain can be decreased for the signal (chopping) frequencies. For gain selections of R « Rs the ti = T2 condition

requires C » Cj, resulting in large Cf values. The ca- pacitance Cf will not be too large if Cj is small. Full frequency compensation was made at R= 10"^ Cl using

Cf = 4.7 nF. No frequency compensation was made for

/? = 10'° n to keep/ high. Full compensation for the high signal gains would make the radiometer very slow.

Partial compensations satisfied the three gain requirements for all the other signal gains.

Figure 3 shows the frequency-dependent loop-gain

characteristics of the above test radiometer. This is a Bode plot [13] where the characteristics can be constructed quickly and fairly accurately by approximating

the curves with piecewise linear regions. The value of

G at low frequencies is equal to AojSq. The first two

roU-offs are at/2 and/;/ determines the roll up. This is the frequency where the signal 3 dB roll-off points

31
Volume 105, Number 2, March-April 2000 Journal of Research of the National Institute of Standards and Technology

10* 10^ 10

10"^°

r-.

JLuml ml I I 111*^1 I I iiiiiaf 10

10^ 10^ 10® 10^°

R[a\

Fig. 2. Time constants-produced frequency roll-off and roll-up points of the test radiometer

calculated for the decadic signal gains. The external feedback capacitor versus feedback resistor

is shown by the dashed curve. The points are connected to help visual separation of the curves.

100

a 60

20 -

^-;

fls=2.2GQ, Cj=410pF N 0A = 0PA111BM

- ^\ a,pF

r=io''Oq. - C=1.25pF Vv^s. fl=io6n. c=4ii pF

_fl=109fl, C=2pF

-wo

full compensation

jS^. ftlO^n, Cb411 pF

ft=108 £J. VV>S. ^^V^j/'

C=21 pF — ^^V \1^ ^^^. R=10*n, C=471

'

, ,N

^vv%^ 10-' 10^ 102 MHz]

10^ 10"=

Fig. 3. Loop-gain characteristics of the test silicon {S5226-8BQ) radiometer. The open circles show the signal 3 dB roll-off points as they are matched to the loop-gain characteristics.

(shown with open circles) are attached to the loop-gain curves (solid lines). AtR= 10'" O, the signal 3 dB point

is 13 Hz without any frequency compensation (Cf = 0). At /? = 10^ n, Cf = 0.8 pF will produce C = 2 pF with a

roll-off frequency of/i =78 Hz. As a result of the high

open-loop gain of the OPAlllBM operational amplifier, the loop gains at these two highest signal gains are 100 (40 dB). Partial frequency compensations were enough for the other signal gains to obtain high enough

loop gains at the signal 3 dB roll-off points. For these

cases, /i = 75 Hz, or higher, was selected. The full fre- quency compensation at the lowest signal gain was made

as a design example.

Figure 4 shows the closed-loop voltage-gain characteristics (solid curves) of the test silicon radiometer. The

open-loop gain curve of the OA is shown with thick

dashed lines. The roll up here is determined by/2. The

roll-off is produced by /i. At the highest gain, /i is relatively far from /a, producing a gain increase of about

two orders of magnitude. The real shape of this gain

change is shown (for /? = 10'° fl only) with the thin dashed curve. The noise boosting at a chopping fre- quency of 9 Hz is still significant.

4, Measurement of Photocurrent Gains

The frequency-dependent signal (transimpedance)

gain of the test silicon radiometer was measured for all (except for the lO'* V/A) signal-gain selections. The sta- ble broad-band radiation of a 100 W tungsten halogen

lamp was measured using a chopper. The frequency of

32
Volume 105, Number 2, March-April 2000 Journal of Research of the National Institute of Standards and Technology

MHz]

flS = 2.2Gn, Cj = 410pF

0A = 0PA111BM

c= ^/ fl=107Q, C=201 pF ^ ' R=^o^Q,c=4^\pF

R=-\O^Q, C=411 pF X / R=10^n, C=47]pF s

full compensation

Fig. 4. Closed-loop voltage-gain characteristics (solid lines) of the test silicon (S5226-8BQ) radiometer. The thick dashed lines show the openloop gain of the OA. The open circles are the signal 3 dB roll-off points as they are matched to the voltage-gain characteristics.

the chopper was tuned from about 10 Hz to 300 Hz by

computer control. A chopper-synchronized, sine-wave

measuring lock-in amplifier was connected to the output

of the radiometer. The measured output voltage V curves

are normalized and shown versus chopping frequency/

in Fig. 5. At low (dc) frequencies, the output voltage Vo

is not attenuated. The 3 dB line on the graph shows

where the signal-gain curves reach the 70.8 % (3 dB

attenuation) value of Vq- The signal attenuation, according to Eq. (1), is caused by the ti = RC time constant, which is different for all signal gain selections. There is no monotonic progression in the measured curves because the 3 dB signal frequencies agree with the design

values (/i) in Sec. 3. The 3 dB frequency for 10^ V/A

gain was larger (about 90 Hz) than the designed 78 Hz

because the very small (calculated) external feedback

capacitor (Cf = 0.8 pF) was not connected. For the most

sensitive signal gain the 3 dB point was calculated from

a curve fit to the measured data points. The fit is shown

with the dashed curve. The fit equation is:

V(f) =

Vo V.i^(f/f)

(7)

o

O)a

o

>a

<O

.sa

E

Oz

0.1

'4^ "^ - - ^

3 dB line

O H g 9 99P lutuimiiant ^^^ 10* V/A

o^

»fA. ^° V^^

-?CP; %\^(f V/A

WV/A-^ \ 10^ V/A

10^ V/A

10 100

/ [Hz]

Fig. 5. Measured frequency-dependent signal-gain curves of the test silicon ra- diometer for different signal-gain settings; Vo is the dc output voltage of the radiometer.

33
Volume 105, Number 2, March-April 2000 Journal of Research of the National Institute of Standards and Technology

The 3 dB point from the fit was 12.9 Hz. The response

at 2 Hz is a rough extrapolation to Vq measured with the other signal gain selections. For a chopping frequency of

9 Hz the amplitude attenuation at the 10'° V/A signalgain selection will be about 17 %. Because the operating

point is on the slope of the roll-off curve, the chopping

frequency should be stabilized for this gain selection. The quantity Vo should be reported instead of V versus frequency if different chopping frequencies are used. The graph also shows that for the other gain selections the signal responses are flat around the 9 Hz chopping

frequency.

5. AC Measurement of Dark Noise

In ac photocurrent measurements, amplifier drifts do

not contribute to measurement uncertainties. It is the noise floor that determines the sensitivity limit. The

dark noise gives basic information about the noise per- formance of a radiometer. In order to make high-sensitivity measurements, the dark noise has to be kept as low

as possible. In our noise tests the output of the test radiometer was connected to the inputs of chopper-synchronized lock-in amplifiers. The photodiode was covered with a light-tight cap in order to measure the dark

noise. The total output noise of the radiometer (dark) was measured at a chopping frequency of 9 Hz with an

electrical bandwidth determined by the low-pass filter at the output of the lock-in amplifier. In these ac measurements the signal magnitudes M were calculated from the lock-in X and Y (filtered) output voltages using

the mathematical vector sum process (M = (X^ + Y^y^).

When measuring noise (or a small signal in the noise),

this process rectifies the noise, causing residual output

offset. In order to estimate the noise measurement uncertainty caused by this problem, several dark noise tests were repeated and evaluated in a different way, i.e., by

calculating the noise fluctuations in both X and Y. The

lock-in X and Y output noise voltages and the magnitudes are shown in Table 1 for 30 s and 1 s integration

time constants. The X and 7 pairs were always simultaTable 1. Lock-in X and Y output noise voltages and magnitudes M,

for the dark S1226-8BQ photodiode and the OPA128LM operational

amplifier at 9 Hz chopping frequency and 10'° V/A signal gain

Lock-in time constant (s) A/((ji.V) X{y.V) Y(ilW)

I 30

3.2 0.78

3.2 0.93

3.5 0.81

neous measurements. The M values, at a given time

constant, were measured consecutively to the measure- ments of X and Y. Each reported noise value was calculated as the standard deviation of at least 20 readings.

The measurement results show that the noise of M can

be 38 % lower than the noise of X or Y, which are free of the residual output offset. The uncertainty of our

noise magnitude measurements is dominated by this 38 % (coverage factor k-2) relative expanded uncertainty.

5.1 Noise Floor Optimization

The noise floor of the test silicon radiometer was

optimized in the ac measurement mode using four

photodiodes with different shunt resistances and three operational amplifiers with low 1// voltage and current

noise. The feedback capacitors were not changed for the

different photodiode-amplifer combinations. Table 2

shows the model numbers and the impedances of the

tested photodiodes. All tested photodiodes had an active area of 1/3 cm^. The models in Table 2 were chosen in order to obtain a wide shunt resistance range for our

tests. The range was extended by selecting the photodiodes for high shunt resistance. (The larger the resistivity

of the photodiode material, the higher the shunt resis- tance.) The measured shunt resistances ranged from 0.5 GO, to 7 GCl. Only photodiodes with small junction

capacitance were selected to obtain small voltage gain

(low noise boosting) in ac signal measurements. Cj is proportional to the photodiode area and can be inversely

proportional to either the square or the cube root of the width of the depletion layer [14]. The depletion layer

Table 2. The tested silicon photodiodes and the calculated voltage gain parameters

Model RsiGO.) Cj(nF) -4^0 /2(HZ)

Data Book Measured Data Book Measured For^ = 10'° CI Min. Typical in the dark Typical in the dark and measured

Rs and C,

S1336-8BQ 0.1 0.4 0.5 0.38 0.18 21 1.9 S5226-8BQ 0.1 1 2.2 0.43 0.32 5.6 0.3 S1227-66BQ 0.2 1 5 0.95 0.62 3 0.08 S1226-8BQ 0.2 1 7 0.95 0.56 2.4 0.07

34
Volume 105, Number 2, March-April 2000 Journal of Research of the National Institute of Standards and Technology

width is proportional to the resistivity of the material. This is why Q was measured to be lower on the selected high shunt resistance photodiodes. During the capacitance measurements on the photodiodes the dc voltage

drop was less than 13 mV and the ac voltage drop was

less than 24 mV. The capacitances were measured in the dark and the diodes were reverse biased. The measured

capacitances ranged from 0.18 nF to 0.62 nF. Table 2

also shows the dc voltage gain and/2 for the 10^° V/A

signal-gain. They were calculated from the measured Rs and Cj values. The 1 //voltage and current noise of the three different types of operational amplifiers are shown in Table 3 for the frequency range between 0.1 Hz and 10 Hz. The

manufacturer's data were helpful only to select candi- date operational amplifiers. As noise figures for the small frequency interval (electrical bandwidth) at 9 Hz

were not available, it was necessary to test the noise

floor experimentally. Both the OPA128LM and the OPA627BM operational amplifiers were tested with all four photodiodes. The OPAl 1 IBM was tested only with

two different shunt resistances using the S5226-8BQ

and the S1227-66BQ photodiodes.

Figure 6 shows the measured noise floors of the dif- ferent photodiode-operational amplifier combinations.

These noise floor measurements were made at a currentto-voltage gain of 10'° V/A and 9 Hz. The time constant

selected on the lock-in amplifier was 3.33 s. The lowpass filters of the lock-in amplifier had a roll-off slope

of 20 dB per decade. For the OPA128LM operational amplifier the output

noise decreased to an equivalent rms photocurrent of

0.28 fA for photodiode shunt resistances of 5 GO and 7 Gfi. At these high shunt resistances the voltage gain was

small enough to make the amplified OA input noise

negligible relative to the dominant Johnson noise. The

0.5 GCl shunt resistance increased the voltage gain by a

factor of seven, resulting in a dominating output noise

from the input voltage noise. Similar results were obtained with the OPAl 1 IBM operational amplifier.

With the OPA627BM operational amplifier a 0.36 fA

noise floor was measured for shunt resistances of 2.2 GO or larger. This noise floor was 0.08 fA higher than

the noise floor with the other two operational amplifiers. As compared to the others, this amplifier had a

0.9

012345678

Shunt resistance [GQ]

Fig. 6. Noise-equivalent photocurrent of photodiode-operational amplifier combinations at a signal-gain of 10'° V/A and a chopping

frequency of 9 Hz.

much larger l/f input current noise and it dominated the OA input noise. With increasing shunt resistance the

input voltage noise drop (caused by the input-current

noise) increased and the voltage gain for it decreased.

The result was a constant 1// noise contribution to the dominating Johnson noise. The output (total) noise spectrum of the radiometer was measured at different chopping frequencies be- tween 8 Hz and about 200 Hz. The signal gain of the radiometer was lowered to 10' V/A to increase the signal

upper roll-off point from 13 Hz to 80 Hz. The time

constant of the lock-in amplifier remained 3.33 s. The

2.2 GCl shunt resistance of the S5226-8BQ photodiode was used in this test. The voltage gain, according to Fig.

4, increases almost two decades from 0.8 Hz to 80 Hz. The upper half of this frequency interval could be tested. As is shown in Fig. 7, the dominating noise (at the radiometer output) is the white Johnson noise, which

makes the noise spectrum flat. The measured noise

spectrum with the OPA128LM was smoother than with

the OPA627BM because of the smaller OA input noise. The input noise of the OPA627BM was dominated by

the above-discussed 1// input current noise. In spite of

Table 3. Catalog data of OA 1// noises from 0.1 Hz to 10 Hz (all voltages and cuiTents are peak-to-peak)

OPA128LM

Voltage CuiTent OPA627BMVoltage Current OPAl 1 IBMVoltage Current

4 |jiV 2.3 fA 1.6 |xV

(0.6 typical)

60 fA

(30 typical)

2.5 |xV 12 fA

(7.5 typical)

35
Volume 105, Number 2, March-April 2000 Journal of Research of the National Institute of Standards and Technology

0)

0)o

c

c

«

3

U

O

oa

1.4

1.2

0.8

0.6 -

OPA627BIVI

10 100

Chopping frequency [Hz]

Fig. 7. Noise-equivalent photocunent versus frequency of the silicon radiometer at a signal gain of lO' V/A and a time constant of 3.33 s. The detector was a S5226-8BQ photodiode (Rs = 2.2 GO; C, = 410

pF).

>

c

Q.

<-» 3o

Signal gain [V/A]

Fig. 8. Measured dark noise versus signal gain at 9 Hz and 3.3 s integration time constant. The S1227-66BQ photodiode and the OPAlllBM operational amplifier were used in the noise-optimized

radiometer.

measured 16 nV input voltage noise is a 1//^ noise which

cannot be reduced much by longer integration.

5,3 Dark Total Noise Versus Electrical Bandwidth

this 1// noise contribution, the noise spectrum remained

flat. The smaller voltage gain compensated for the higher 1//" noise at the lower frequencies. Because of the

flat noise floor at this signal gain, any signal (chopping)

frequency can be selected within the tested frequency

interval. However, the 3 dB point at 80 Hz will restrict the upper signal frequency limit. If the external feed- back capacitor is not connected, this limit can be ex- tended to about 130 Hz. In this case the loop gain at this signal frequency can be too low, resulting in poor current-to-voltage conversion accuracy. To avoid this problem, either a high open-loop gain operational amplifier

(e.g., OPAlllBM) has to be selected or the partial fre- quency compensation (e.g., for 80 Hz) has to be applied.

5.2 Dark Total Noise Versus Signal Gain

me optimized radiometer, witti tne oiZZ/-0oj3v<j

(Rs = 5 GO,) photodiode and the OEM 1 IBM operational amplifier, was tested for output total noise versus

signal-gain performance. Again, the signal (chopping)

measurement frequency was 9 Hz and the time constant of the lock-in amplifier was 3.33 s (0.05 Hz bandwidth).

The measurement results are shown in Fig. 8. The out- put total noise is shown by the dashed curve and the

noise-equivalent photocurrent is represented by the solid curve. The shape of the total noise curve shows that with

high feedback resistances the Johnson noise dominates

the output noise. With small feedback resistances,

where the Johnson noise is low, the input voltage noise

of the amplifier (amplified by the unity voltage gain

here) dominates the output noise of the radiometer. The

The Johnson noise in Fig. 8 can be further reduced by

longer integration. The noise-optimized radiometer with

the S1226-8BQ (/?s = 7 GO) photodiode and the OR\128LM operational amplifier was tested at a signal

gain of 10'° V/A and a measurement frequency of 9 Hz. A digital lock-in amplifier (Stanford SR830) was used

in this test. The time constant of the lock-in amplifier was changed between 100 s and 0.1 s. The waiting time was three times the time constant before each dark noise measurement. The measurement results are shown in

Fig. 9.

<

1.2

< k o 1 :\ : (0o \

c 0.8 \

4rf \ c %

1- 0.6 N

3

o

o 0.4 \

xzo V a. 0.2 "••^

E

Q

^^,^

0.1 1 10 1C Time constant [s]

Fig. 9. Noise-equivalent photocurrent versus time constant of the digital lock-in amplifier for the S1226-8BQ photodiode and the OPA128LM operational amplifier at 9 Hz chopping frequency and

10'° V/A signal gain.

36
Volume 105, Number 2, March-April 2000 Journal of Research of the National Institute of Standards and Technology

The dark noise floor was 0.1 fA with the 10 s time

constant. This noise is equal to the earlier reported dc

dark noise obtained with a measurement time of 400 s

[4]. The present 9 Hz (ac) noise test needed a 40 s total measurement time to obtain the same noise-equivalent

photocurrent. At the 100 s time constant the noise equivalent photocurrent decreased to 0.05 fA. The noise

equivalent power (NEP), which is the ratio of the 0.05 fA

to the 0.36 AAV peak responsivity of the diode, is equal

to 0.14 fW. This test required a total measurement time

of 400 s. The roll-off slopes of the low-pass filters, within the digital lock-in amplifier, were always selected

to 80 dB per decade (24 dB per octave). This very steep

roll-off slope produced a well-defined electrical bandwidth. The Johnson noise could be calculated from Rs = 7 GO and R= 10 GCt. The parallel connection of R and Rs

gave a source resistance of i?so = 4.1 X 10^ H. The rms

noise voltage of the source resistance, at the output of

the radiometer, was

Vn = (4kTRsoAf)"^=lM |xV, (8)

where k= 1.38 X 10"^^ J/K is the Boltzmann constant, r = 300 K was the temperature of the radiometer during

the test, and A/= 0.048 Hz was the measurement bandwidth as calculated from the 3.33 s time constant of the

lock-in amplifier used in the noise measurements of Fig.

6. The 0.28 fA noise-equivalent photocurrent in Fig. 6 was calculated fi-om the measured 2.8 |jlV radiometer

output noise voltage and the 10'° V/A photocurrent-tovoltage gain. A/ in that measurement was larger than in Eq. (8) because of the shallow (20 dB per decade) slope

of the low-pass filter. That measurement was repeated

with the digital lock-in amplifier, using a 3 s time constant with a roll-off slope of 80 dB per decade. With this time constant, the A/= 0.053 Hz bandwidth resulted in a calculated Johnson noise voltage of 1.9 ijlV. In accor- dance with Fig. 9, the measured value was 2 |jlV. This

noise voltage corresponds to a 0.2 fA photocurrent noise

at a signal gain of 10'° V/A. The 80 dB per decade

roll-off still does not give a perfect square shape for the measurement bandwidth. The 10 % (coverage factor k = 2) uncertainty of these Johnson noise determinations is well within the 38 % relative expanded uncertainty {k = 2) of the ac noise measurements.

6. DC Dark Noise Measurements

The silicon radiometer, noise-optimized with the S1226-8BQ photodiode (i?s = 7 Gft) and the OPA128LM operational amplifier in the ac mode, was

tested in the dc measurement mode as well. As in our

earlier reported dc measurements [4], the bandwidth was again 0.3 Hz determined by the 100 power-line cycle integration time (1.7 s) of the dc digital voltmeter

connected to the output of the radiometer. The temperature of the radiometer during the dc test was controlled

to 25 °C ± 0.02 °C. The increase in the standard deviation of the measured noise data points due to drift was

negligible. The dc dark noise measurement results are shown in Fig. 10.

>

c

ffl Eo

X3

CO DC 10* 10^ 10® lO'' 10' 10^ 10^" 10

Signal gain [V/A]

Fig. 10. The dc dark noise of the radiometer noise-optimized in the

ac mode (with S1226-8BQ photodiode and OPA128LM operational

amplifier) versus signal gain. The integration time is 1.7 s.

At the two lowest signal gains (lO"* V/A and 10^ V/A)

the output total noise of the radiometer was dominated

by the 0.2 |xV input voltage noise of the OA. This l/f noise fits to the earlier reported 0.2 |jlV to 1 fxV noise

interval [4] measured on several OPA128LM operational

ampHfiers. It should be noted that the ac and the dc noise

versus signal-gain tests were made with different photodiode-amplifier pairs. However, before the tests (both ac and dc), the two radiometer combinations were optimized to the same noise floor (0.28 fA) at 9 Hz, as discussed in Sec, 5.1. At the highest (10'° V/A) signal gain of the radiometer, the noise-equivalent photocurrent was 1.5 fA. The

noise-equivalent photocurrent increased to about 20 pA

at the lowest (10'' V/A) signal gain. When the equivalent

photocurrent noise curve was extrapolated to the 10"

V/A gain, a noise floor of about 0.7 fA was obtained,

equal to the noise floor of our previous dc measurements

(using the same signal gain and the same 0.3 Hz bandwidth) [4]. The lower noise floor at 10" V/A can be

utiUzed only at very slow measurements because the

settling time constant at this gain is 16.2 s [9]. At 10'° V/A signal gain the settling time constant is shorter than one power line cycle (16.7 ms). This three orders of

magnitude setding-time difference rejects the application of the 10" V/A signal gain from fast measurements.

37
Volume 105, Number 2, March-April 2000 Journal of Research of the National Institute of Standards and Technology

The expanded relative uncertainty (coverage factor k = T) of our dc noise measurements was 25 %.

7. AC and DC Dark Noise Comparison

In dc measurements, the noise-boosting effect (shown

in Fig. 4) can be avoided if we restrict the measurement

frequency and bandwidth to a limit which is lower than

the frequency where the voltage-gain increase begins.

We used this method in our previous work [4] where a 400 s measurement time (1.25 mHz bandwidth) elimi- nated the noise-boosting effect at the 10" V/A signal

gain and equalized the resistor noise to the 1// noise. Another method to eliminate (or decrease) noise

boosting is to apply frequency compensation for the

different signal gains of the radiometer. In a typical

example, where the shunt resistance is 6.5 Gfi and the junction capacitance is 1.3 nF, full-frequency compensation will decrease the signal 3 dB roll-off points to 19 mHz at the two highest signal gains. (This requires a 85

pF capacitor parallel to /? = 10" Cl and 850 pF parallel

to /? = 10'° O.) Again, the result would be very slow

signal measurements at high signal gains. However, full- frequency compensation is not needed at high signal

gains because the large feedback resistance and shunt

resistance make the Johnson noise dominate (as dis- cussed in Sec. 5.1) relative to the amplified (boosted)

input noise. In both dc and ac measurements, partial frequency

compensation give the best results. The voltage gains are decreased (with the partial compensation) by lowering

f\ (closer to/2) until the signal response is not too low for the signal frequency. This was the design consideration

for our test radiometer (as described in Sec. 3) where the

signal roll-off frequency was at least 10 times the chopping frequency. As is shown in Figs. 3 and 4, the value of the compensating Cf capacitor depends on the chosen

signal gain (/?). The input voltage noise at 9 Hz was 16 nV with the OPAlllBM (as shown in Fig. 8) and 23 nV with the OPA128LM. The 1// noise of each amplifier at this measurement frequency is much smaller than at very low (dc) frequencies. Earlier [4], a 50 nV to 200 nV II

input noise interval was reported on several OPAl 1 IBM

operational amplifiers at very low frequencies. The llf noise interval was higher (about 0.3 |xV to 1 |jlV) for the OPA128LM.

The decrease of the llf noise at higher frequencies

made it possible to increase the signal measurement

frequency from dc to 9 Hz. At 9 Hz the noise-boosting

effect was still significant. However, the feedback resis- tor {R) could be lowered by a factor of 10, relative to the previously reported i? = 100 GO in the most sensitive dc

measurements [4]. The result of the smaller R was de- creased voltage gain (Ay) and resistor noise. Figure 8 shows that the dark noise floor measured at 9 Hz is about a decade lower than the dc dark noise floor shown in Fig. 10. The silicon radiometers in the ac and

dc noise floor measurements were noise optimized (in ac mode) to the same 0.28 fA rms current level (as described in Sec. 5.1). The measurement times are rea- sonably short (a few seconds) in both cases. At 9 Hz, the

integration time to obtain the same 10"'^ A noise floor

(as in the previous dc measurements) became shorter because of the lower resistor noise. Using the radiometer

with the OPA128LM operational amplifier and a 30 s integration time constant (as shown in Fig. 9), an output rms l//noise of (0.93^ - 0.6^)"^ )jlV = 0.71 \xN could be

calculated. The 0.6 |xV was the calculated rms Johnson

noise and the 0.93 |jlV was the total rms output noise

measured by the lock-in X channel (as shown in Table

1). The X-channel noise was used because it was free of

the residual output offset in M. The calculated voltage

gain (at 9 Hz) was 710 nV / 23 nV = 31. The relative uncertainty (coverage factor k = 2) of this voltage gain

determination was 66 %. In this ac measurement, the Johnson noise was roughly equalized to the amplified

llf noise. The noise equivalent photocurrent (from the

lock-in magnitude M) was 8 X 10"'^ A. According to Fig. 9, further increase of the lock-in integration time

constant will not yield a significant decrease in the out- put total noise of the radiometer. The lowest noiseequivalent photocurrent of 5 X 10"'^ A was measured

with an integration time constant of 100 s. The total duration of this ac measurement was 400 s.

8. Conclusion

An experimentally verified noise analysis for silicon photodiode current meters of improved dynamic characteristics has been described. Transimpedance gain, loop

gain, and voltage gain were optimized versus frequency

using partial frequency compensation for the different

signal gains. The effect of the Johnson noise, the OA

input voltage noise, and the current noise of both the OA

input current and the photocurrent were discussed. The

transimpedance (current-to-voltage) gains of the test ra- diometer were measured versus frequency. The noise

floor was optimized at a signal chopping frequency of 9

Hz by testing the combinations of four photodiodes of

different shunt impedance and three selected operational

amplifiers. The dominating Johnson noise at the tested

10'° V/A signal gain was further decreased by increas- ing the integration time constant of the ac signal measurements. At an integration time constant of 30 s (after 90 s wait), the Johnson noise was equalized to the ampli38
Volume 105, Number 2, March-April 2000 Journal of Research of the National Institute of Standards and Technology

fied l/fnoise of the operational amplifier, resulting in an rms noise equivalent photocurrent of 0.08 fA. This photocurrent noise corresponds to an NEP of 2.2 fW at the 0.36 AAV peak responsivity of the photodiode. Earlier

[4], a 400 s measurement (averaging) time was needed

in the dc measurement mode to obtain an rms noise

floor of 0.1 fA. The silicon radiometer optimized in the ac measure- ment mode was tested in the dc measurement mode as

well. The dc tests verified that a radiometer optimized

for ac measurements may also have an optimum perfor- mance in the dc mode. Integrating-type digital volt- meters measured the radiometer output voltages for the duration of 100 power line cycles (1.7 s) to avoid long

measurement (averaging) times. Also, the signal gain of

the radiometer was maximized to 10'° V/A to avoid long

settling times. The dc test resulted in a practical rms

photocurrent sensitivity limit of 1.5 fA. In contrast, the

practical sensitivity limit in the ac measurement mode

(with a 10 s integration time constant) was 0.1 fA. The

conclusion from comparing the ac and the dc photocurrent measurement modes is that well-designed ac ra- diometers can measure weaker optical signals with

shorter measurement times. The described frequency- and noise-optimized sili- con photodiode current meters can be used as building

blocks of high-sensitivity radiometers, photometers, pyrometers, and colorimeters. These radiometers have a

signal (radiant power or photocurrent) dynamic range of

greater than 14 decades. The discussed ac (including dc)

noise-optimization method can be extended for ultraviolet and near-infrared photodiode current meters as well.

[8] J. Graeme, Photodiode Amplifiers Op Amp solutions, McGrawHill, New York, NY (1996).

[9] G. Eppeldauer, Chopped Radiation Measurements With Large Area Si Photodiodes, J. Res. Natl. Inst. Stand. Technol. 103 (2), 153-162(1998).

[10] G. Eppeldauer, Electronic characteristics of Ge and InGaAs

radiometers, SPIE, Proceedings, Vol. 3061-97 (1997) pp. 833-

838.

[11] G. P. Eppeldauer, A. L. Migdall, and L. M. Hanssen, InSb Working Standard Radiometers, NEWRAD'97, Tucson, AZ,

October 27-29, 1997, Metrologia 35, 485-90 (1998).

[12] P. Horowitz, W. Hill, The Art of Electronics, Cambridge University Press, Cambridge (1987) pp. 127.

[13] J. W. Nilsson, Electric Circuits, Third Edition, Addison-Wesley

Publishing Company, Reading, MA (1990) pp. 639-648.

[14] Photodiodes, Hamamatsu Cat. No. KPD 0001E05, Hamamatsu

Corporation, Hamamatsu City, Japan (1996) p. 8.

About the author: George P. Eppeldauer is a Ph.D.

Electronics Engineer in the Optical Technology Division of the NIST Physics Laboratory. The National Institute of Standards and Technology is an agency of the Technology Administration, U.S. Department of Commerce.

9. References

[1] G. Eppeldauer, Measurement of very low light intensities by

photovoltaic cells, 1 1th Int. Symp. on Photon Detectors, Weimar

(GDR), Proc. 182, IMEKO, Budapest (1984).

[2] G. Eppeldauer and A. R. Schaefer, Application of PN and

avalanche silicon photodiodes to low-level optical radiation measurements, in Second Workshop on Improvements to Photometery, Gaithersburg, 1987, NASA Conf. Publ. CP-10015

(1988) pp. 111-151.

[3] R. Friedrich, J. Fischer, and M. Stock, Accurate calibration of

filter radiometers against a cryogenic radiometer using a trap

detector, Metrologia 32, 509-13 (1995/96).

[4] G. Eppeldauer and J. Hardis, Fourteen-decade photocurrent measurements with large-area silicon photodiodes at room temperature, Appl. Opt. 30 (22), 3091-3099 (1991).

[5] G. Eppeldauer, Temperature monitored/controlled silicon photodiodes for standardization, SPIE, Proceedings, Vol. 1479

(1991) p. 71-77.

[6] G. H. Rieke, Detection of Light: from the Ultraviolet to the Submillimeter, Cambridge University Press, GB (1994) p. 142.

[7] Product Data Book of Burr-Brown, Burr-Brown Corporation, Tucson, AZ (1984) pp. 1-38.

39

Opto-mechanical and electronic design of a Tunnel-Trap Si-Radiometer

George P. Eppeldauer

Optical Technology Division

National Institute of Standards and Technology

Gaithersburg, MD 20899 USA

and

Donald C. Lynch

Reyer Corporation

New Market, MD 21774

Abstract

A transmission-type light-trap silicon radiometer has been developed to hold the NIST

spectral power and irradiance responsivity scales between 406 nm and 920 nm. The device

was built from different-area replaceable input apertures and tightly packed different-size

silicon photodiodes. The photodiodes were positioned in a triangular shape tunnel such that

beam clipping was entirely eliminated within an 8° field-of-view (FOV). A light trap was

attached to the output of the radiometer to collect the transmitted radiation and to minimize

the effect of ambient light. The photodiodes, selected for equal shunt resistance, were

connected in parallel. The capacitance and the resultant shunt resistance of the device were measured and frequency compensations were applied in the feedback network of the

photocurrent-to-voltage converter to optimize signal-, voltage-, and loop-gain characteristics.

The trap-radiometer can measure either dc or ac optical radiation with high sensitivity. The

noise-equivalent power of the optimized device was 47 fW in dc mode and 5.2 fW at 10 Hz

chopping. The deviation from the cosine responsivity in irradiance mode was measured to be

equal to or less than 0.02 % within 5° FOV and 0.05 % at 8° FOV. The trap-radiometer can

transfer irradiance responsivities with uncertainties similar to those of primary standard

radiometers. Illuminance and irradiance meters, holding the SI units (candela, color- and

radiance-temperature), will be calibrated directly against the transfer standard trap-radiometer

to obtain improved accuracy in the base-units.

Keywords: detector, irradiance, photo-current, photodiode, radiant power, reference

detector, responsivity, spectral response, transfer standard.

1. Introduction

Light-trap detectors have been used as radiometric standards since 1983 [1]. At that time

UDT UVIOO' n-on-p inversion layer silicon photodiodes were used in either four element

(Model QED-100) or three element (Model QED-200) reflectance-type light-trap

configurations [2, 3]. These primary standard devices measured the total power of the

' Identification of commercial equipment to specify adequately an experimental problem does not imply recommendation or endorsement by the National

Institute of Standards and Technology nor does it imply that the equipment identified is necessarily the best available for the purpose.

41
incident, well collimated, radiation. Their power response uncertainty was 0.03 % (coverage

factor A:=l) between 440 nm and 460 nm where bias voltage was not applied to the

photodiodes [4]. These non-linear devices had a limited dynamic range of operation [5].

Later, Hamamatsu S-1337 p-on-n silicon photodiodes were used in the Model QED-150 trapdetectors in an arrangement similar to the QED-200. These detectors were called "quantumflat" because they have external quantum efficiencies (EQE) that are constant to within 0.1 %

from 550 nm to 860 nm. The spectral responsivity of quantum detectors is proportional to

their EQE and wavelength. The proportionality factor is e/hc, where e is the elementary

electron charge, h is Planck's constant, and c is the velocity of light. Using the silicon

photodiode self-calibration technique [6] for a single element S-1337 photodiode, the

quantum flatness of these trap-detectors could be extended to 400 nm [7]. The SI 337 trapdetectors with the constant relative spectral responsivity were calibrated against either a QED200 between 440 nm and 460 nm or an electrical substitution cryogenic radiometer. The

responsivity of SI 337 trap-detectors could be extrapolated from the 440 nm to 460 imi range

to longer wavelengths with very little loss of accuracy because the shape of the internal

quantum efficiency (IQE) does not depend on typical diode-to-diode variations in the doping

profile. IQE is the ratio of the number of collected electrons to the number of photons

absorbed by the detector after the front surface reflection loss. EQE=(l-p)*IQE where p is the reflectance. Since the spectral shape of the IQE of SI 337 type photodiodes can be

modeled with very small uncertainty [8, 9], the spectral responsivity of SI 337 reflectancetype trap-detectors could be interpolated between 406 nm and 920 nm with an uncertainty of

0.03 % (coverage factor ^1) if two or more absolute tie points were measured.

The reflectance-type (three-element) trap detectors have polarization dependent response

variations of about 1 part in 10"^ [10]. The reflectance loss of the S-1337 reflectance-type trap

detectors increases from 0.21 % at 920 nm to 1 % at 406 nm [9]. We measured the

responsivity ratios of a QED-150 to a SI 337 reflectance-trap versus wavelength. The ratio

changed from 1.0005 at 920 nm to 1.0085 at 406 nm, indicating that the reflectances in the

blue for the same SI 337 photodiode model can be different by several tenths of a percent.

The reflectance depends on the oxide thickness of the selected S1337 photodiode. A spatial

response non-uniformity of 0.03 % was measured on the same SI 337 reflectance-trap where

the photodiodes were individually aligned to optimize the device FOV [11]. Later, 0.2 %

spatial response non-uniformities were measured on three different QED-150 devices using

the same characterization facility [12]. The measured active areas of the QED-150 trap

detectors were neither symmetrical nor similar. The higher response non-uniformities and the

different shapes of the measured areas indicated that either the FOV was smaller and nonsymmetrical or the reproducibility of the photodiode device to device positioning was poor.

Typically, trap detectors have a small FOV. On a QED-150 we measured a 4° FOV when it was equipped with a 3.5 mm diameter aperture. The response deviation from the cosine

function was 0.2 % in this angular range. The alignment of reflectance-type trap detectors can

be difficult when measuring non-parallel beams. The beam convergence-angle should be

always less than the FOV of the trap-detector to avoid beam clipping on the photodiodes. It is easy to obtain a false maximum in the output signal owing to reflections from shiny surfaces

other than the active areas of the photodiodes.

42
At present, trap detectors are not commercially available. Also, the characteristics described

above of reflectance-type trap detectors show that they should be significantly improved to transfer the 0.01% to 0.03 % uncertainties of primary standard radiometers with a minimum

loss of accuracy. Our measurement-transfer policy is to shorten the scale derivation chain by

making direct responsivity calibrations against transfer standard radiometers that have

uncertainties similar to those of the primary standards.

Tunnel-trap detectors were reported several years ago that were constructed using four [13]

and six photodiodes [14]. They were free of back reflectance, therefore separately calibrated

filters or other optical components could be attached to their inputs without introducing

additional uncertainties. The six-element version had a polarization independent responsivity

[10, 13], lower reflectance loss, and improved spatial response uniformity. Because of these

advantages, the six-element transmission-type trap-radiometer is the best choice to transfer

responsivity with the lowest possible uncertainty. In order to make the transfer for an

extended wavelength range, we wanted to utilize the physical model for IQE of SI 337

photodiodes. In addition to traditional radiant power mode measurements, irradiance mode

measurements are needed within a larger FOV for an extended range of applications. The

sensitivity had to be increased because the collected flux in irradiance measurements is much

smaller than in power mode where the total power in the beam is measured. The responsivity

uncertainty in irradiance mode also had to be similar to the uncertainties of the primary

standards.

We measured the angular response of the transmission-type trap-detector we developed earlier

where six equal size photodiodes were used and the aperture diameter was 3.5 mm. In this

experimental device, the positioning of the photodiodes was not designed and implemented

carefully enough. The angular response of this device (#0 1 trap) will be shown below. The

FOV was about 4° and the deviation from the cosine function was about 0. 1 % in this angular

range. The asymmetry was caused by beam clipping on the sixth photodiode.

The design goal for the new tunnel-trap radiometer was to achieve a deviation of less than

0.02 % from the cosine function in an angular range of 5° minimum. A signal dynamic range

of eleven decades is needed to perform irradiance measurements over seven decades with a

signal to noise ratio of 10'*. In order to achieve this requirement, a noise equivalent

photocurrent of 0.1 pA had to be achieved.

A high accuracy current meter is necessary to measure the photocurrent. The lowest

uncertainty of commercially available current meters is 0.03 %. The lowest signal level this

uncertainty can be achieved is 0.1 \iA. Higher sensitivity current preamplifiers have

temperature coefficients of 0.022 %/°C at a gain selection of 10^ V/A. These meters require

ambient temperature control to within 0.5 °C to perform current-to-voltage conversion close

to the 0.01 % uncertainty of trap-radiometer based measurement transfer. Also, these

preamplifiers require source resistance (photodiode shunt resistance) greater than the used

feedback resistance to achieve the specified current-to-voltage conversion accuracy. For

instance, with a sensitivity selection of 1 nA/V a source resistance of larger than 1 GO. is

43
needed. A 3.37 % conversion error was obtained at this preamplifier gain selection when the

photocurrent of our 31 MQ shunt resistance trap-detector was measured.

A procedure had to be introduced to select and group different size Hamamatsu SI 337

photodiodes according to shunt resistance and junction capacitance. The photocurrent meter

for a photodiode group had to be optimized to achieve an adequate noise floor and a 0.01 %

uncertainty in the current-to-voltage conversion. Discussed in section 2 of this paper is a

careful optical-mechanical design that made it possible to fabricate devices of equal

performance. Section 3 describes a careful electronic design and circuit implementation that

was necessary to achieve the electronic characteristics described above.

2. Opto-mechanical design

Medium and large size silicon photodiodes, equivalent to the SI 337 model, were selected to

utilize the physical model for spectral responsivity extrapolation and interpolation. Also, by

choosing different size photodiodes, the aperture area and the FOV could be maximized.

Different arrangements of six photodiodes were investigated to determine the most suitable

geometry for construction in terms of ease of fabrication, accuracy of mounting surfaces, and

optimization of the aperture size and FOV. The FOV is dependent on two parameters: the

total path length from the aperture to the last detector and the size of the aperture placed in

front of the first detector. To obtain a large FOV, the total path length must be kept as short

as possible.

The analysis began with the polarization-independent arrangement shown in Fig. 1, where six

detectors are arranged such that the input and output beams are collinear [13]. The lower left portion of the figure depicts a parallel cylindrical beam being reflected from the six detector

surfaces. As can be seen from the upper portion of the figure, the input and output beams

have the same orientation. The total path length is at a minimum when the detectors begin to touch each other. In the early stages of the development, it became apparent that using

detectors of two different sizes could shorten the path length. Smaller detectors can be used in

the first two positions because a diverging beam (focused onto the aperture) covers only small

portions of these two detector surfaces.

The arrangement shown in Fig. 1 was rejected for two reasons. First, it is difficult to produce

a holder accurately for the detectors. Second, the first and sixth detectors mechanically

interfere with each other when using the two different size detectors, unless the path length is increased which would reduce the FOV.

44
ORIENTATION OF BEAM

IS PRESERVED

Fig. 1 . Generic transmission-trap detector arrangement. The input and output beams

are collinear.

Many detector arrangements can be produced by starting with the generic arrangement shown

in Fig. 1 and simply rotating one, two or three adjacent detectors at a time about a portion of

the optical axis that lies between two adjacent detectors. Of all the detector arrangements that were produced by rotating various groups of detectors, only two arrangements preserved the

input and output beam orientation, the arrangement in Fig. 1 and that shown in Fig. 2. The

arrangement in Fig. 2 was derived from that shown in Fig. 1 by rotating detectors numbered

four through six about the axis between the third and fourth detector centers by 180 degrees.

Here, for simplicity, all six detectors were of the same size.

As can be seen from the figure, the central view has a triangular-like shape, Vv'here views 1 through 3 show that each side of the triangle contain two detector surfaces. Each pair of

detectors form the side of an equilateral triangle and two pairs form planes with a dihedral

angle of 60 degrees. This tunnel-trap arrangement, which will be called the triangular tunneltrap, was selected because it allowed a simple method of construction and minimized the total

path length.

45
/

Fig. 2. The triangular tunnel-trap detector where the last three detectors of the generic

arrangement were rotated by 180°.

The triangular tunnel-trap detector is shown in Fig 3 with a 6° diverging beam reflecting off

the planes of the detector surfaces of two different sizes. The detectors are shown offset from

the beam path to clearly show how the planes of the detector pairs of different sizes are

parallel, but do not lie in the same plane, whereas the detectors of the same size (shown in Fig.

2) lie in the same plane.

The final photodiode arrangement is shown in Fig. 4. In this arrangement the detectors

numbered three and six were left out so the placement of the detectors can be seen. The

positions of both the photodiodes and the aperture were obtained from ray-tracing an f/4

incident beam focused on and normal to the reference plane. The reference plane, needed for

irradiance measurements, is the front surface of the aperture. The diverging beam leaving the

opening of the overfilled aperture was collected and measured by all of the photodiodes to maintain the cosine function of irradiance responsivity measurements. The input and output

beams lie in the same plane which is parallel to the base plane of the radiometer housing. The

triangular holder is mounted in this plane which is also parallel to the front surfaces of

photodiodes two and five. The output beam is shifted relative to the input beam by 41.3 mm.

This shift does not cause any measurable polarization dependence in the signal responsivity of

the trap radiometer. The figure also shows that the first and second detector surfaces are more

efficiently utilized and the position of detector four as well as detector three are not as critical.

46
Fig. 3. Photodiode arrangement and beam geometry in the triangular tunnel-trap

detector. The input beam hits photodiode 1 and then it propagates to photodiodes 2 to 6.

The last detector was rotated in the plane of the block to maximize the detector area with

respect to the elliptical shape of the beam.

The construction, shown in Fig. 5, is made up of three blocks arranged in a triangular fashion.

Six silicon photodiodes of two different sizes were used as detectors in the tunnel-trap

radiom^eter. Two 1 mm by 1 mm. photodiodes at the front were followed by four 1 8 mm by

18 mm devices. Windowless photodiodes were used to eliminate problems caused by

additional reflections and laser interference. There are two blocks that hold detectors of two

different sizes and therefore have a step to allow the smaller detector to be closer to the center

of the triangle. The third block holds the larger detectors at the same distance from the center

of the triangle. The three blocks are held in a triangular shaped block that has been ground

both on the inside and outside to achieve flatness and thickness accuracy within a few

hundredths of a mm. This holder simplified the alignment of the photodiodes before

installation inside of the radiometer housing.

47
OUTPUT

BEAM

DETECTORS

Fig. 4. Photodiode arrangement and beam propagation in the triangular tunnel-trap detector.

BLOCK 2 BLOCK 3 DETECTORS DETECTORS

1 AND 4 «««,nii^^ -i AMn fi

BLOCK 1 DETECTORS

2 AND 5

/

INPUT

BEAM

OUTPUT

BEAM

Fig. 5. Construction of the triangular tunnel-trap detector holder

The triangular shaped detector assembly block is housed in a square housing as shown in an

exploded view of the triangular tunnel-trap radiometer (Fig. 6). Two precision apertures, with

internal diameters of 5 mm and 3.5 mm and made of black-nickel coated copper disks of 0.1

mm thick can be applied at the input alternatively. They are mounted in a recess of 0.1 mm

deep in the front cover to extend the aperture front plane to the overall front surface of the

48
trap-radiometer. This arrangement facilitates the distance measurements in irradiance mode.

The aperture mounting positions are invariant. The FOV is 6° with the 5 mm and 8° with the

3.5 mm aperture. The installed aperture is fixed by a cylindrical holder threaded outside for

either a protecting cap or an input baffle tube. The aperture retainer is beveled inside at the

front with an angle of 45° relative to the aperture plane. This input geometry minimizes the

stray radiation at the front of the radiometer. The incident radiation, overfilling the aperture,

is reflected back from the front surfaces such that the reflected beams cannot enter the

aperture opening. A light trap can be attached to the radiometer output to reject the ambient

light from the trap detector. This can keep the blocked signal reading and the signal

fluctuations low. The light trap and the protecting cap are attached to the housing most of the

time to keep the dust outside. When the light trap is removed, the transmitted radiation can be

measured. Also, the transmitted light can expedite the radiometer alignment. The cavity of

the light trap is covered with specularly reflective black paint.

BACK COVER

Fig. 6. Exploded view of the triangular tunnel-trap radiometer

The tunnel trap radiometer built according to the above design considerations was tested for

optical performance. Angular response scans were made by rotating the radiometer around

the center of its 3.5 mm diameter aperture. The output signal was measured while the

aperture was overfilled with the uniform irradiation from a point source. The source was a

stable and low noise Wi-4 1 G tungsten lamp located at a distance of 3 m from the aperture.

Since the projected area of the rotating aperture changes with cosine versus rotation angle,

the irradiance response, which is proportional to the projected area, also should follow the

cosine function. Deviations from the cosine response can be caused by internal reflections,

beam clipping, stray radiation, and angular response dependence of the under-filled

49
photodiodes. When the source is different from a point source, the accuracy of irradiance

measurements strongly depends on the deviation between the realized angular response and

the cosine response within the angular range determined by the source size, the diameter of

the detector aperture, and the separation between source and aperture. The radiometer FOV

gives the final limitation for the angular range of an irradiance measurement. The FOV has a major impact for the maximum source size and/or the minimum source to aperture distance.

1 -

>«

c

o

Q.W

0) ocT3

0) ,N

"(5E

0.999 -

0.998 -

0.997 -4-3-2-101234

Angle of Rotation [degree]

Fig. 7. Irradiance mode angular responses of tunnel-trap radiometers using 3.5 mm

diameter apertures. The experimental #01 trap was built with six equal size

photodiodes. The beam was clipped on the sixth (last) photodiode. The horizontal

and vertical angular response scans of the optimized tunnel-trap radiometer #03 are very close to the expected cosine response within an angular range of 5°.

The normalized angular responses of the experimental #01 trap discussed earlier and the

optimized #03 tunnel trap radiometers are shown in Fig. 7 and compared with a perfect cosine

distribution. During the horizontal scan, radiometer #03 was rotated in the horizontal plane

around its aperture center. Thereafter, it was rotated 90° around its optical axis and the

"vertical" scan was done in the same way as the horizontal one. The graph shows that the

deviation of the realized angular response from the expected cosine function is less than 0.02

% within a 5° FOV and about 0.05 % at 8° FOV. The cosine response of the optimized device

is five times better than that of the experimental device where six equal size photodiodes were

used. Also, the FOV increased significantly. These measurement results verified the optical

and mechanical design expectations.

50
3. Electronic characteristics

To optimize the overall performance of the tunnel-trap radiometer, the photocurrent-tovoltage converter had to be optimized for the three fundamental gains: current-, voltage-, and

loop-gains [15].

The impedance of the feedback components determines the photocurrent gain and the high

frequency signal roll-off [15]. A high resistance feedback resistor gives high signal gain and

can produce a low signal roll-off frequency even with a small feedback capacitance.

The loop gain of the photocurrent meter is the product of the open loop gain of the operational

amplifier and the attenuation of the feedback network. The feedback network is a signal

attenuator from the converter output to its input, implemented by the feedback impedance and

the shunt impedance of the photodiode. The loop gain is frequency dependent. It is very

important to keep the loop gain high enough at the signal frequency because the accuracy of

the current-to-voltage conversion depends on its magnitude [15].

The closed loop voltage gain is equal to the reciprocal of the feedback attenuation of the

converter if the loop gain is high enough [15]. The voltage gain depends on the signal

frequency. The voltage gain determines the amplification for the input noise and the

temperature-dependent offset-voltage of the operational amplifier. The voltage gain can be

kept low if photodiodes with high shunt resistance are used. When ac signals are measured,

the voltage gain has to be low at the selected signal frequency.

In order to optimize the fundamental gains, the SI 337 photodiodes had to be selected for

shunt resistance and the resultant junction capacitance of the parallel connected photodiodes

had to be measured. Selection of the different size photodiodes for equal shunt resistance [16]

was necessary to maximize the resultant shunt resistance of the six diodes connected in

parallel.

The medium and large photodiodes were selected from several groups purchased at different

times. The two photodiodes located directly behind the aperture were Model 1337-11

photodiodes with a 10 mm by 10 mm active area. The diode shunt resistances varied between

275 MQ and 325 M^ in the first group and between 130 MQ and 267 M^ in the second

group. The last four diodes in the trap arrangement were Model 6337-01 photodiodes with an

active area of 18 mm by 18 mm. The shunt resistances of these large area photodiodes varied

between 355 MQ and 500 MQ in the first group and between 150 MQ and 260 MQ in the

second group. Two 1337-1 1 and four 6337-01 photodiodes of similar shunt resistance were

selected and connected in parallel in one radiometer. Eight such photodiode groups were

assembled for the eight trap radiometers we built. Resultant shunt resistances between 30 MQ

and 55 MQ were measured on the eight radiometers. A shunt resistance of 31 MQ was

measured on trap radiometer #03, which is characterized in detail in this paper.

In order to know the impedance of the parallel connected six photodiodes, the resultant

capacitance of each photodiode group was measured. The capacitance of radiometer #03 was

7.5 nF in the dark.

51
3.1. Loop-gain characteristics

The loop gain at the signal frequency has to be high enough for all signal gain selections of

the current-to-voltage converter to obtain a small enough uncertainty in the current-to-voltage

conversion. For example, to achieve a 0.01 % uncertainty in a dc mode current-to-voltage

conversion, a minimum loop gain of 10 is required for signal frequencies lower than 0.3 Hz

(see below). Because the loop gain is the product of the amplifier open loop gain and the

attenuation of the feedback network, it is also signal gain, and thus, feedback resistor

dependent. Care should be made when high sensitivities are needed because increasing

feedback resistance results in decreasing loop gain [15]. Frequency and feedback resistor

dependent optimization of loop gains is one of the most important electronic design

considerations in high accuracy photocurrent measurements and will be discussed in detail

below.

The theory of loop-gain calculations in silicon radiometers has been described in a previous

work [15]. The relatively small shunt resistance of the tunnel-trap-detector can cause a large

attenuation in the feedback network especially at high feedback resistor selections. The large

attenuation can result in low loop gains in the current-to-voltage converter. The feedback

network in this case was implemented by the complex impedance of the six photodiodes

connected in parallel and that of the feedback resistance and capacitance cormected in parallel.

Also, the large 7.5 nF capacitance of the parallel-connected photodiodes increased the

integrating time constant in the analog control loop. Because of these two reasons,

oscillations occurred in the output voltage of the current-to-voltage converter even at the

highest signal-gain settings. In order to eliminate loop oscillations and to achieve 0.01 %

current-to-voltage conversion accuracy and stability, the loop-gain characteristics of the trapradiometer had to be analyzed and optimized versus frequency and feedback-resistor

selections for both dc and ac mode optical radiation measurements.

G[dB]

- Rf=10»n

80

40

-40

Rp10"^n

RplO^fi

J L

10

-2

OA=OPA627BM

Rs=31 MQ., Cj=7.5 nF

Cf= 160 pF

'v^Cf = 16 pF

10° 10^

f[Hz] 10^ lO*^

Fig. 8. Calculated loop gain characteristics of trap-radiometer #03 for the highest three signalgains. The open-loop gain roll-off frequency of the operational amplifier is/j. The dashed

lines show the effect of the partial frequency compensations at frequency 7c- The open circles

show the signal 3 dB roll-off points matched to the loop gain curves.

52
The calculated loop gain characteristics of the tunnel-trap radiometer for the highest three

signal gain selections are shown in Fig. 8. The feedback resistor could not be higher than

1 Gt^ to obtain a minimum dc loop gain of 10"* (80 dB). The solid lines show the loop gain

curves when no external capacitors are connected parallel to the feedback resistors. For 10^ ^

and 1 0^ Q feedback resistor selections, two roll-off points can be seen on both curves above

the dB line causing a 180° phase shift lag at high frequencies. The roll-off points are caused

by integrating type time constants. The larger time constant Xi is equal to the parallel

connected photodiode shunt resistance and feedback resistance times the sum of the detector

and feedback capacitance [15]. The shorter time constant Ti=l//i is produced by the open-loop

gain roll-off of the operational amplifier. The additional 180° phase shift, caused by the

negative feedback itself, produces a total of 360° phase shift resulting in oscillations at high

frequencies in the loop. At signal-gain 10^ V/A, T2 differentiating time constant gives the roll- on (roll-back) in the loop gain. This time constant, produced by the feedback resistor and the

parallel stray capacitance, is large enough to decrease the 1 80° phase lag caused by the two

integrating time constants. At this signal gain selection, oscillations will not happen if an

operational amplifier with high enough open loop gain and roll-off is selected. Our choice

was the OPA627BM where the open loop gain is 10^ and the roll-off of the open loop gain is at 1 Hz. The roll-off is only 1 Hz for the popular OPAl 1 1

Frequency compensations can be applied in the feedback network of the operational amplifier

to modify loop gain characteristics [15]. Partial frequency compensations have been applied

for the next three signal gains of the trap-radiometer to eliminate oscillations. When an

external capacitor of 1 60 pF was connected parallel to the 1 0^ Q, feedback resistor and a 1 6 pF

to the 10 Q. resistor, the signal roll-off points were tuned to 7^=100 Hz (shown with open

circles) and the phase lag was decreased enough to eliminate oscillations. Similarly, a compensating capacitor of 1.6 nF was connected parallel to the feedback resistor 10^ Q. Full

frequency compensations were applied for the signal gains of 10^ Q and 10"* Q. In a full compensation, the differentiating time constant of the loop was equalized to one of the loop

integrating time constants. This integrating time constant was produced by the parallel

connected photodiode shunt resistance and feedback resistance times the sum of the detector

and feedback capacitances [15]. The values of the feedback components and the final signal

roll-off frequencies of the trap radiometer are shown in Table 1 . The circuit diagram of the

trap radiometer is shown in Fig, 9. To minimize 60 Hz ripple and noise pick-up, the length of

the wires, connected to the high-resistance inverting-input of the operational amplifier, was

minimized and both the circuit board and the photodiodes were shielded. The temperature

coefficient of the feedback resistors is equal to or less than 100 ppm/°C.

The optical radiation signal can be measured in either dc or ac (chopped) modes. In dc mode,

if the integration is done for the duration of 100 power line cycles the electrical bandwidth is limited to 0.3 Hz. In this frequency range, the loop gain is 3 x 10 or higher for any signal

gain selections. However, the upper frequency limit is determined by the integration time of

the digital voltmeter (DVM) attached to the output of the current-to-voltage converter.

Frequency compensations are still needed to avoid oscillations in the analog control loop of

the current-to-voltage converter.

53
Table 1 Current-to-voltage converter feedback components and signal roll-off points

for a silicon trap-detector of 3 1 MQ shunt resistance, 2 pF stray capacitance,

resultant junction capacitance of 7.5 nF, and operational amplifier OPA627BM.

Feedback resistor Feedback capacitor Signal roll-off frequency Compensation

m [pF] [Hz] type

\0' 80 No

10^ 16 100 Partial

10^ 160 100 Partial

10^ 1600 100 Partial

10^ 7480 213 Full

10^ 7500 2123 Full

+15V6 6 6.15V

OV

Fig. 9. Circuit diagram of the tunnel-trap radiometer.

In ac mode, the chopping frequency was selected to be 10 Hz, a decade lower than the 3 dB

roll-off points, to obtain operating points on the plateau of the frequency-dependent signal

gain curves. To achieve high current-to-voltage conversion accuracy in ac mode as well, the

54
loop gain had to be high enough at 10 Hz for all signal gain selections. The lowest 10 Hzloop gain was equal to about 3 x 10^ at the highest signal gain (10^ Q). This loop-gain

resulted in the largest current-to-voltage conversion uncertainty of 0.03 %.

3.2. dc mode measurements

Figure 10 shows the dc noise measurements in the dark versus signal gain selections. The

electrical bandwidth dominated by the integrating type DVM was 0.3 Hz. The noise

equivalent rms photocurrent is shown with the solid line. The noise floor at 10^ V/A signal

gain was 32.2 fA. This corresponds to a noise equivalent power of 47.4 fW at 845 nm where

the responsivity of the trap detector is 0.6794 A/W. The graph also shows the dc output offset

voltage of the current-to-voltage converter. The dc output offset voltage can be subtracted

together with the dark reading if a shutter is applied at the light source being measured by the

trap radiometer.

c

Vk

3o

o

o

JZa.

(0E

c

73>

3

O"

0)

a>

(0oz

10 10^ 10^ 10" 10^

Signal gain [V/A]

Fig. 10. dc noise and output offset voltage measurements in the dark versus signal gain.

The noise sources in dc mode photocurrent meters were discussed in an earlier work [16].

The Johnson (thermal) noise, which is caused by thermal motions of charge carriers in

resistive circuit elements, could be calculated for the trap radiometer. At the highest signal

gain, the source resistance, which is the parallel connection of 7?s=31 MQ. and R=\ GQ, is 7?so=3xl0 Q. The 3 1 MQ shunt resistance dominates the source resistance at the highest two

signal gains. The rms noise voltage of the source resistance, at the output of the trap

radiometer is

55
Fn= i4kTRsoAf)''^ - 0.39 ^iV, (1)

where A:=1.38 * 10' J/K is the Bohzmann constant, 7'=300 K was the temperature of the

radiometer during the test, and A/= 0.3 Hz was the measurement bandwidth determined by

the DVM. The 0.39 |iV is equivalent to an rms photocurrent of 0.39 fA. (The Johnson noise

atR=0.1 GQis0.34^V.)

The total noise of 32.2 fA measured in dc mode indicates that the dominant noise originated

from the 1//" noise of the operational amplifier. In 1//" noise, the noise power goes inversely as

the frequency. The 1 //"noise is very large in the measured frequency interval, below 0.3 Hz.

The signal frequency had to be increased to get closer to the elbow of the 1/f noise spectrum.

This way the 1 //"noise contribution could be decreased.

In dc mode photocurrent measurements, the effect of the operational amplifier drifts has to be

taken into consideration as well. The drift in the output voltage of the current-to-voltage

converter originates from two sources. The first one is the amplified offset voltage drift of the

operational amplifier. At a signal-gain selection of 10^ V/A this will be 26 |aV (0.8 fiV/°C

times the dc voltage gain of 33) for a temperature change of 1 °C. The other drift component

is the roughly 0.02 pA/°C offset current drift that produces an output voltage of 20 ]iW

through the same feedback resistor for the same temperature change. The signal produced

voltage at the output of the current-to-voltage converter should be always 10"^ times larger

than the resultant output drift voltage to achieve 0.01 % measurement uncertainty. In a worst

case situation, the output signal should not be lower than 0.46 V for a temperature change of

1 °C. This signal requirement applies for the output noise component of the converter as well.

The 0.46 V output signal is also more than lO'* times larger than the measured 32.2 |i"V output

noise (corresponds to the 32.2 fA noise discussed above). If the temperature of the

operational amplifier is regulated to 0. 1 °C the drift components in the output voltage of the

converter will be lower than 5 jiV and the noise will limit the output signal at about 0.3 V.

3.3. ac noise measurements

According to the calculated voltage-gain curves in Fig. 11, trap radiometer #03 has a voltagegain increase with increasing signal frequency for the input 1//" voltage-noise between 1 Hz

and 100 Hz. This is the freauencv interval where ac measurements can be made. The

voltage-gain curves are shown with solid lines for the highest three signal-gains. In each

voltage-gain curve Tj is a differentiating time constant producing a roll-on and Tj is an

integrating time constant producing a roll-off [15]. The long-dashed curve shows the

frequency dependent open-loop gain of the OPA627BM operational amplifier which limits the

voltage-gain at high frequencies. Frequency /i shows the roll-off of the amplifier ODen-loop

gain curve. The short-dashed lines show how the partial frequency compensations discussed

above (at7^=100 Hz) can modify the shape of the voltage-gain curves.

56
gain [dB]

A

100-

Rs=31 M^, Cj=7.5 nF, and C = 2 pF

\ ^^^ OA=OPA627BM

^ f [Hz]

'i -c Fig. 1 1 . Calculated voltage gain characteristics of the trap-radiometer. The open-loop gain

roll-off frequency of the operational amplifier is/. The short dashed lines show the effect

of the partial frequency compensations at frequency y^.

The output total noise of the trap-radiometer was measured in the dark between 1 Hz and 40

o Hz when the signal gain was 10 V/A and the signal roll-off was tuned to 400 Hz. The tuning

was made by a 2 pF external capacitor connected parallel to the 10 Q feedback resistor.

Figure 12 shows that the 7.2 fA noise equivalent photocurrent at 10 Hz increased to 9.3 fA at 40 Hz. This result indicates that the effect of the increasing voltage-gain with increasing

frequency supersedes the decrease of the l//noise.

3

O

o

oc

a

3

e

Chopping frequency [Hz]

Fig. 12. Measured noise floor versus chopping frequency of the trap-radiometer at a signal

gain of 10^ V/A

57
The total noise of the trap-radiometer was measured at the optimum 10 Hz chopping

frequency for all signal gain selections. An integrating time constant of 3.3 s was selected for

the lock-in amplifier. The results, converted to noise equivalent power (NEP) using the 845

nm trap-detector responsivity, are shown with a solid curve in Fig. 13. The NEP is equal to the noise divided by responsivity.

3.4. Comparison of dc and ac noise

The dc noise measured in the dark, also converted to NEP, is shown with the dashed curve in

Fig. 13. The lowest NEP, equal to 5.2 fW, was measured in ac mode at a signal gain of 10^

V/A. The curves show that the ac NEP is about an order of magnitude smaller than the dc

NEP. According to these NEP results, the dynamic range of trap-radiometer #03 is between 5

X 10' W and 10' W. This range is larger than twelve decades. However, the output voltage

produced by the signal should not be lower than 35 mV if a signal-to-noise ratio of lO'^ is to be

achieved. The 35 mV corresponds to 52 pW at 845 nm in ac mode.

Table 2 shows the dc to ac input voltage-noise, Vi, ratios for the two highest signal gains of

the trap-radiometer. The ratios were calculated from the measured total noise Vj from Fig. 13

and the calculated voltage gains. Ay, (at dc and 10 Hz) from Fig. 11. The 1//" current noise

and the Johnson noise were much smaller than the amplified 1// input voltage-noise, though

the calculated input 1//voltage noise, Vi, at 10^ ^ was 28 % higher (as compared to 10^ Q,)

owing to some Johnson-noise contribution in the measured total noise. The 1//" input voltagenoise decreased by about a factor of 50 when the signal frequency was changed from dc (less

than 0.3 Hz) to 10 Hz. At the same time, as shown in Table 2, the voltage-gain increase from

dc to 10 Hz was only a factor of 10. If we take the factor of 6 bandwidth difference between

the dc and ac measurements into consideration, the one order of magnitude noise-floor

difference in Fig. 13 can be understood. The results show that the highest sensitivity can be

achieved at 1 0^ V/A signal-gain selection in ac measurement mode with a chopping frequency

of 10 Hz. The uncertainty of these noise measurements was 18 % (coverage factor ^1).

Table 2

dc input voltage-noise to ac input voltage-noise ratios

calculated from the measured total noise and calculated voltage-gains.

Signal Total noise, Vj [fiV] Voltage-gain, Av Vr-- Vt/Av Vi(dc)/Vi(ac)

Gain dc ac dc ac dc ac

10^ 32.2 6.6 33.3 333 0.97 0.02 48.5

10^ 5.24 0.9 4.23 42.3 1.24 0.021 59

While the electrical bandwidth of the dc measurements was 0.3 Hz, that of the ac (10 Hz)

measurements was six times smaller (0.05 Hz).

58
UJ

Signal gain [V/A]

Fig. 13. Comparison of the measured dc and ac NEP values versus signal gain.

3.5. Calibration of the current-to-voltage converter

For state-of-the-art radiant power, radiance, and irradiance responsivity calibrations [19, 20],

the calibration accuracy of the photocurrent meter has to be similar to that of the spectral

power responsivity and aperture area measurements. As it was discussed earlier, the real

values of the feedback resistances should determine the current-to-voltage conversion in a

well designed converter. However, a feedback resistance is usually different from its nominal

value. To achieve the expected high accuracy requirement, primary level current-to-voltage

gain calibrations will be made against standard resistors. The standard resistors have

temperature coefficients of less than 10 ppm/°C and are located in a temperature controlled

and shielded box. They can be switched in decadic steps up to a maximum of 1 GQ. The

standard resistors can be serially connected to the input of the current-to-voitage converter.

The source can be either a voltage or a current source. Both sources need high stability, but

the voltage source does not need a large dynamic signal range. The feedback resistor of the

converter can be calculated from voltage measurements at the input and output. The

calibrated current-to-voltage converter can be used to calibrate other (test) current-to-voltage

converters. A low drift and wide range current source, such as the Keithley Model 263

Calibrator/Current Source, can be switched to the inputs of either the standard or the test current-to-voltage converter while the converter output voltages are measured. This

substitution type calibration-transfer can be used for all signal-gain selections of the currentto-voltage converters. Using the above described two-step method, an 0.01 % uncertainty

level can be anticipated in current-to-voltage gain calibrations.

59
4. Conclusion

The optical and electronic design of the new power and irradiance measuring tunnel-trap

radiometer is described here in detail. This improved performance transfer standard is used to realize and/or hold the high accuracy spectral power, irradiance, and radiance responsivity

scales ofNIST [19, 20].

At present, trap detectors are not commercially available. Also, previously developed trap

devices cannot satisfy the increasing requirements of modem spectral power and irradiance

responsivity measurements. In order to transfer responsivity scales to applications with

uncertainties similar to those of the primary standards, the national standard laboratories,

including NIST, had to develop their own improved performance transfer- standard trapdevices [17, 18,]. We improved the performance of the tunnel-trap radiometer we developed

earlier from six equal size SI 337 photodiodes. In the new optical and mechanical design, six

photodiodes of two different sizes and an input aperture were packed tightly. A second light

trap was attached to the radiometer output to absorb transmitted radiation, to minimize

measurement of ambient light, and to simplify alignment and spectral responsivity

calibrations. The stray radiation at the input was minimized as well. The separation between

the aperture and the first photodiode was large enough to insert additional optical components,

such as 1 mm long filter packages, without degrading the geometrical performance of the

trap-device.

Because of the improved optical-mechanical design and fabrication of the new trap

radiometer, the 0.1 % deviation from the cosine function within 4° FOV (as performed on the

previously made experimental device) decreased by a factor of five within a FOV of 5°. The

0.02 % deviation increased to about 0.05 % at 8° FOV.

Commercially available current meters cannot achieve the 0.01 % uncertainty requirement of

trap-detector photocurrent measurements. It was necessary to design a current-to-voltage

converter that is matched to the impedance of the trap detector package to perform the

expected accuracy of signal measurements.

The photodiodes in the trap-detector package were selected with similar shunt resistances to minimize voltage-gain for the 1// input voltage noise and drift of the operational amplifier.

The voltage-gain, the loop-gain, and the signal-gain were optimized for a signal (chopping)

frequency of 10 Hz. A noise equivalent power of 47.4 fW was obtained in dc measurement

mode and 5.2 fW at 10 Hz signal frequency for a wavelength of 845 nm. The bandwidth was

0.3 Hz in dc mode and 0.05 Hz in ac mode. The measured one order of magnitude noise-floor

difference between dc and ac NEP was verified by a noise analysis. It was shown that the

drift in the output voltage of the converter is roughly equal to the noise produced output

voltage (in dc mode) if the temperature change of the operational amplifier is not larger than

1 °C.

As a result of the electronic device optimization, a simple and inexpensive trap-radiometer

could be implemented with a signal dynamic range from 5x10" W to 10" W. This dynamic

range is larger than twelve decades.

60
Linearity, polarization dependent responsivity, spatial response uniformity, spectral power

and irradiance responsivity of the triangular trap-radiometer will be discussed in a following

publication.

5. Acknowledgement

The authors would like to thank Yuqin Zong and Miklos Racz for participating in the angular

response measurements, and Paul Thompson for measuring and selecting the photodiodes for

shunt resistance. This work was supported by the U. S. Air Force Metrology under contract

number 98-439.

6. References

[1] E. F. Zalewski and C. R. Duda, "Silicon photodiode device with 100 % external quantum

efficiency," Appl. Opt. 22, 2867-2873, 1983.

[2] United States Patent, No. 4,498,012, February 5, 1985.

[3] UDT Brochure on QED-200 Absolute Radiometric Standard, United Detector

Technology, 12525 Chadron Avenue, CA 90250, February, 1986.

[4] J. Geist, R. Kohler, R. Goebel, A. M. Robinson, and C. R. James, "Numerical Modeling of

Silicon Photodiodes for High-Accuracy Applications, Part II. Interpolating Oxide-Bias

Experiments," J. Res. Natl. Inst. Stand. Technol. 96, 471-479, 1991.

[5] J. L. Gardner and F. J. Wilkinson, "Response time and linearity of inversion layer silicon

photodiodes," Appl. Opt. 24, 1532-1534 (1985).

[6] E. F. Zalewski and J. Geist, "Silicon photodiode absolute spectral response selfcalibration," Appl. Opt. 19(8), 1214-1216, 1980.

[7] N. P. Fox, "Trap Detectors and their Properties," Metrologia, 28, 197-202, 1991.

[8] J. Geist, A. M. Robinson, and C. R. James, "Numerical Modeling of Silicon Photodiodes

for High-Accuracy Applications, Part III. Interpolating and Extrapolating Internal QuantumEfficiency Calibrations," J. Res. Natl. Inst. Stand. Technol. 96, 481-492, 1991.

[9] T. R. Gentile, J. M. Houston, and C. L. Cromer, "Realization of a scale of absolute

spectral response using the NIST high accuracy cryogenic radiometer," Appl. Opt. 35, 4392-

4403 (1996).

[10] R. Goebel, S. Yilmaz, and R. Pello, "Polarization dependence of trap detectors,"

Metrologia, 33, 207-213, 1996.

61
[11] J. M. Houston, C. L. Cromer, J. E. Hardis, and T. C. Larason, "Comparison of the NIST

high accuracy cryogenic radiometer and the NIST scale of detector spectral response,"

Metrologia, 30, 285-290, 1993.

[12] Private communication from Thomas C. Larason.

[13] J. L. Gardner, "Transmission trap detectors," Appl. Opt. 33(25), 5914-5918, 1994.

[14] B. C. Johnson, C. L. Cromer, R. D. Saunders, G. Eppeldauer, J. Fowler, V. I. Sapritsky,

and G. Dezsi, "A Method of Realizing Spectral Irradiance Based on an Absolute Cryogenic

Radiometer," Metrologia, 30, 309-315, 1993.

[15] G. Eppeldauer, "Chopped Radiation Measurements With Large Area Si Photodiodes," J. Res. Natl. Inst. Stand. Technol. 103(2), 153-162, 1998.

[16] G. Eppeldauer and J. Hardis, "Fourteen-decade photocurrent measurements with large- area silicon photodiodes at room temperature," Appl. Opt. 30(22), 3091-3099, 1991.

[17] R. Friedrich, J. Fischer,, and M. Stock, "Accurate calibration of fiter radiometers against a cryogenic radiometerusing a trap detector," Metrologia, 32(6), 509-513 (1996)

[18] T. Kubarsepp, P Karha, and E. Ikonen, "Characterization of a polarization-independent

transmission trap detector," Appl. Opt. 36(13), 2807-2812, 1997.

[19] Steven W. Brown, George P. Eppeldauer and Keith R. Lykke, "NIST Facility for

Spectral Irradiance and Radiance Response Calibrations with a Uniform Source," Newrad'99

Madrid, Spain, 1999. To be published in Metrologia.

[20] G. P. Eppeldauer, S. W. Brown, T. C. Larason, M. Racz, and K. R. Lykke, "Realization

of a Spectral Radiance Responsivity Scale with a Laser-based Source and SiRadiance

Meters," Newrad'99 Madrid, Spain, 1999. To be published in Metrologia.

62
Electronic characteristics of Ge and InGaAs radiometers

George Eppeldauer

Optical Technology Division

National Institute of Standards and Technology

Gaithersburg, Maryland 20899

ABSTRACT

Custom-made Ge and InGaAs photodiodes were tested for high sensitivity DC and AC radiometric applications.

Equal size, large-area photodiodes were selected and used as optical sensors in NIST's near-infrared (NIR) standard

radiometers. The DC electronic characteristics of the Ge and InGaAs radiometers were measured versus photodiode

temperature. At -30 °C, a limit-sensitivity of 22 fA and a dark-current stability of 0.2 pA/16 hours was achieved

with the InGaAs radiometer, which was three times better than the results obtained with the Ge radiometer. The Ge

radiometer was used for DC signal measurements only, because at frequencies higher than 0.3 Hz the noise boosting

effect decreased the photocurrent sensitivity. The frequency dependent gain characteristics were calculated and

compared for the two types of radiometer. The InGaAs radiometer could measure optical radiation with a chopping

frequency of 10 Hz without any response or limit-sensitivity degradation.

Keywords: dynamic range, frequency dependence, near infrared, noise, photocurrent, photodiode, radiometry,

sensors, standard, temperature dependence

1. INTRODUCTION

Germanium (Ge) and Indium-Gallium-Arsenide (InGaAs) radiometers were designed and fabricated at NIST' to measure NIR radiometric quantities with high accuracy over a wide range of signal levels. Large-area, planarstructure InGaAs photodiodes with dielectric passivation were selected for most of the applications. For comparison

purposes, large-area Ge photodiodes, with diffused, shallow n-type junction over the p-type base material, were built and tested as well.

Large photodiode surfaces of optical quality (polished) were necessary to make optical alignments simple and to eliminate radiation scatter. The diameter of the active area was 5 mm for both the InGaAs and the Ge photodiodes.

The plane of the photodiode surface was 2° out of parallel with the wedged window to avoid interference during laser measurements. The photodiodes were selected for high shunt resistance to obtain low amplification of the voltage

noise2. AH photodiodes were hermetically sealed in standard housings of the same size and were cooled by two-stage

thermoelectric coolers. The temperatures of the photodiodes were monitored by thermistors and controlled by

temperature controllers^.

2. LOW FREQUENCY (DC) CHARACTERISTICS OF THE NIR RADIOMETERS

The Ge and InGaAs photodiodes were temperature controlled between 25 °C and -30 °C in order to measure their temperature dependent characteristics. Short circuit current measuring circuits of low noise and low drift were

attached to the photodiodes2 to achieve linear operation over a wide radiant power range. The radiometer electronic characterizations included measurement of shunt resistance, voltage gain, output offset voltage, input noise,

photocurrent sensitivity, and short term instabilities.

The shunt resistance of the selected Ge photodiode was 17 kQ. at 25 °C. This value increased to 20 MQ. at -30 °C. The three orders of magnitude shunt resistance change of the Ge photodiode had a large impact on the voltage gain^

of the photocurrent-to-voltage (I-V) converter. The measured shunt resistance and the calculated DC voltage gain are shown versus temperature in Figure 1 . The same measurements were repeated on the selected InGaAs photodiode

SPIE Vol 3061 • 0277-786X/97/$10.00

63
radiometer. The shunt resistance and the DC voltage gain are shown versus the InGaAs photodiode temperature in

Fig. 2. The changes with the InGaAs radiometer are about 40 times smaller as compared to the changes with the Ge

radiometer.

—»-Voltage Gain I

D

O

10* <

o

10^ I

I

-30 -20 -10 10 20

Temperature [°C]

Figure 1. Temperature dependent shunt resistance and DC voltage gain of the Ge radiometer

10^

a^ 10^ u

c - o- -Shunt Resistance I "°~"

10"

o

o

10* <

0)

-30 -20 -10 10 20

Temperature [°C]

Figure 2. Temperature dependent shunt resistance and DC voltage gain of the InGaAs radiometer

The output offset voltages of the two radiometers were also measured versus temperature. The results are shown in

Fig. 3. The output offset voltage of the Ge radiometer changed by more than 300 mV because of the large change in the voltage gain with temperature. The output offset voltage change with the InGaAs radiometer was only 6 mV.

The maximum value was 290 mV with the Ge radiometer and 8.2 mV with the InGaAs radiometer. The estimated

relative uncertainty (coverage factor k=l) of the offset voltage measurements was 5 % and that of the shunt resistance measurements was 10 %.

The input voltage noise characteristics were determined for both radiometers. The input voltage noise is the ratio of

the measured output voltage noise to the voltage gain. The output voltage noise of the radiometer is equal to the

standard deviation of the mean output offset voltage (when no optical radiation is measured by the photodiode). In

Fig. 4, the measured input voltage noise characteristics are shown versus temperature for both radiometers. Both

devices exhibit similar behavior. The same Model OPAllH operational amplifiers were used in both cases. The

64
noise at low photodiode temperatures is higher than at room temperature. At low temperatures the shunt resistance noise of the photodiode is comparable to the l/f voltage noise of the operational amplifier. This is also illustrated in

Fig. 5. The total input voltage noise is the superposition of these two major noise components. The total noise measurements of Fig. 5 were made on the InGaAs radiometer at a current-to-voltage gain of 10^ V/A. At this gain

the resistor noise was dominated by the 55 MQ shunt resistance of the InGaAs photodiode (at -30 °C). The 1// voltage noise of the operational amplifier was flat for shunt resistances less than about 10 MQ. The resistor noise was calculated using the 0.3 Hz electrical bandwidth of our measurements.

>

n

o>

(0

3

a

"5o

o -30 -20 -10 10 20

Temperature [°C]

3

o

>

(0O

c

c

(A<O

J*

D) (Q

(D3

<

Figure 3. Temperature dependent output offset voltages of the Ge and InGaAs radiometers

0)

S

>

0)

(0oz

0)O)

(So>

3

a

c

1.4

1.2

1

0.8

0.6

0.4

0.2

-30

'

' 1

' ' '

'

1

' ' ' 1

' ' ' '

1

'

' \

- \ -o-lnGaAs

- y'K —Ge ' \\ - \ V -

. \ \ . \ '^ . _ \ ^ _ \ "^ \ >» - \ ^ - \ >.

_ V >3-.^ -

- —

D- — — — — — ^

1 . 1 1 i i 1 1 . 1 i 1 1 1 . i 1 -20 -10 10

Temperature [°C]

20

Figure 4. Temperature dependent input voltage noise of the Ge and InGaAs radiometers

The noise equivalent photocurrent is the ratio of the output voltage noise to the current-to-voltage gain (the feedback

resistor of the I-V converter). The noise equivalent current gives the photocurrent sensitivity of the radiometer.

Despite of the similar input noise characteristics of the Ge and InGaAs radiometers, the photocurrent sensitivities and

their temperature dependences are different. This is shown in Fig. 6. The change of the photocurrent sensitivity

with the InGaAs radiometer was less than a factor of 8, whereas that of the Ge radiometer was a factor of 290. To

achieve high sensitivity and stability, temperature controlled cooling was required for the highly temperature

dependent Ge photodiode. Temperature control was not necessary to get similar performance from the InGaAs

photodiode. 22 fA noise equivalent photocurrent was measured at a bandwidth of 0.3 Hz with the InGaAs radiometer

when the photodiode was cooled and controlled at -30 °C. The relative uncertainty (coverage factor k=l) of the noise measurements was 26 %.

65
>

<noz

V

O)

(0 ^^o>

a

c

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

BANDWIDTH: 0.3 Hz

Resistor Noise ^ ^

(V K3

Shunt Resistance [MQ]

100

Figure 5. Shunt resistance dependent input total voltage noise (measured) and resistor noise (calculated) of the InGaAs radiometer.

^ ">'

c 10^

(0

£ 10^

3

U

O

o

.c

0.

, , , . .

,-^

- -o -Current Sens. InGaAs

—i»— Current Sens. Ge

-o— "" "

, — o

"*

)

1 . I.-I L..l_... >..! 1_.>.......^._< i 1—

1-

_^ .^ ***

-30 -20 -10 10

Temperature [°C]

20

Figure 6. Temperature dependent photocurrent sensitivities of the Ge and InGaAs radiometers

During an 8 hour stability measurement, when the temperature was regulated at -30 °C and the signal gain was

109 v/A, the Ge radiometer showed a DC dark-current change of 0.5 pA. The DC dark-current change of the InGaAs

radiometer under similar conditions was 0.2 pA during 16 hours.

3. DYNAMIC (AC) CHARACTERISTICS OF THE NIR RADIOMETERS

It is important to know the current-, voltage-, and loop-gain characteristics versus frequency for any photodiode I-V

converter. The current gain is important, because the signal is the photocurrent. The high frequency roll-off of the

current gain (response) curve is determined by the time constant given by the feedback resistor and capacitor of the I-V converter^. The voltage amplification of the I-V converter is equal to the closed loop voltage gain. The voltage

gain versus frequency characteristics are important for all current (signal) gain ranges because these curves show

whether the meter has any noise boosting effect (increased gain for a certain frequency interval) within the

66
measurement bandwidth.

Figure 7 shows the calculated voltage gain curves of the two NIR radiometers at a current-to-voltage gain of

109 v/A. The only capacitor connected in parallel to the R=l Gi2 feedback resistor is the C=2 pF (estimated) stray capacitance. The voltage gain roll-on for the Ge radiometer starts at 0.23 Hz. This roll-on frequency is determined

by the time constant calculated from the product of two factors. One factor is the resultant resistance of the parallel

connected feedback and photodiode shunt resistances. The other factor is the sum of the photodiode and feedback

capacitances^. For this time constant, the dominating resistance is the shunt resistance, R^, and the dominating

capacitance is the junction capacitance, Cy The junction capacitance is 36 nF for the Ge photodiode and 0.5 nF for

the InGaAs photodiode. The shunt resistance of the Ge photodiode is 20 MI2 and that of the InGaAs photodiode is 55 MQ at -30 °C. Accordingly, the roll-on frequency of the InGaAs radiometer is about 40 times higher than that of

the Ge radiometer. The noise boosting effect starts at the roll-on frequency. The noise boosting can be eliminated if the roll-off time constant (given by the feedback impedance) is tuned to the roll-on time constant. This is called full frequency compensation. Frequently, full compensation cannot be achieved at high signal gains because the roll-off of the signal gain curves can be too low. In this situation partial compensation will decrease the noise boosting

effect while keeping the signal gain roll-off at high enough frequencies.

log gain [dB]

i

100-

R=10^Q, C = 2pF,

OA=OPA627BM

^

log f[Hz]

Figure 7 Frequency dependent voltage gain characteristics of the Ge and InGcLAs radiometers

The DC characteristics were measured at a bandwidth of 0.3 Hz for both radiometers. Consequently, all measurements were made outside of those frequency intervals where the noise boosting is significant. The voltage

gain curves also show that the low frequency (DC) amplification of the input voltage noise is about three times

larger with Ge as compared to InGaAs. Similarly, the noise boosting effect at higher frequencies is roughly two

decades higher with Ge as compared to InGaAs.

The shape of the loop gain curve (of the open analog control loop) shows whether the loop gain, G, is high enough

at the signal frequency to achieve accurate and stable current-to-voltage conversion*^. This requirement is important

for both chopped (or modulated) and low frequency (DC) signal measurements. The OPA627BM operational

amplifier selected for chopped radiation measurement has a larger DC open loop gain and a higher open loop gain

roll-off point, /j, than the OPAl 1 1 used at DC signal measurements. f\ is determined by the dominating integration

time-constant of the operational amplifier. The shape of the loop gain curve indicates whether the phase shifts are small enough for frequencies within the loop bandwidth. Phase shifts for noise frequencies, equal to 180° or larger, can produce oscillations in the analog control loop of the I-V converter.

67
logG[dB]

A

100

60

20

_R=^Cp^, C=2pF

partial

compensation

no compensation

10^

fls=55 Ma, Cj =500pF (5 mm InGaAs)

OA=OPA627BM

R=10^Q to lO^n, C=0.50 nF

full compensation

^=10"^^, C=200pF

- R=10^n, C=20pF

log f[Hz]

Figure 8. Frequency dependent loop gain characteristics of the InGaAs radiometer for different feedback resistors

Figure 8 shows the calculated loop gain versus frequency curves of the InGaAs radiometer for different feedback

resistors. The roll-off points of the signal gain curves are shown with circles as they are matched to the loop gain

curves. As a result of partial and full compensations, the roll-off points of the signal gain curves are at 80 Hz or

higher. At a chopping frequency of about 10 Hz the loop gains are all larger than 10^. If the chopping frequency is increased to 80 Hz, the loop gains are still equal or larger than 103. Because of the large loop gains at frequencies

below 80 Hz, the relative uncertainty (coverage factor k=l) contribution from the loop gains will not be higher than

0. 1 % in the photocurrent measurements.

REFERENCES

1G. Eppeldauer, "Near Infrared Radiometer Standards," in Optical Radiation Measurements III, J.M. Palmer,

Editor, Proc. SPIE 2815. 42-54 (1996).

2. G. Eppeldauer and J. Hardis, "Fourteen-decade Photocurrent Measurements with Large-area Silicon

Photodiodes at Room Temperature," Appl. Opt., Vol. 30, No. 22, 3091-3099 (1991).

3. G. Eppeldauer, "Temperature Monitored/Controlled Silicon Photodiodes for Standardization," in Surveillance Technologies, S. Gov/rinathan, R.J. Mataloni, and S.J. Schwartz, Eds., Proc. SPIE 1479, 71- 77 (1991).

4. Identification of commercial equipment to specify adequately an experimental problem does not imply

recommendation or endorsement by the National Institute of Standards and Technology nor does it imply

that the equipment identified is necessarily the best available for the purpose.

5

G.H. Rieke, Detection of Light: from the Ultraviolet to the Submillimeter (Cambridge University Press, Cambridge, GB, 1994), 143.

6. Product Data Book of Burr-Brown (Burr-Brown Corporation, Tucson, AZ, 1984), 1-38.

7. P. Horowitz and W. Hill, The Art of Electronics (Cambridge University Press, Cambridge, GB, 1987), 127-128.

68
metrologia

InSb working standard radiometers

G. P. Eppeldauer, A. L. Migdall

and L. M. Hanssen

Abstract. InSb radiometers have been developed and characterized for use as transfer standards at the National

Institute of Standards and Technology (NIST). The InSb radiometers will hold a portion of the recently realized

infrared spectral response scale of the NIST and will serve as working standards for the calibration of test detectors. These radiometers will measure radiant power or irradiance from 2 |xm to 5.4 [xm. They have a 17° field-of-view.

The InSb detectors were selected for high shunt impedance to achieve high sensitivity. The transimpedance-gain,

voltage-gain, and loop-gain of the current-to-voltage converters were optimized for optical radiation chopped at 40 Hz. At the peak response, the noise-equivalent-power is 0.6 pW in an electrical bandwidth of 0.3 Hz. The ratio of the dc ambient-background current to the ac noise-equivalent current is 10^. Spatial and angular responsivities,

hnearity, stability, and flashing were also characterized.

1. Introduction

The spectral-power response scale of the NIST from

2 |jLm to 20 fxm [1,2] has been realized on a cryogenic

Si composite bolometer. The bolometer was calibrated

against a primary-standard ci^ogenic radiometer at the NIST [3]. The infrared spectral response scale of the bolometer will be transferred to workingstandard radiometers. The working standards, InSb and

HgCdTe radiometers, will hold the infrared spectral response scale for everyday use. Test detectors will be calibrated against the working-standard radiometers.

The design considerations and characterizations of the InSb working-standard radiometers are discussed here. The InSb radiometers are suitable to measure both

radiant power and irradiance. They will be used either

at the output of an infrared monochromator where the

signal level is low [4], or to measure the irradiance

from a monochromatic uniform source [5]. The desi goals for these radiometers are high sensitivity (low

noise) and wide dynamic-signal range, large detector

area with a high-precision aperture at the front, uniform

spatial response, cosine angular response, linearity,

high photocurrent-to-voltage conversion accuracy at the

signal chop frequency, and high stability.

2. Optical and mechanical design considerations

The radiometers were designed to minimize background

signal, to include a high-precision aperture for irra- diance measurements, and to maintain cosine-law

G. P. Eppeldauer, A. L. Migdall and L. M. Hanssen: Optical

Technology Division, National Institute of Standards and

Technology, Gaithersburg, MD 20899, USA.

Metrologia, 1998, 35, 485-490

response for use with incident beams away from

normal incidence [5]. The liquid-nitrogen-cooled InSb

photovoltaic detectors (4 rrun diameter) were set 1 mm

behind a 3.5 mm diameter aperture. The geometry of a long-snout InSb detector Dewar is shown in Figure 1. A second aperture situated about 50 mm from the highprecision aperture limits the field-of-view (FOV) to

17°, yielding an overall view angle of about 26°. A

recess at the front of the FOV aperture-holder allows

optional cold filters to be mounted. The high-precision

aperture can be either underfilled or overfilled. These

radiometers have been designed to measure either the

//4 output beam of a monochromator or the radiation

from a laser-based, small-sphere source, underfilling

the high-precision aperture for radiant-power-response

calibrations and overfilling for irradiance measurements

[5]. A baffle between the two apertures helps maintain

cosine response by minimizing internal reflections. A

gn 3° horizontally wedged window allows the detectors

to be used for the measurement of either coherent

or incoherent radiation. In a short-snout version, the

separation between the apertures is only 7 mm, but

external optics can be easily added to the Dewar.

3. Electronic design considerations

The detector preamplifier, which is integral with

the detector Dewar, was designed for maximum

sensitivity and current-to-voltage conversion accuracy

at the chop frequency. The high shunt resistance,

i?s, of the InSb detector reduces voltage gain, which

minimizes amplification of input noise voltage (which is dominated by the 1// noise of the operational amplifier

[6]). Figure 2 shows the voltage gain, Gy, versus

frequency [7].

69
G. P. Eppeldauer et al.

Cold

finger

Wedged

window

Mounting

holes

Figure 1. InSb Dewar mount with cold apertures and

entrance window.

R = 10 Mn, C = 2pF

R. = 1 Mn, q =6nF

100 — s

\

CQ s D \

\

\ /OA ^(0 60 L X

ys

^ ^^ CD ^ X 'r

or\. ^A s N

\

y ' Au \ J'

, ° ,

1

1 1 1 1 . l\

10- 10^ 10^ f/Hz

10^ IQt

Figure 2. The voltage gain, Ay, of the InSb photodiode

current-to-voltage converter is shown with the solid line. There is a noise-boosting effect from about 30 Hz to

8 kHz. The open-loop gain of the operational amplifier OA

is shown with the dashed line.

An operational amplifier with low input-voltage

noise and high dc-open-loop gain was selected for the photocurrent-to-voltage converter. The feedback

resistor was limited to i? = 10 MO to avoid saturation by the dc radiation background. The time-constant

determining the roll-on frequency /r is the product of

two factors: the parallel resistance of R and R^ and the sum of C and Cj [8], the InSb junction capacitance. In our case, /^ was dominated by the detector impedance

(i?s = 1 Mn and Cj = 6 nF). For i? = 10 MQ, the lowfrequency voltage gain, Ay^ r; 20. The gain Ay starts to increase at the chop frequency of approximately 40 Hz. At 4 kHz the noise voltage gain would be 100 times

larger, assuming only stray capacitance (estimated to be C = 2 pF).

Figure 3 shows the loop gain [9], Gioop, versus frequency with i? = 10 Mil. The loop gain must be

high at the chopping frequency to achieve accurate photocutxent-to-voltage conversion. The solid curve

70

f/Hz

Figure 3. Loop gain, G, versus frequency. The solid curve is the uncompensated loop gain. The dashed curve shows the loop gain after full frequency compensation.

The compensated 3 dB roll-off point of the signal response

curve is shown with an open circle as it is matched to the dashed loop-gain curve. At low frequencies, G = Ao/3o,

where A^ is the dc open loop gain of the OA and /3o is the dc feedback attenuation.

shows the uncompensated C = 2 pF gain with a long - 40 dB/decade slope because /^ and /; are close to each other and far from /i. The frequency f\ was

determined from the dominant time-constant of the

operational amplifier. In this figure, /r shows a roll-off

as opposed to the roll-on of Figure 2. The frequency /i

is determined by the time-constant (i?C) of the feedback

impedance. The loop gain reaches unity at about 3 kHz,

which is lower than the 8 kHz signal 3 dB roll-off point

calculated from the parallel i? = 10 MQ and C = 2 pF

impedances [10]. In this case, the loop bandwidth is smaller than the signal bandwidth, which is a condition

to be avoided. Also, two integrating time-constants that are close in frequency can cause gain peaking, yielding

a sharp increase in amplitude at high frequencies and

ringing.

An external 544 pF capacitor was connected in parallel to i? = 10 MO to achieve full frequency

compensation. Tuning /i to /r cancels the roll-off at

/r with the /i roll-on. The fully compensated (/r = /i = 30 Hz) loop-gain curve, indicated by the dashed line

in Figure 3, also eliminates the noise-boosting effect shown in Figure 2 (Ay = Ay^ for all loop frequencies).

However, the original /i = 8 kHz 3 dB roll-off point

decreased to 30 Hz. To operate on the plateau of

the signal gain curve, the chop frequency must be a decade lower than the 3 dB point. A 3 Hz chopping

frequency satisfies this requirement but because 3 Hz

is much lower than the planned 40 Hz frequency, full compensation could not be made for the highest signal

gains.

The chopping frequency can be increased if partial

frequency compensations are performed for the high

signal gains as shown in Figure 4. Increasing the

3 dB roll-off points to a minimum of 400 Hz allows

a 40 Hz chopping frequency. For i? = 10 MO, the loop gain is still about 100 at the signal 3 dB roll-off

point, yielding a 1 % error in the current-to-voltage

.Metrologia, 1998, 35, 485-490
InSb working standard radiometers

100

CO

:? 60

1 Mn, q = 6 nF

partial compensation

full compensation

CD

R = 10 kn, C = 5.9nF R = 100 kn, C = 4nF R = 1 Mn, C = 0.4 nF

10 Mn, C = 0.04nF

flHz

Figure 4. Partially and fully compensated loop-gain

characteristics of the InSb photodiode current meter. The open circles show the 3 dB roll-off points of the photocurrent response functions matched to the loop-gain

curves for each feedback resistor.

conversion. For the 1 Mf2 and 100 kO feedback

resistors, the loop gain increases further, resulting in higher signal-measurement accuracies. At i? = 10 kJ7,

full compensation can be realized with the 3 dB point

still above 400 Hz. The loop gain at this 3 dB point is about 4000. At 40 Hz, the loop gain equals or exceeds

3 X 10^ for all R.

Figure 5 shows the voltage-gain curves for the

partially and fully compensated signal-gain ranges. At 40 Hz, the noise-boosting effect is practically

eliminated, even for the partially compensated signalgain ranges.

CQ 80

•acO 40

10-' 10"

Rs= 1 Mn, Ci = 6nF

partial "•.. compensation '* ^

'^R = Wil, C = 0.04nF

-. R = ^O^Q., C = 0.4nF ^ R = 10'n, C = 4nF >^\ R = 10''n, C = 5.9nF

^- full compensation

IC^ f/Hz

Figure 5. Voltage-gain curves (solid lines) for the partially and fully compensated signal gains of the InSb photocurrent

meter. The signal chopping frequency is 40 Hz.

4. Radiometric characterizations

4.1 Responsivity versus time; flashing

A 0.25% response change was observed during the 15.5 h hold time of the Dewar (see Figure 6). This

hold time depends on the Dewar vacuum level. Immediately after repumping, Dewar hold times in excess of 24 hours are possible. The 0.1 % instability

in the second half of Figure 6 was measured after 18:00 h, when the environment of the setup was at

its quietest. The radiation source was a quartz-halogen

lamp, operated at half of its nominal 100 W operating

power. The low temperature of the source and the

2 |xm cut-on (order-sorting) filter were required to maintain the stability to within 0.1 % because radiation

wavelengths shorter than about 2 jxm produce response

fluctuations due to trapped charges accumulating within

the detector. These variations, seen as sudden jumps

in the output level, are referred to as "flashing".

Flashing can reach the level of a few percent if the visible/near-infrared radiation reaches the detector. Figure 7 shows the typical flashing seen when the

tungsten-halogen lamp is used at its full 100 W power,

providing more short-wave radiation. The radiation

from the lamp passed through a monochromator set

to 3.6 |xm and a 2 (xm cut-on filter. The 10"^ filter blocking was not enough to cut out the short-wave

radiation from the detector, which had a dynamic

range of nine decades. The fluctuations measured this way indicate the extreme sensitivity of flashing to

2.005

1.990

Figure 6. Test of InSb stability versus time at 3.8 fjim.

2.96

2.95

> 2.94

0)O)

(Q 2.93

jsO

> 2.92

3

a

3

2.91 o

2.90

2.89

2.88

Figure 7. InSb flashing.

Metrologia, 1998, 35, 485-490 71
G. P. Eppeldauer et al.

short-wave radiation. For accurate measurements, the flashing effect must be smaller than the expected

uncertainties. This can be achieved by limiting the incident radiation below about 2 fjim by employing cut- on filters and/or appropriate source-power distributions which have relatively low short-wavelength output.

Flashing may also be reduced by better detector design,

such as by applying an integrated aperture on the InSb

chip outside the photosensitive area [11]. The InSb

detector output should be monitored for a period of

about 1 h to verify that flashing effects are below the desired level.

4.2 Responsivity versus frequency

The normalized, measured, frequency-dependent signal

responsivities of the InSb radiometers at gains of lO"*, 10^, and 10^ V/A are shown in Figure 8. The results are in good agreement with the design values shown in Figure 4. The 3 dB point could not be measured at gain

10' V/A because no cold filter was installed in front of the detector. The detector measured the background

radiation with its full broadband responsivity, resulting

in a too-large dc background current for this signal-gain

range.

1 o

Q.

I

0.9 o

JQ

_c

TJ

<U

"co E

O

z

0.8

100 200

Frequency / Hz

300

Figure 8. InSb radiometer response versus frequency,

normalized to unity at dc, for three different gain settings. One-time-constant response curves are fitted (solid lines)

to the measured data points.

4.3 Responsivity nonlinearity

The nonlinearity of the InSb radiometer was tested by comparison with a calibrated transfer-standard Ge

detector over a range of input power levels. The

measurements were made using a chopped diode-laser

beam at 1.3 ixm where the two detectors overlap

spectrally. Neutral-density filters inserted into the beam

were used to vary the radiant power level. The two

detectors were substituted for each other.

1.03

1 1 1 1 iiiii 1 Jill iii| 1 1 1 r rrrq r—i i i i i ii

>> G^

•> 1.02 - -

(AC

2 1.01 _ Q.

<A

^ a •!• - = 0.99 - §-

gks c O 0.98 L _ Z

0.97

n QR

-

10-^ 10- 10"^ Power / W

10' 10"

Figure 9. Ratios of InSb to Ge response (for identical radiant-power inputs) divided by a constant to yield a mean

value near unity (see text).

Figure 9 shows the InSb to Ge response ratios measured versus radiant power (the ratios have been

normalized by the average value over the range

2 X 10"' W to 2 X 10^ W). The uncertainty bars in the

figure represent only the standard deviation of repeated measurements. If we exclude the two points in Figure 9

which show very large relative standard deviations

owing to flashing (Section 4.1), the estimated overall

relative standard uncertainty for the entire measurement

range is 1 %. This includes major contributions from

flashing, the lock-in-amplifier gain calibration, and

the current-to-voltage amplifier calibration. The InSb

detector is linear up to about 0. 1 mW with evidence of

about 1 % nonlinearity at 0.75 mW.

4.4 Dynamic range

The noise component from the input-voltage noise

density of the operational amplifier was calculated at 43 Hz. At i? = 1 MO, where the voltage gain was

small {Ay = 2 as shown in Figure 5), the equivalent

photocurrent noise was 0.06 pA/Hz""^. The equivalent

photocurrent of the Johnson noise was 0.1 pA/Hz~''^.

The 1// noise component was calculated from the

amplifier catalogue for the 0.1 Hz to 10 Hz bandwidth.

The equivalent effective photocurrent of this noise

is about 0.6 pA/Hz"''^. At 43 Hz the 1// noise is significantly lower. The RMS total noise current was measured with

an electrical bandwidth of 0.3 Hz at 43 Hz, at different wavelength settings of a monochromator. The total noise scale (left y-axis of Figure 10) indicates low

background signal at 2 [xm, and a large 1// noise

component. No heated IR source was used in this measurement. The background radiation was chopped

72

Metrologia, 1998, 35, 485-490
InSb working standard radiometers

at 43 Hz, producing the detector ac mean current (right

j/-axis of Figure 10). The total current noise increased

by more than a factor of two as the monochromator

was tuned from 2 |xm to 5 |j.m. The steep slope of

the solid curve shows the background noise component

increasing with wavelength. The total noise current was

about 30 times smaller than the mean ac backgroundproduced detector current at 5 jxm. The dominant

component of the total noise current in the longwavelength range is the shot noise of the dc ambient

background current. In an independent test, a 13.4 |ulA

dc background current was measured without any

spectral selection of the input radiation. The current

noise, calculated from this dc background current, was

1.13 pA, just slightly lower than the total noise current observed at the longest wavelength measured. The total noise current of the detector determines the limiting

noise-equivalent power (NEP) of the InSb radiometer.

The measured NEP at the peak response (2 AAV) was

0.6 pW (RMS) in an electrical bandwidth of 0.3 Hz. The ratio of the dc ambient background current to the RMS total noise current was about 10^.

< _

' 1 1 1 1 ——i-.

Q.

- rr— J N

1 / / ?7 /

r / - _A / 1S / /

••-> — X / e /^

a> J /

fc y 4 3

O -__—-a——^ 1

0> P /

M O.b - / O L

/ > c

/ %

- / tn

- • s /

ce. n'

h —

-r----T'-—

1 1 1

40

30

<a.

20

- 10

o

D) J£U

ni .ao

2 3 4 5 Wavelength / ^m

Figure 10. Total noise and ac background current versus monochromator wavelength.

-3-2-10123

Horizontal position / mm

Figure 11. InSb radiometer: variation in horizontal spatial response. The inset shows the data on the expanded scale marked on the right.

1.1

0)

(0c

oa

«

0)

L. T3

0) _N

75E

oz

0.9

0.8

0.7

cos {a)

\

Response

-10 -5 5 10

Incidence angle a/ degree

The maximum detector current can be measured

at a gain of 10"* V/A. A 1 mA maximum current on

the 10 V full-scale output corresponds to a maximum

measurable radiant power of 0.5 mW at the InSb peak

responsivity, and thus the dynamic range of the InSb

radiometer is nine decades.

4.5 Spatial/angular responsivity

Spatial-response variations were measured along the horizontal and vertical diameters of the InSb detectors. Figure 11 shows a variation of less than 2% in the horizontal scan within the 3.5 mm diameter of the highprecision aperture. The angular response was tested by

rotating the detector around its vertical axis. The axis of rotation was close to the centre of the high-precision

Figure 12. InSb radiometer: variation in angular response.

aperture. The measurement results shown in Figure

12 were obtained using a point source 1.2 m from

the detector. The measured field-of-view is 17°. The

maximum deviation of the measured angular response

from a cosine law is ± 1 %. There was no baffle installed

in the FOV-limiting tube during this measurement. The

slight measured deviation may indicate a need for a

baffle in the input beam, as shown in Figure 1.

5. Conclusion

Standard-quality InSb radiometers have been developed

as working standards to hold the spectral response

scale of the NIST between 2 fxm and 5.4 )xm. The

Metrologia, 1998, 35, 485-490

73
G. P. Eppeldaiier et al.

radiometers can measure radiant power or irradiance

in a signal range of nine decades. The NEP

is approximately 1 pW/Hz"^. Signal (photocurrent)-

gain, voltage-gain, and loop-gain were optimized for operation at approximately 40 Hz. The area of the highprecision aperture is 0.1 cm^, with an FOV of 17°. The

spatial-response non-uniformity and the deviation of

the angular response from a cosine function are about

1 %. The response non-linearity at the high-signal end

(about 0.7 mW) is about 1 %. The 8 h stability of the radiometers is about 0. 1 %.

References

1. Eppeldauer G., Migdall A. L., Gentile T. R., Cromer C.

L., Absolute response calibration of a transfer standard cryogenic bolometer, In Photodetectors and Power

Meters II (Edited by K. Muray and K. J. Kaufmann),

Proc. SPIE, 1995, 2550, 36-46.

2. Migdall A., Eppeldauer G., Realization of an infrared

spectral radiant power response scale on a cryogenic

bolometer, Metrologia, 1998, 35, 307-315.

3. Gentile T. R., Houston J. M., Hardis J. E., Cromer C. L., Parr A. C, National Institute of Standards and Technology

high accuracy cryogenic radiometer, Appl. Opt., 1996, 35, 1056-1068.

4. Migdall A., Eppeldauer G., Cromer C, IR detector spectral

responsivity calibration facility at NIST, In Cryogenic

Optical Systems and Instruments VI (Edited by J. B. Heaney and L. G. Burriesci), Proc. SPIE, 1994, 2227,

46-53.

5. Eppeldauer G., Near Infrared Radiometer Standards, In Optical Radiation Measurements III (Edited by J. M.

Palmer), Proc. SPIE, 1996, 2815, 42-54.

6. Eppeldauer G., Hardis J., Fourteen-decade Photocurrent Measurements with Large-area Silicon Photodiodes at Room Temperature, Appl. Opt., 1991, 30, 3091-3099.

7. Eppeldauer G., Electronic Characteristics of Ge and

InGaAs Radiometers, In Infrared Technology and Applications XXIII, Proc. SPIE, 1997, 3061, 833-838.

8. Product Data Book of Burr-Brown, Tucson, Arizona, Burr-Brown Corporation, 1984, 1-38.

9. Horowitz P., Hill W., The Art of Electronics, Cambridge,

Cambridge University Press, 1987, 127-128.

10. Rieke G. H., Detection ofLight: from the Ultraviolet to the

Submillimeter, Cambridge, Cambridge University Press, 1994, 143 p. 11. EG&G Judson Company, personal communication, 1997.

74

Metrologia, 1998, 35, 485-490
Domain-engineered pyroelectric radiometer

John Lehman, George Eppeldauer, J. Andrew Aust, and Miklos Racz

We built a large-area domain-engineered pyroelectric radiometer with high spatial and spectral response

uniformity that is an excellent primary transfer standard for measurements in the near- and the

mid-infrared wavelength regions. The domain engineering consisted of inverting the spontaneous polarization over a 10-mm-diameter area in the center of a uniformly poled, 15.5 mm x 15.5 mm square, 0.25-mm-thick LiNbOg plate. Gold black was used as the optical absorber on the detector surface, and

an aperture was added to define the optically sensitive detector area. Our results indicate that we

significantly reduced the acoustic sensitivity without loss of optical sensitivity. The detector noise

equivalent power was not exceptionally low but was nearly constant for different acoustic backgrounds.

In addition, the detector's spatial-response uniformity variation was less than 0.1% across the 7.5-mmdiameter aperture, and reflectance measurements indicated that the gold-black coating was spectrally

uniform within .2%, from 800 to 1800 nm. Other detailed evaluations of the detector include detector

responsivity as a function of temperature, electrical frequency response, angular response, and field of

view.OCIS codes: 040.0040, 120.5630, 230.0230.

1. Introduction

Recently it was shown that techniques employed for domain engineering of lithium niobate (LiNbOg) optical parametric oscillators could be used to create

large-area, pyroelectric detectors that have reduced

acoustic sensitivity.^ On the basis of our earlier success, we incorporated a unique, concentric-ring patterned, domain-engineered pyroelectric detector into a complete radiometer. First, we discuss the

domain-engineering aspects of our design. Then we

describe the most important optical and electronic

design considerations along with our measurement

results.

2. Acoustic Nulling

Ferroelectric pyroelectric detectors are also piezoelectric; therefore the acoustic sensitivity is related to the

mechanical structure of the detector, its environment, and anything to which it is attached. A stratJ. Lehman (lehman@boulder.mst.gov) and J. A. Aust are with

the Optoelectronics Division, National Institute of Standards and

Technology, Boulder, Colorado 80303. G. Eppeldauer is with the

Optical Technology Division, National Institute of Standards and

Technology, Gaithersburg, Maryland 20899-3460. M. Racz is a guest researcher at the National Institute of Standards and Technology from the Hungarian Academy of Sciences Research Insti- tute for Technical Physics and Materials Science, Budapest,

Hungary.

Received 23 June 1999; revised manuscript received 3 September 1999.

egy to reduce the pyroelectric detector acoustic

sensitivity is shown schematically in Fig. 1. Two

detector regions, (a) and (b), with equal and opposite

acoustic sensitivities, are exposed to ambient conditions, whereas radiant power reaches only one detector region. The two detectors are connected

electrically in parallel so that the current signal from

one is superimposed on the other. The result may be

expressed as

^a.pyro "'" ^a.piezo h. (1)

where f„„j.o "pyro is the current generated from radiantpower input and ipi^zo is the current generated from

ambient acoustic noise surrounding the detector. If

the piezoelectric current generated by detector (a) is equal to detector (b) (that is, if both detectors are

mechanically identical), then simply,

^ 'a.pyro* \^J

In the present device, the center of the detector is effectively region (a) and region (b) is the outer ring.

One electrode is placed on each face of the LiNbOg

plate, and, consequently, the two detector regions are

electrically connected in parallel. The outer ring is optically and acoustically sensitive, but an aperture

prevents incoming optical radiation from being received. In the past we observed 40-dB reduction in com- mon mode signals over a range of frequencies and

nearly 120 dB at what appear to be resonant frequen1 December 1999 / Vol. 38, No. 34 / APPLIED OPTICS

75
Signal

(a) +(b)

Optical aperture

Acoustical energy

Optical energy

Fig. 1. Diagram of the acoustic nulling concept with equal and

opposite pjrroelectric domain areas.

cies in a bicell detector with bilateral symmetry. We

chose a concentric-ring pattern to simplify the radiometer construction. In the future we expect to model different package geometries and domain pat- terns rather than rely on the process of trial and error

to optimize the nulling capability of each detector. In Section 4 (which deals with acoustic measurement) we compare two detectors. The steps for fabricating each detector are identical, with the

exception of several intermediate steps taken in one

of the detectors, to accomplish the selected-area electric field poling or the domain engineering. When

we subsequently describe our measurements, the

uniformly poled detector was designated J 15 and the

domain-engineered detector was designated JIO.

Detector JIO is then incorporated into the radiometer.The pyroelectric detector elements were con- structed from a commercially available, z-cut LiNbOs

wafer. The wafer was 75 mm in diameter, 250 jo-m

thick, and optically polished on both the positive and

the negative z faces so that thickness variations were

less than ±0.25% (manufacturer specification). The

wafer was cut into 15.5 mm X 15.5 mm squares to form plates, which would eventually become the in- dividual detector elements. To perform the domain

reversal, the positive z face of the plate was coated

with photoresist. A 10.8-mm-diameter opening was

patterned in the center of the plate by use of standard

photoresist processing. The sample was then

clamped in an acrylic fixture with silicone O rings as shown in Fig. 2. Liquid electrodes were used to pro- vide independent electrical contact to the positive

and the negative z faces of the plate. The portion of

the sample that underwent domain reversal was defined by the opening in the photoresist. Complete

domain reversal of this area was achieved by application of a 24.5-kV/mm electric field across the elec- trodes.

The detector electrodes were fabricated by deposiAcrylic fixture

Photoresist mask

Poled region

LiNbO,

Fig. 2. Schematic diagram of the fixture for applying a highvoltage (HV) electric field across the LiNbOg plate.

tion of circular nickel fihns, 15.2 mm in diameter and

25 nm thick in the center of each z face of the plates.

The final step in constructing the detector element was the deposition of the gold-black absorbing layer.

The process by which the gold black is deposited is similar to that documented by others, most notably

Blevin and Brown,^ but is not substantially different

from that documented by Harris et al. in 1948.3 Qur

process depends on the product of the pressure of the

nitrogen environment in which the gold is evaporated

and on the distance from the filament source and the

target (the nickel-coated LiNbOg plate). A rule of

thumb is "10 Torr cm." In other words, the product

of the distance between the evaporation source and

the target should equal 12 Pa m (10 Torr cm). Depositing gold black on a thin, fragile, dielectric material, remains an art. The ability to conduct heat

away from the crystal is crucial during the deposition, but a uniform and substantial heat sink (without contact resistance) is difficult to attach without

scratching or breaking the LiNbOg plate. In this case we used gold foil sandwiched between the plate

and a 3-mm-thick aluminum stage. The plate was

held lightly with a spring retainer.

A schematic view of the domain-engineered pyroelectric detector element is shown in Fig. 3. A cross- sectional view of the complete detector assembly is shown in Fig. 4. The detector element was attached

electrically and mechanically to the container with

electrically conducting epoxy on the perimeter of the

aperture. As a result the signal electrode was not

attached to a rigid heat sink and therefore provided a

front view |

section view

. ^ Domain-reversed area

-' EH Electrode area n 1 5.5 mm X 1 5.5 mm LiNbO^ plate ^^' Aperture/gold black boundary — Gold black

\~t] Relative spontaneous polarization

orientation

Fig. 3. Exploded view of spontaneous polarization, electrodes, aperture, and gold black.

APPLIED OPTICS / Vol. 38, No. 34 / 1 December 1999

76
Original domain ^ p^

Reversed domain

- Aperture

Case

Conductive epoxy

Nickel electrode (ground)

Domain-engineered

LiNbOs plate

Nickel electrode (signal) Conductive epoxy

Conductive wire (signal)

Fig. 4. Perspective-section view of LiNbOg packaging.

more spatially uniform response to optical input.

The grounded case provided electromagnetic shielding for the signal electrode.

Because pyroelectric materials are also piezoelectric, the pjrroelectric detector response may contain

frequency components in the range of the optical

chopping frequency. The typical detector figure of

merit, noise-equivalent power (NEP), is normally

specified (or should be) along with the wavelength,

chopping frequency, bandwidth, detector area, and

sometimes temperature and feedback resistance.

NEP is a well-accepted, commonly used noisesensitivity figure of merit for all types of optical detectors, but it is dubious for pjrroelectric detectors,

because it does not account for the acoustic background.

We compared the acoustic response of our domainengineered detector, JIO, which has equal and opposite areas of acoustic sensitivity, with an otherwise

identical, uniformly poled detector, J15. We measured the relative acoustic frequency response by us- ing a loudspeaker located 45 mm away from the

detector aperture and facing it. The loudspeaker

output was coupled to the pyroelectric detector

through the surrounding air. The pyroelectric detector output was sampled and recorded over the fre- quency range of 5—100 Hz with a lock-in amplifier.

The results are shown in Fig. 5. We were interested

in low-frequency responsivity, because the minimum

NEP typically is found at a frequency of less than 100

Hz.4 Over the chopping frequency range of interest

the responsivity of the domain-engineered detector

was 7-15 dB less than that measured by the uniformly poled detector, for identical measurement conditions.

3. Radiometer Construction

The domain-engineered p5n'oelectric detector was

placed in the radiometer assembly shown in Fig. 6. The detector and the connecting wires were mounted

in an aluminum block. This block was attached to the aluminum, electrical-shield housing of the elec- tronics. The output leads of the pyroelectric detector were connected to the current-to-voltage

0.020

0.018 h

0.016

— J15 (uniform poling) JIO (domain engineered)

% 0.014

Jr> / $ 0.012 / c

Q. 0.010 ^ 0.008 / , . ,

0.006 J /

0.004 ^v_^/ /

0.002 / ••"

0.000

. L... . J . 1 . r , 10 30 50 70 90 Frequency [Hz]

-7

20logG10/j15)

2,

J"'

c

o

(0

i

-11

•{35 1

a: -15 -

-19 —1—.—1

.—1

,—1— „ 1 10 30 50 70 90 Frequency [Hz]

Fig. 5. Acoustic frequency response fur two pyroelectric detectors

that were identical except for the poling orientation (detector J15,

uniform poling; detector JIO, domain engineered).

converter input. To avoid 60-Hz pickup, the housing

of the electronics and the detector block were continuously grounded. To avoid ground loops, the signal

common and the shield were connected only at the

0-V output of the ± 15-V power supply. A thermistor was mounted inside a copper plate with good thermal

contact to the detector to monitor the detector temperature.^

We use a custom-made current-to-voltage converter (current preamplifier) along with a commercially available lock-in amplifier and chopper to obtain a usable signal from the pyroelectric detector.

1 December 1999 / Vol. 38, No. 34 / APPLIED OPTICS

77
Detector block Detector leads Housing of electronics / Signal-gain switch

633-nm He-Ne laser Beamsplitter^ Controlled chopper Lens

Pyroelectric detector

Detector case \ \ Copper plate Thermistor Thermistor output

Signal output

Connector to power supply

Fig. 6. Radiometer construction incorporating the domainengineered pyroelectric, j 10.

This is a common approach with pyroelectric detectors. However, there are many subtleties in designing and using the current-to-voltage converter to optimize the detector performance.

The equivalent circuit for any pyroelectric detector

is modeled as a current generator along with a resis- tor and a capacitor, electrically connected in parallel.

The current-to-voltage converter was used to measure the short-circuit current from the p3rroelectric

detector signal electrode. Connecting external ca- pacitors, parallel to the feedback resistors of the converter, optimized the signal- and loop-gain

requirements. The signal roll-off frequencies were

tuned to a range between 100 and 1000 Hz. Optimization of the converter-voltage gain-versusfrequency curve was not necessary, because the

dominant noise was the current noise of the pyroelectric detector. Consequently, selection of operational

amplifiers for the converter was not a critical issue.

To avoid signal distortion, including amplitude de- crease and signal phase shift, the signal shape of the

output voltage must be similar to the shape of the

chopped optical signal. To achieve this similarity,

the fundamental gains of the photocurrent meter (including the detector and the converter) must be op- timized at the signal frequencies.^ The signal gains

should be frequency independent (flat) around the

signal (chopping) frequency to avoid signal-gain instabilities. To achieve this requirement, the 3-dB

roll-off frequencies of the signal-gain characteristics

v/ere tuned 1 decade higher than the chopping fre- quency. Also, the chopping frequency was selected

low. For the highest feedback resistor, the stray ca- pacitance produced a relatively low signal roll-off fre- quency. It was necessary to carefully connect the

feedback components of the converter to keep the

stray capacitance low and the 3-dB roll-off signal fre- quency high. The 3-dB points should not be much

more than 1 decade higher than the signal frequency,

especially at low signal-gain ranges; otherwise the

loop-gain at the chopping frequency can be too small,

resulting in low-accuracy current-to-voltage conversion. All of our electronic and radiometric tests were made with an ac data-acquisition system. '^ The volt- age output of the pyroelectric radiometer was at- tached to the input of a dual-phase, sine-wave

/ K

Baffle Test detector

/ ' I Up.

Silicon monitor detector Controlled shutter Y-Z translation stage I Down a

Fig. 7. Arrangement for frequency-response and spatial-response

uniformity measurements.

measuring lock-in amplifier. The in-phase- and the

quadrature-analog lock-in outputs were recorded by

two simultaneously triggered digital voltmeters

(DVM's) that served as analog-to-digital converters

for the lock-in. These two DVM output channels (X

and Y) are summed in quadrature digitally by the

computer to extract the signal magnitude. Lowpass filtering of the analog signals is achieved by the

integrating-time constants of the averaging times of

both the lock-in outputs and the DVM's. In our measurements the lock-in output time constant was set to 333 ms. The DVM's were always operated with an

averaging time of 100 power-line cycles.

4. Measurements

The frequency-dependent response of the radiometer was tested with the optical arrangement shown in

Fig. 7. The primary beam from a He—Ne laser was

chopped with a mechanical chopper and focused onto

the pyroelectric detector with a plano-convex lens.

The monitoring beam was reflected with a beam split- ter and directed to underfill a silicon-monitor detector. The p3nroelectric-detector signal was corrected

with the monitor-detector signal to compensate for

optical power fluctuations in the primary beam. A

shutter and baffle minimized uncertainties due to stray radiation.

Figure 8 shows the gain-versus-frequency characteristics of the domain-engineered pyroelectric detector for the two highest signal-gain selections. Both

curves were normalized to the zero-signal frequency.

Two signal-gain ranges, 10^ and 10^ V/A, were the

only ranges for which no external compensating ca- pacitors were needed. The 3-dB roll-off point was 61

(0 1 c

0.8 Gain=10^V/A '""^

3 0.6 3-dB level ' """^

a.

-*-" 3

O

o

0.4 ^V

(UN

roE

o 0? Gain=10^V/A\^ z

,1 , . , . ' '

, , , , , . 1 10 100

Frequency [Hz]

Fig. 8. domainMeasured signal gain-versus-frequency curves of the engineered pyroelectric radiometer.

APPLIED OPTICS / Vol. 38, No. 34 / 1 December 1999

78
lU

--

;

10° *—

J

10-^ -

i rvvv^r^^-^ I

; ':

10^

%' r

' V '•/x

-

in 3

l\' ' f i

1

:

5.74

5.73

7)

5.72 ST. <

o

5.71 w

3

fi> 5.7

3.69

633 nm He-Ne laser A Con It

Controlled chopper Neutral filter Baffle Test detector

(0c

w

o

>«

o -6-4-20246

Horizontal position [mm]

Fig. 9. Horizontal spatial-response scan of the pyroelectric radi- ometer.

Hz for the 10^ V/A gain and 570 Hz for the 10^ V/A

gain. Figure 8 also shows that the signal-ampHtude

attenuation will be negligible even at the highest

signal gain (10^ V/A) if a sufficiently low chopping

frequency is selected, in this case, 8-10 Hz.

The spatial-response uniformity of the pyroelectric

detector was measured along two perpendicular axes

across the center of the detector. The spot diameter

of the probe beam on the detector was less than 0.5

mm. The horizontal- and the vertical-response scans are shown in Figs. 9 and 10. The graphs show

that the spatial-response changes are 0.3% (maximum to minimum) across a properly positioned 7.5- mm-diameter aperture. With this aperture the

standard deviation, calculated from the scanned

points, was 0.03% for the horizontal and 0.09% for the

vertical diameters. These uncertainties will be decreased if larger beam spots are used and positioned

systematically at the center of the aperture. The

response increase at the edges was caused by the

reflected (converging) beam from the shiny housing

around the detector.

The radiant-power response and the noise floor were measured with a mechanically chopped, 633-

nm-wavelength laser beam for optical input.

Neutral-density filters were used to attenuate the

laser power at seven levels ranging from 624 |j,W to 1.7 nW. The chopper was positioned close to the

ET3

Controlled shutter Silicon standard detector

Y-Z translatiori stage

^-

Up- Down

Fig. 11. Arrangement of the pyroelectric radiometer response and noise measurements.

laser to minimize detection of frequency-modulated

stray radiation. Also, a baffle was located close to the detector to keep the field of view for the chopped

radiation small. The reference for the power re- sponse and the response nonlinearity of the pyroelectric detector was a silicon photodiode with an area of

1 cm^. During the test the p3T-oelectric detector position was alternated with the reference silicon photodiode position. The optical arrangement of the

measurements is shown in Fig. 11. The radiant-power response and the noise-floor

measurements were used to calculate the detector's

NEP at each radiant power. In nearly each case the

power measurement was followed by a dark measurement. The difference between the power and the

dark measurements was equal to the signal. The

photocurrent-to-voltage gain for the pyroelectric detector preamplifier was 10^ A/V, and the chopping

frequency was 10 Hz. A pyroelectric detector re- sponse of 0.1045 )jlA/W was measured at 578-|jlW

laser power.

For high signal-to-noise ratios the signal was cal- culated and averaged from approximately twenty

samples. When the signal-to-noise ratio was low,

the noise in the X and the Y channels was rectified,

resulting in residual output offset. To avoid the out- put offset, the signal was calculated differently. In- stead of subtracting a dark measurement result from

the corresponding power measurement result, we

made the averages separately for both the power and

the dark values of the X and the Y channels . Thereafter, the difference of the average-dark measure- ment and the average-power measurement was

calculated with the vectorial sum process. We calculated the NEP values shown in Fig. 12

-4-2024

Vertical position [mm]

Fig. 10. Vertical spatial-response scan of the pyroelectric radiometer.

10"^ 10"^ 10'^ IQ-^ 10 Power [W]

10"" 10-

Fig. 12. Response linearity and NEP of the domain-engineered

pyroelectric radiometer versus radiant power.

1 December 1999 / Vol. 38, No. 34 / APPLIED OPTICS

79
from the standard deviations of the power readings

by evaluating the quadrature sum of the X and the Y

output readings. The dark measurements were not

used, to avoid the quadrature sum of the two noise

readings.

Figure 12 shows that the NEP was flat from 1.7 nW

to —0.1 mW (soHd curve) and is equal to —38 nW/

Hz^^^. At high radiant power the measured NEP

was twice the low-level NEP, probably because of

additional noise sources, such as laser noise, in the

measurement system. The relative uncertainty

{k = 1) of the NEP determinations (calculated from 20

measurements) was 16%.® The results suggest that

it is enough to measure NEP at one signal level,

which can be in the dark. The typical dark NEP,

measured separately (not shown in the figure), was

32 nW/Hz^/2.

Figure 12 also shows the pjrroelectric detector re- sponse linearity compared with a previously characterized silicon photodiode.^ The ratio of the

pyroelectric detector signal to the silicon detector signal (left-hand axis in Fig. 12) shows linear detector

responsivity over 6 decades. The outlying point is caused by the poor signal-to-noise ratio of the pyroelectric detector at the low-power end. Here the uncertainty is 2.6 times larger than the measured ratio. This large error bar is not shown in the graph. The

error bars (the uncertainties calculated from the rel- ative standard uncertainties of the measured ratios) are shown for all the other ratios. At 29 nW the

error bar can be seen well. At higher power the

error bars are too small to be seen on the graph.

The ultimate check of our NEP measurements is practical and somewhat qualitative. Pyroelectric

detectors are notoriously sensitive to ambient noise

ranging from fan motors to slamming doors and other

laboratory equipment. We measured the noise levels under various conditions. The radiometer was

wrapped with insulation foam and situated in differ- ent locations on the detector stage when the servo- motor (which moves the stage) was on and off. Identical tests were also performed without the insulation foam and in other locations in the lab. The

NEP did not show any significant change during the

tests. The NEP for other types of pyroelectric detectors varied by a factor of nearly 10, during similar

tests. In 1975 Byer described a complementary domainengineered pyroelectric detector with reduced sensitivity to temperature changes. He also suggested

that a domain-engineered detector with equally and

oppositely poled areas within a single crystal should

have a response completely independent of ambient

temperature fluctuations. However, his results do

not indicate that complete independence is achievable, nor do ours.i° This is perhaps an area for fu- ture study, because LiNbOg (and LiTaOg)

pyroelectric detectors have a strong ambient temperature dependence, which is undesirable for highly

accurate radiometers. For now, we are satisfied

with slightly reduced temperature dependence in the

domain-engineered pyroelectric detector and rely on

o

(0c

o

Q.

tn2

a>n

1.06

1.05

1.04

28 32 36

Temperature [°C]

Fig. 13. Domain-engineered pyroelectric radiometer, relative re- sponse versus temperature.

correction factors, or active thermal stabilization, to ensure that the radiometer response is independent

of ambient temperature fluctuations.

The temperature-dependent response of the pyroelectric detector was tested to determine the response

correction factors for a range of ambient temperatures. During the test the 633-nm laser beam, incident on the detector, was stabilized. An insulatedelectric heater was attached to the outside surface of

the detector package. The temperature was increased slowly from 23.5 to 40 °C. The signal and

the temperature outputs were simultaneously re- corded during both the heating and the cooling cycles

at several different temperatures. The relative

response-versus-temperature curve is shown in Fig.

13. A response temperature coefficient of 0.15%/°C was obtained from a linear fit to the measured data

points. The error bars represent a 0.25% uncertainty (coverage factor, ^ = 1) for the measured values. From the data shown in Fig. 13, the

relationship for the response of the pyroelectric detector at a calibration temperature T^ is R^. The

response at a different measurement temperature T^

will be

J^m - Rcf- (3)

The response correction factor may be used where f ~

1 + {^T X Ct), ^T ^ T, - tJ^, and the response

temperature coefficient is Cj- = 0.0015.

Pyroelectric materials are inherently spectrally

flat over a broad wavelength range. ^^ Therefore the

spectral responsivity of a pyroelectric detector is dependent on the reflectance of the face electrodes and

other materials placed on the detector surface to ef- ficiently convert optical energy into thermal energy.

The advantages and disadvantages of commercially

available optical coatings have been well documented. ^^ Though easily damaged by the slightest touch,

or excessive heat (greater than 200 mW/cm^), gold

black is our absorber of choice.

Published data show that gold-black coatings dif- fusely reflect less than 1% of incident radiation, over

a spectral range from the ultraviolet to 15 jxm.^^ \Ye

APPLIED OPTICS / Vol. 38, No. 34 / 1 December 1999

80
have been unable reproduce these results on a material that has a small thermal mass and that is a poor

heat conductor (such as a small LiNbOs plate). At

shorter wavelen^hs, such as 633 nm, reflectance

from the gold-black coating is diffuse and small. i'* From 2.5 to 10 iJim, the reflectance gradually becomes more nearly specular and gradually increases to as much as 15%.

The absorptance of the gold-black coating determines the relative spectral responsivity, provided

that the transmission through the detector is negligible and the reflectance is low. Then the relative

spectral response of the detector can be determined

from a spectral-reflectance measurement, if we as- sume that the gold-black transmittance is negligible

and the relative detector response is proportional to 1 minus the measured reflectance.

The spectral reflectance was compared with a white polytetraflouroethylene (PTFE) reflectance

standard. An oval beam, oriented at a 6° angle of

incidence over the wavelength range 0.8 and 1.8 |xm,

made an 8 mm X 6 mm image at the detector. The

10-mm-diameter aperture of the detector was re- moved to avoid baffling. A 20-cm-diameter integrating sphere collected the diffuse radiation reflected

back from the detector surface.

The measured signal from radiation reflected from

the white-PTFE standard was used as the value for the 100% reflectance. Zero reflectance was recorded

with a light trap, which replaced the detector at the

sample port of the sphere. Ten wavelength scans were made in each measurement mode to improve

the poor signal-to-noise ratio. The diffuse spectral

reflectance of the detector was calculated from the

averages of the ten measured reflectance values.

The reflectance p at wavelength \ was calculated with

P(X) =

A,{k)-A{k)

(4)

In this expression, A^{X) is the average signal of the

white standard spectral-reflectance measurements,

A^{X) is the average signal of the detector spectralreflectance measurements, and A^(X) is the average

signal of the light trap spectral-reflectance measurements.

Figure 14 shows the average reflectance, and stan- dard uncertainty versus wavelength. We improved

the signal-to-noise ratio of approximately 5:1 of the

reflectance measurements by a factor of nearly 2 by

averaging the measurement results of five neighboring wavelengths. A second-order polynomial fit to the calculated reflectance. The figure shows a spectral reflectance of 0.5-0.7% between 0.8 and 1.8 |xm.

This corresponds to a detector response change of

0.2% in this spectral range. Overall, the absolute

reflectance from the gold black was low (less than

1%).

The angular response change of the detector was

first measured in power measurement mode in which

the detector aperture was underfilled by a 3-mmdiameter, He-Ne (633-nm) laser beam. Thereafter,

1

0.8

I—

?;ii

a> n.R

(Jc

ni

•!- u

0> 0.4

M=

<u

qe: 0.2 Standard uncertainty

o-o-o-(?Yo.o.o-c>-^-o-P-o-ao•O

800 1000 1200 1400 1600 1800

Wavelength [nm]

Fig. 14. Domain-engineered pyroelectric detector total reflec- tance and measurement standard uncertainty versus wavelength.

Solid curve, polynomial fit to the averaged reflectance data.

the angular response was measured in irradiance

mode in which the detector aperture was overfilled

with a halogen lamp beam. For both measurement

modes the aperture was circular and 8 mm in diameter. Figure 15 shows the optical arrangement for

these tests. The detector was positioned a distance,

D, 0.9 m from the laser and 0.55 m from the halogen

lamp. The detector reflectance was then evaluated

by rotation of the detector, incremental values of angle e, relative to the optical axis, up and down (cf) =

90°, e = ±40°), and side to side (cf) = 0°, e = ±40°).

The directional error in underfilled mode was cal- culated as

Erie, 4)) (5)

where E^ie, ^) and S^(e = 0°) were the detector readings for the incident radiation, E, arriving at incidence angles of e and 0°. This definition is similar to the Commission Internationale de I'Eclairage (CIE)

recommended directional error /"a (e, ^)M

Figure 16 shows the directional error, /'2(e), at a

detector orientation of cj) = 90°. The results of the

horizontal (cb — 90°) and the vertical (cb = 0°) scans were very similar to each other. The response

change was less than the measurement uncertainty

in the range e = ±11° and increased to —0.1% at e =

Halogen lamp Choppei Rotation stage; Test detector

with scale

Fig. 15. Arrangement of the angular response measurements. The laser is used in underfilled mode, and the lamp is used in

overfilled mode.

1 December 1999 / Vol. 38, No. 34 / APPLIED OPTICS

81
0.1

-0.1

-0.2

-0.3

-0.4

-0.5

. 1 1 1

1

. I'M'''' !--• ^ ' 1 ' ' ' ' 1 i

: • •

• ;

: • :

'

1 . 1 1 1 1

1 . . . , ... 1 ... •

Table 1. Summary of Radiometer Properties

-40 -30 -20-10 10 20 Angle of incidence [°]

30 40

Fig. 16. Directional (relative angular) error of the pyroelectric detector in the vertical plane versus incidence angle.. The inci- dent laser radiation underfilled the detector aperture.

±30°. The relative uncertainty (k = 1) of the directional error determinations was 0.04%.

The directional error in the overfilledmeasurement mode was calculated according to the

CIE recommendation, with the expression

/2(e, <\>) =

Erie, c|>)

£",(6 = 0°)COS 6 -1, (6)

where the denominator is the cosine response of an

ideal detector-irradiance measurement. ^^ The measurement results of the horizontaldetector scan are shown in Fig. 17. According to the

graph the angular response of the pyroelectric irradiance meter follows the cosine function, with a di- rectional error of less than 0.1% within a f/2 field of

view (31° full angle). The e = 2° angular offset was

caused by the asymmetric detector alignment on the

rotation stage. The relative uncertainty of the di- rectional error determinations in the irradiance mea- surement mode was 0.06% (coverage factor k = 1). Comparison of the available detector candidates for infrared radiometric applications would constitute a paper in itself, but there are several key performance

issues on which we can focus to abbreviate our dis-

'

• . -1

: •

-2

; •

-3 •

-20 -10 10 Angle of incidence [°]

20

Fig. 17. Directional (relative angular) error of the pyroelectric detector in the horizontal plane versus incidence angle. The in- cident lamp radiation overfilled the detector aperture.

Property Value

1.05 X 10-^ A/W

0.15%/°C

32 nW/Hz^/^

38 nW/Hzi/2

Power response at 633 nm

Temperature coefficient between 24 and

40 °C Dark NEP

NEP in the 1-nW-lOO-p.W input radiant power range 3-dB point with the OPAlll I-V converter 570 Hz

in the lO^-V/A range 3-dB point with the OPAlll I-V converter 60.5 Hz

in the 10^-V/A range

Spatial response nonuniformity within a ±0.1%

7.5-mm-diameter (633-nm, 0.5 mmdiameter) probe beam

Angular error in underfilled mode for /^(e) <0.1%

e < 30° incident angles

Angular error with 8-mm overfilled aperture CIE /"2(e) < 0.1%

for 6 s 15° Spectral reflectance variation (800-1800 nm) <0.2%

Cussion. In general, the uncertainty in radiometric

measurements is reduced when detector variables

such as response linearity, spatial and spectral uniformity, and temperature dependence are well characterized or known to be invariable.

The biggest drawbacks to using a pyroelectric detector are low optical sensitivity, high acoustic sensitivity, and the need to use an optical chopper.

However, pyroelectric detectors can be operated at room temperature, and the chopper and the necessary electronics are not much more cumbersome than

what is necessary for the competing alternatives.

Photoconductors, such as mercury cadmium telluride

(HgCdTe) and indium antimonide (InSb), have high

sensitivity and are commonly used for transfer standards, but large-area (3-5-mm-diameter) devices are

not highly uniform spatially and spectrally. The

best photoconductors of this type have spatial nonuniformity variations as great as 3% and coramonly

to as great as 20% or more.^^ On this basis alone a

pyroelectric detector with nearly four times the area (compared with the competing alternatives) and with

0.1% spatial-response variation is an excellent choice. In addition, we have demonstrated that domainengineering techniques can reduce the acoustic sensitivity and give us confidence that the NEP is constant and linear at low power.

A summary of the properties of the domainengineered pyroelectric radiometer is given in Table

1. Future improvements will be directed at reducing the temperature dependence and optimizing the

domain-engineered areas and pattern, to further re- duce the acoustic sensitivity. Further evaluation

will include spectral responsivity and reflectance

measurements at longer infrared wavelengths between 2 and 20 \xm..

5. Conclusions

We have successfully used domain engineering to build a practical and convenient pyroelectric radiAPPLIED OPTICS / Vol. 38, No. 34 / 1 December 1999

82
ometer with low acoustic sensitivity and high spatial and spectral response uniformity. We have

demonstrated that a properly designed, applied,

and characterized pyroelectric radiometer is well

suited as a high-accuracy transfer standard for optical power and irradiance measurements. The

domain-engineered pyroelectric radiometer is the

only alternative compared with HgCdTe, InSb photoconductors, or commercially available pyroelectric detectors, capable of measurement uncertainty

of the order of 0.1%. The primary role of the radiometer will be to extend and improve the National

Institute of Standards and Technology spectralresponsivity scale from the visible to the nearinfrared wavelength range.

References

1. J. H. Lehman and J. A. Aust, "Bicell pyroelectric optical detector made from a single LiNbOs domain-reversed electret," Appl. Opt. 37, 4210-4212 (1998).

2. W. R. Blevin and W. J. Brown, "Black coatings for absolute radiometers," Metrologia 2, 139-143 (1996).

3. L. Harris, R. McGinnies, and B. M. Siegel, "The preparation

and optical properties of gold blacks, "J. Opt. Soc. Am. 38, 582-589 (1948).

4. E. L. Dereniak and D. G. Crowe, Optical Radiation Detectors

(Wiley, New York, 1984), p. 177.

5. G. Eppeldauer, "Temperature monitored/controlled silicon photodiodes for standardization," in Advanced Fiber Communications Technologies, L. G. Kazovsky, ed.. Commission In- ternationale de I'ficlairage, Proc. SPIE 1479, 71-77 (1991).

6. G. Eppeldauer, "Chopped radiation measurements with large area Si photodiodes," J. Res. Natl. Inst. Stand. Technol. 103,

153-162 (1998).

7. A. L. Migdall and G. P. Eppeldauer, Spectroradiometric Detec8.

9.

tor Measurements: III. Infrared Detectors,Nat\. Inst. Stand.

Technol. Spec. Publ. 250-42 (National Institute of Standards

and Technology Measurement Services, Gaithersburg, Md.,

1998).

L. Lyons, A Practical Guide to Data Analysis for Physical

Science Students (Cambridge U. Press, Cambridge, UK, 1991),

p. 15. T. C. Larason, S. S. Bruce, and A. C. Parr, Spectroradiometric

Detector Measurements: I. Ultraviolet Detectors and II. Visible to Near-Infrared Detectors, Natl. Inst. Stand. Technol.

Spec. Publ. 250-41 (National Institute of Standards and Technology Measurement Services, Gaithersburg, Md., 1998).

10. N. E. Byer, S. E. Stokowski, and J. D. Venables, "Complementary domain pyroelectric detectors with reduced sensitivity to mechanical vibrations and temperature changes," Appl. Phys.

Lett. 27, 639-641 (1975).

11. S. B. Lang, Sourcebook of Pyroelectricity (Gordon & Breach,

New York, 1974), 40-48. W. L. Wolfe and G. J. Zissis, The Infrared Handbook (Envi- ronmental Research Institute of Michigan, Ann Arbor, Mich.,

1989), p. 7-79.

D. J. Advena, V. T. Bly, and J. T. Cox, "Deposition and characterization of far-infrared absorbing gold black films," Appl.

Opt. 32, 1136-1144 (1993). G. W. Day, C. A. Hamilton, and K. W. Pyatt, "Spectral refer- ence detector for the visible to 12-^.m region; convenient, spectrally flat," Appl. Opt. 15, 1865-1868 (1976). Central Bureau of the Commission Internationale de

L'ficlairage, Methods of Characterizing the Performance ofRadiometers and Photometers, CIE Publications, 53 (TC-2.2)

(Central Bureau of the Commission Internationale de

L'ficlairage, Vienna, Austria, 1982). E. Theocharous, N. P. Fox, and T. R. Prior, "A comparison of

the performance of infrared detectors for radiometric applications, in Optical Radiation Measurements III, J. M. Palmer,

ed., Proc. SPIE 2815, 56-68 (1996).

12

13

14.

15

16

1 December 1999 / Vol. 38, No. 34 / APPLIED OPTICS

83

Wp "^^^ American Society of

Mechanical Engineers

Reprinted From

HTD-Vol. 277, Thermal Phenomena at Molecular

and in Cryogenic Infrared Detectors

Editors: M. Kaviany, D. A. Kaminski, A. Majumdar,

P. E. Phelan, M. M. Yovanovich, and Z. M. Zhang

Book No. H00908 - 1994

A CRYOGENIC SILICON RESISTANCE BOLOMETER FOR USE

AS AN INFRARED TRANSFER STANDARD DETECTOR

G. Eppeidauer, A. L. Migdall, and 0. L. Cromer

Radiometric Physics Division

National Institute of Standards and Technology

Gaithersburg, Maryland

ABSTRACT

We are developing an infrared bolometer to meet the needs of two detector calibration facilities at the National Institute of

Standards and Technology (MIST). These facilities require

transfer standard detectors with high sensitivity, accuracy,

stability and dynamic range as well as a large detector area, fast time response and flat spectral response. We describe the design and testing of a bolometer to meet these requirements.

This device has a dynamic range of 5 decades, a noise floor of 36 pW/VHz, a nonlinearity of less than 1%, a spatial response nonuniformity of about 0.3% and a flat frequency response out

to about 100 Hz.

1 INTRODUCTION

Absolute calibrations of infrared (IR) detectors are of

increasing importance. In general, detector calibrations are made absolute by comparison to a primary standard detector, which is internally calibrated, or to a transfer standard detector

that has itself been tied to some primary standard. Two

specific needs currently exist at the National Institute of

Standards and Technology (NIST) for absolute calibrations that require the use of transfer standard detectors. An ambient

temperature facility for the calibration of IR detectors is under

development. Additionally, new spectral capability is being

added to the Low Background Lifrared Facility (LBIR) at NIST

which is used for the calibration of cryogenic detectors and

sources. Both of these facilities require transfer detectors with high sensitivity, accuracy, and dynamic range as well as a

large detector area, fast time response and flat spectral response. The goal of this work is the development of a

transfer standard detector in the 2 to 20 |im spectral region for use in these two q^plications.

2 BOLOMETER DESIGN

The detector requirements of our two applications,

particularly the wide dynamic range and flat spectral response,

match best the characteristics of cryogenic bolometers. Since we also require a sensitive area of about 4 mm diameter, we

chose a bolometer of composite design. This allows for a larger

detector area while maintaining the detector speed, by using a

large, thin, low heat capacity absorber bonded to a small

thermal sensor. The dynamic range requirement of the bolometer is determined by two factors. The bolometer must be

able to accept a large enough power to allow it to be calibrated

against the NIST's fsimary standard radiometer which requires ~1 mW to achieve maximum accuracy. The low end of the dynamic range is determined by the two amplications for this device, both of which require measurements in the nW to p.W

range. Since stabili^ is important for standards work and since the response stability of bolometers can be problematic, we

have made efforts, which are discussed later, to measure and

reduce response variations.

Our transfer standard detector development started with a commercial bolometer [1,2] which we characterized and

modified to better meet our requirements. The composite

bolometer consists of a sapphire disk (O.OS mm thick by 5 mm

diameter) coated with gold black to absorb incident radiation. Gold black was chosen because it has a high absoiptance, while

its thermal mass is extremely low. The density of gold black

has been reported as low as 1/SOO that of solid bulk gold (Harris

and Beasley, 1992). This allows a much faster detector response than is possible with more common absorbers such as black paint or solid resistive metal films. Also, the absorptance of gold black can be greater than 90%. as opposed

to the resistive metal films which may absorb up to only 50%

of the incident radiation.

The temperature rise due to absorbed radiation is sensed by a

silicon resistance thermometer (SRT) bonded to the back of the sapi^ire disk. The SRT is a doped Si chip that is commonly

used in both regular (Downey et al., 1984) and composite

bolometers (Dereniak and Crowe, 1984). The resistance of the

85
SRT dq>ends on both the temperature and the bias currenL At

4.2 K the resistance of our SRT changed firom 3.6 to 1 MQ as the DC bias current was changed from to 3.5 ^A (Eppeldauer

et al.. 1993).

4.2K

iv

J-FET

64K

/\AA

300K

Heater

11

Fig. 1 SRT biasing circuit and ampUner. Rd is the SRT

resistance, Rj^ is the current limiting resistor and Rj is the JFET source resistor. The temperatures of each section is indicated.

^ 2M >

s

z

oa

(A

Ui

PE

UJ

O

C0a

2j07

IM

246

IM

Bias currant = 1.3 ^

AC amp. gain = 200i

400 SM we 700 too too WAVELENGTH (nm)

Fig. 2 Visible spectral response of the first bolometer as determined by comparison to the NIST absolute spectral response scale. The estimated 1 a uncertainty of the spectral response measurement is 0.2 %.

The SRT resistance change is measured using a \mity gain

Junction Field Effect Transistor (JFET) [3] followed by a

selectable gain AC amplifier. The DC bias circuit of the SRT

conqx>site bolometer is shown on Fig. 1. The JFET stage is a

unity gain impedance transformer between the high resistance (Rd=23 Mil, Rl=10 Mfl) SRT circuit and the AC amplifier.

The JFET is located in the cryogenic space near the bolometer

and operates at about 64 K. The JFET's dominant noise comes

from its inverse transconductance (resistor noise). Since the transconductance rises with increasing drain current, Rj should

be small, but because at large drain currents the offset voltage

drift, the common mode rejection, and the voltage gain

stability are worse, a compromise was necessary, so Rs=10 kil was chosen.

3 BOLOMETER CHARACTERIZATION

The first version of our SRT composite bolometer had a flat frequency re^xmse (for chopped radiation) up to 1 1 1 Hz and a 3

dB rolloff point of 250 Hz. The responsivity was 10^ V/W at a SRT bias current of 1.3 ^.A. At the nominal operating point the SRT resistance is about 2 MQ and the electrical power

dissipated in the bolometer is ~2 |iW. The spectral response of

the bolometer presented a problem. The spectral absorptancc of

the original gold black coating was found to vary a few percent

in the visible and to fall to as low as 30% in the JR. Figure 2

shows the absolute peak-to-peak spectral response of the bolometer at an AC amplifier gain of 200. as calibrated against

the NIST absolute spectral response scale between 400 and 900

imi (Cromer, 1991). The response variation across this range is 2%, which is significantly larger than the lo uncertainty of the

scale realization which is 0.3% between 400 nm and 440 nm

and 0.1% between 440 ran and 900 nm. Figure 3 shows Fourier

Transform Infrared Spectrometer (FTIR) measurements of the

total reflectance of two different gold black coatings. The

reflectance of the first bolometer coating rises &om less than

10% at 2 \im. to greater than 70% at 14 fim. Since we intend to use this bolometer out to 20 ^m we made additional specular

reflectance measurements on another FTIR instrument capable

of measuring up to 25 ^m. Those results show that the

reflectance peaks at 16J \un and falls toward a local minimum

at 20 \im. These wide variations required us to work toward

improved coatings.

The variation of response across the surface of the bolometer was checked at 900, 1200, and 1550 run with a scan resolution of 1.1 mm. The measured variations were smaller than 0.3%

over the entire 10 mm^ aperture area. We measured the signal and noise levels of the first bolometer with a KRS-5 window at a chop frequency of 57 Hz. The signal to noise ratio was 2x10^ at an incident radiant power

of 7 \iW. The incident power was equal to the noise floor at 20

pW with an electrical measxirement bandwidth of 0.3 Hz

(Eppeldauer and Hardis. 1991). We estimate the bolometer's
OJ

Ot7

III uz 06 <

K

u OlS u

-1

II. u 04 c

^ 03 <

e 02

01

—FIRST GOLD BLACK SECOND QOLO BLACK

• » 10 WAVELENGTH( (Un)

12 14

Fig. 3 Total (specular + diffuse) spectral reflectance of the first and second bolometers in the 2 to 14 |im spectral range.

minimum detectable temperature difference to be about 1 jiK/VHz from the 36 pW/VHz noise density and the -50 jiW/K

thermal conductance of the SRT leads. The bolometer dynamic

range at the low power end was limited by fluctuations in the thermal background. This noise was reduced to 4 pW/VHz

when a large sj^rical gold mirror was placed in front of the bolometer wiiulow to image the cold bolometer absorber back on to itself (Makai and Andor. 1993). This noise is close to, but greater than, the calculated rms resistance noise of 2.2 pW/VHz, due to the Johnson noise of Rd and Rl, scaled by the bolometer responsivity. The effective rms input noise of the AC amplifier was determined to be 1.4 pW/VHz (using a

responsivity of 10* V/W) which is also less than the calculated bolometer noise.

decrease in the bolometer responsivity after 1 1 hows, probably

due to degradation of the dewar vacuum. Above 1.33x10*2 Pa

(1(H Torr), the poor vacuum affects the temperature of the cold

plate on which the detector is mounted (Lange et al, 1983). To

maintain good stability, the dewar had to be repumped every

third day. Ehiring a 24 hour run, we found a period of 1 1 hours

where the bolometer responsivity was constant to about

±0.25% (Eppeldauer et al., 1993). We suspect that the

variations before and after this stable period is due to temperature variations of the cold plate and bolometer mount

The design of a new dewar with improved vacuum

characteristics, temperature sensing and temperature

stalnlization has also been started. A carbon resistor has been

added to the detector mount of the current bolometer to monitor

its temperature variation.

1.1

04

—mo oo«TMa O OOLO KACK CM'tlfct|

200 300 400 SOO FREQUENCY (Hz)aoo TOO

Fig. 4 Frequency response of bolometer before aiid after coating with gold black.

If we assume that the window passes all ambient

background radiation below 100 ^m, the calculated total radiant power within the f/4 field of view and incident on the bolometer is -260 uW with fluctuations of 1.7 pW/VHz due to shot noise (Boyd, 1983). It is not too surprising that the observed background effect is larger, as there was no attempt

to control variations of the room temperature or atmospheric

humidity. Note that noise observed with the bolometer

looking into the room was measured only at 57 Hz with a 0.3 Hz bandwidth, so no information on the spectral variation of

this noise was taken.

4 IMPROVEMENTS TO THE SILICON

COMPOSITE BOLOMETER

Changes were made to improve the overall convenience of

the bolometer, as well as its accuracy. There was a monotonic

Because the first gold black coating showed high reflectivity

in the IR, an imfnoved second gold black coating was produced on a new sapphire absorber. A literature search indicated that a

very low density gold black with a thickness of about 20 |Jjn is required to achieve -90% absorption in the 2 to 14 jim spectral

region (Harris and Beasley, 1952; Harris et al., 1948). This was

the goal of the second coating, although our expertise did not

allow gold black coatings to be so precisely tailored. The

difficulties in reproducing gold black are well noted in the

literature (Advena et al., 1993; Harris, 1967). The AC frequency

response of this second bolometer was measured before and after coating (see Fig. 4). The additional thermal mass of the coating

shifted the 3 dB roll off point of this bolometer from 400 Hz

(before coating) to 300 Hz (after coating). This is somewhat

faster than the 250 Hz 3 dB point of the original bolometer. The spectral reflectivity of the second bolometer is compared to

87
the original in Fig. 3. This coating shows significantly lower

reflectivity beyond ~6 \im, although it still does not spptoach

the design goal of 90% absorption. More coating

development is needed to improve this.

The responsivity of the modified bolometer was calibrated against the MIST absolute spectral response scale. The low

frequency responsivi^r of the bolometer in the visible was 10'^ V/W at a bias current of 1.3 \iA (and before the AC amplifer), similar to the responsivity of the first bolometer.

The AC amplifier of the bolometer was also modified to allow for one decade lower gain. This allowed us to extend die point at which high power nonlinearity occurred and to determine whether the nonlinearity is due to the electronics or

the sensor itself. We measured the non-linearity by measuring

the transmittance of a neutral density filter at different levels of incident laser power (Eppeldauer et al., 1993). We found

that the level of incident power where the non-linearity

reached -1% was the same for both the original and the modified amplifiers, although the 4% nonlinearity point in the modified unit occurs at "3 times higher power (20 \iW) (Fig.

5). The nonlinearity rises steeply beyond 1% and 4%

nonlinearity points of the original and modified bolometers

respectively, indicating amplifer saturation at these points.

This test indicates that for incident powers below 20 ^W the modified bolometer linearity is limited not by the amplifier, but by the sensor.

Nonlinearity of the bolometer can result from three effects. We assume that any variation of the signal, (AVd = ^(R^^Ib)

where Ig is the bias current and Rd is the bolometer resistance)

is due solely to a linear dependence of Rq on temperature. So

any variation of I3 or any nonlinear dependence of Rq with

temperature will result in a nonlinear response. The measured

nonlinearity due to the variation of Ig as a function of incident radiation accounts for only one tenth of the observed 4%

nonlinearity. This was determined by measuring the SRT

resistance change of 5.4% as the incident laser powo- varied from 22 ^W to zero. The bulk of the nonlinearity was due to the variation of the SRT resistance with bias current and

nonlinear teii^)erature dq)endence of the SRT.

Background radiation variations can also affect the

resistance of the SRT. When the background radiation for the bolometer was blocked by a reflective aluminum plate,

positioned cm its window, a 1 V increase was measured across the SRT. The voluge increase was only 66 mV when the choiq>ed 22 ^.W laser beam was blocked by a shutter far from

the bolometer. This means a 15 times larger Rq change for the aluminum plate caused background change. To keep the bias current constant at large background changes like this, Rj^ should be increased. Even if the bias current is constant, the

0.100

U 0.096 z

<

1-S 0.092

(AZ

<X

H 0.088

DCUJ

I-^ 0.084

0.080

. INDIVIOUAL ryiEASUREMENTS

o AVERAGE

a m B

10- » 10' LASER POWER (mW)

10- =

Fig. 5 Measured filter transmittance vs incident laser power

with the filter removed using the second version of the bolometer. Deviation of the data from a constant value

indicates nonlinearity of the bolometer. Individual measurements and the average of measurements are shown. The

error bars are the standard deviations of each group of individual measurements. The apparent shift in transmittance between the two sets of points is due to repositioning the filter rather than measurement nonlinearity.

SRT resistance (and responsivity) still signiHcantly changes

for different background levels. Thus, it is important to measure the bolometer responsivity at a range of background

levels. Smaller linearity and responsivity errors can be

achieved if care is taken to minimize changes in the background

radiation and to make Rj^ as large as necessary.

The dynamic range from the noise floor (with a 1 Hz

bandwidth) to the 4% non-linearity point at an incident power

level of 20 ^W was over 5 decades. This extended high end

measurement range is important for our applications as transfer standard detectors. Even with the nonlinearity, the extended range will help in tying the bolometer calibration to the primary standard High Accuracy Cryogenic Radiometer (HACR)

of NIST. The signal to noise ratio of a radiometer similar to the HACR was measured to be 1.7x10^ at an incident power of 200

^W, so we expect that at 20 |i.W the signal to noise ratio should be at least 1.7x103 (Martin et al.. 1985). The HACR at NIST

(Houston, 1994) has achieved similar signal to noise

performance as the radiometer described by Martin et al. (1985).

This signal to noise ratio for the HACR at this power level allows a scale transfer significantly better than measurement

uncertainties due to the bolometer itself.
In addition to tying the bolometer caliln'ation to the HACR,

we will also use the newly acquired spectral capability of the LBIR facility mentioned earlier to independently determine the bolometer spectral response over a continuous range of IR

wavelengths. The LBIR facility includes its own high

sensitivity electrically calibrated absolute radiometer which

has an overall absolute uncertainty of 0.12% (la) (Datla et al., 1992). By tying the spectral calibration of the bolometer to

this absolute radiometer we will not have to depend on the accuracy of the bolometer coating spectral absorptance measurements.

5 CONCLUSION

We are developing a (pyogenic transfer standard detector for use in dw infrared wavelength range. This device will be used

to tie IR detector calibrations to the nation's primary

radiometric detector standard. Our characterization of the bolometer indicates that with the improvements already made

and currently planned, we can expect to meet the requirements

needed for that purpose.

ACKNOWLEDGEMENTS

We thank T. C. Larason for his help in measuring the absolute response of the bolometer in the visible. We also thank L. M. Hanssen and Z. M. Zhang for their help in measuring the reflectance of the gold black coatings.

REFERENCES

[1] References made in this paper to particular brand names

or specific suppliers are for the ease of understanding by the reader and do not constitute an endorsement of products or

services by the National Institute of Standards and Technology

over other competitive suppliers of similar products or

services, which may be equally or better suited for the purpose.

[2] Bolometer Unit #1646 in Dewar HD-3, Infrared Uboratories. Inc.. 1808 E. 17th St. Tucson, AZ 85719.

[3] Siliconix family of ultra-low noise JFETs. 2N6484-

E230-J230.

Advena, D.J.. Ely, V.T.. and Cox. J.T., 1993. "Deposition

and Characterization of Far-Infrared Absorbing Gold Black

Films." Appl. Opt., Vol. 32, pp. 1136-1144.

Boyd. R.W.. 1983. Radiometry and the Detection of

Optical Radiation, John Wiley & Sons. New York, pp. 243.

Cromer. C.L.. 1991. "A New Spectral Response Calibration Method Using a Silicon Photodiode Trap Detector," presented at the 1991 Proceedings of Measurement Science Conference,

Anaheim, CA, Jan. 31 -Feb. 1.

Datla, R.U., Stock. K.. Parr. A.C.. Hoyt, C. C. Miller, P.J., and Foukal. P.V., 1992, "Characterization of an Absolute

Cryogenic Radiometer as a Standard Detector for Radiant-Power

Measurements," Appl. Opt., Vol. 31. pp. 7219-7225.

Dereniak, E.L.. and Crowe. D.G.. 1984. Optical Radiation

Detectors, John Wiley & Sons. New York, pp. 156-166.

Downey, P.M., Jeffries. A.D.. Meyer. S.S., Weiss, R., Bachner. F.J,. Donnelly, J.P.. Lindley. W.T., Mountain, R.W,

and Silversmith, D.J., 1984, "Monolithic Silicon Bolometers,"

Appl. Opt., Vol. 23, pp. 910-914.

Eppeldauer, G., and Hardis, J.E., 1991. "Fourteen-Decade

Photocurrent Measurements with Large-Area Silicon

Photodiodes at Room Temperature," Appl. Opt., Vol. 30, pp. 3091-3099.

Eppeldauer. G., Migdall. A.L., and Cromer, C.L., 1993.

"Characterization of a High Sensitivity Composite Silicon

Bolometer", Metrologia, Vol. 30. pp. 317-320.

Harris. L.. 1967. "The Optical Properties of Metal Blacks

and Carbon Blacks." The Eppley Foundation for Research,

NewpOTt. RI. Monograph Series No. 1. Dec. 1967.

Harris. L.. and Beasley. J.K.. 1952. "The Infrared Properties

of Gold Smoke Deposits." J. Opt. Soc. Am., Vol. 42. pp. 134- 140.

Harris. L., McGinnies, R.T.. and Siegel. B.M.. 1948, "The

Preparation and Optical Properties of Gold Blacks," J. Opt. Soc. Am., Vol. 38. H>. 582-589.

Houston, J.. 1994. private communication.

Lange. A.E.. Kreysa, E., McBride, S.E.. Richards, P.L., aiKi Haller, E.E., 1983. "Improved Fabrication Techniques For

Infrared Bolometers." Int. J. IR and Mm Waves, Vol. 4, pp. 689-706.

Makai. J.P., and Andor, G., 1993, private communication.

Martin, J.E.. Fox. N.P., and Key. P.J.. 1985. "A Cryogenic

Radiometer for Absolute Radiometric Measurements,"

Metrologia, Vol. 21, pp. 147-155.

89

Linear HgCdTe radiometer

G. Eppeldauer and L. Novak

Radiometric Physics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899

ABSTRACT

The tjasic modes of electrical operation of photoconductive optical radiation detectors are analyzed. The

nonlinearity inherent in "voltage mode" measurements can be eliminated by using "current mode"

measurements. A HgCdTe photoconductive radiometer has been designed, based on this analysis, which

measures the current through a biased detector. A built-in calibrating capability in the circuits of the

radiometer makes it possible to eliminate the effects of a long-term drift in the bias voltage, thereby achieving

a higher precision.

1. INTRODUCTION

Photoconductors exhibit a change in conductance (the inverse of resistance) when radiant power is applied to them.

In order to sense the photogenerated conductance change, the photoconductor is operated with a bias current. A tradi- tional biasing circuit^ consists of a DC source and a load resistor, as shown later in Fig. 1. Manufacturers often

recommend measurement of the voltage change across the detector while passing a constant current through it^"*.

These practices give an output voltage that is a nonlinear function of the conductance change. The conductance

change, to a good approximation, is proportional to the incident flux on the detector^. In multidecade radiant power

measurements, the nonlinear response of the detector circuit introduces unwanted errors. In order to eliminate them,

either the nonlinearity has to be electrically compensated using additional circuits^ or an inherently linear circuit has to be used. The latter solution promises higher accuracy and simpler implementation. Therefore, we proceed to analyze

the different ways a photoconductor can be used in a circuit, with a goal of designing a photoconductive radiometer

which has an output signal proportional to the conductance change of the detector. This kind of design can be used more accurately for radiometric measurements over a wide dynamic range.

2. MODES OF ELECTRICAL OPERATION

2.1. Voltage mode measurements

A basic photoconductive detector biasing and measuring circuit is shown in Fig. 1. A steady voltage source Vq

produces a biasing current /g through the serially connected detector resistance Rq and load resistance f?^

Vb = Ib{FIl + ^d) (1)

The voltage across the load resistance is formed by the bias current,

Vi_ =I8Rl (2)

From Eqs. 1 and 2, Vi_ depends on the detector resistance Rq as:

As the detector resistance Rq is the reciprocal of its conductance, Gq,

cro (4)

Vi^ depends upon the conductivity Cq as: Ri<5D

V^iao) = Vb

(1 + Rl^d] (5)

^ Present Address: Czechoslovak Academy of Sciences, Prague, Czechoslovakia

SPIE Vol. 7 7 W Imaging Infrared: Scene Simulation. Modeling, and Real Image Tracking (7983) /

91
I/, ^4^ V D ^^

B Ve

FIGURE 1: Voltage Mode

Eq. 5 shows that the output voltage on the load resistance is a nonlinear function of the detector conductance.

Further, the relative magnitudes of R!_ and Rq affect the measurement.

When Ri » Rq, V^-^. Vq

When Ri_ « Rq , Vi_= Vq R^ cq

(6)

(7)

In the first case, the output signal is insensitive to changes in Gq. In the second, there is a linear approximation at the expense of signal strength (/?^ Gq « 1). All told, measuring Vi_ to determine changes in Gq (as when optical

radiation is measured) leads to inaccuracies.

Alternatively, one can derive an output signal by measuring the voltage across the detector.

From Eqs. 1 and 8, we can express the detector voltage as a function of the detector resistance,

Ffn

VoiFio) = ^B

and as function of detector conductance:

Voi^D) = Vb

{Rl + Rd]

(1 + RlOd]

(8)

(9)

(10)

Eq. 10 shows that again the voltage measurement is a nonlinear function of the detector conductance. Proceeding as

before. When Ri_ « Rq , Vq= Vq

When Ri_» Rq, Vq= ' b/

(11)

(12)

Neither of these conditions are attractive. In the first, the output voltage is again insensitive to changes in detector

conductance. In the other, where V^ and Ri_ act to form a constant current source Iq , the response is inversly

proportional to the detector conductance. Both situations may lead to measurement errors when changes in Vq are presumed to be proportional to changes in Gq .

2.2. Current'mode measurements

Another basic photoconductive detector biasing and measuring circuit is shown in Fig. 2.

/ SPIE Vol mo Imaging Infrared: Scene Simulation. Modeling, and Real Image Tracking (1989)

92
^Hr^

B Vb

FIGURE 2: Current Mode

A current meter A measures the "short circuit current" of Vq and Rq treated together as a Thevenin voltage

source, and is the limiting case of the previous circuit as f?^ (and V^ ) -^

/e(<^D) = ^e^D (13)

This current, rather than a voltage, is linearly proportional to the detector conductance. For conductance changes (as

when optical radiation is detected) it can be written

/fi = ^S (<^D + ^^d] (14)

or as: Ib = Ib+ ^B^^D (15)

We see that there is both a constant biasing current, /g°, and a "useful" current component which is proportional to the conductance change and to the biasing voltage. This part is generally the small difference of two large numbers,

/g and /g°. To achieve high accuracy, the biasing voltage has to be very stable. Its internal resistance, as well as the

internal resistance of the current meter, has to be much smaller than the detector resistance in order to satisfy the

assumptions of this derivation.

3. ELECTRONIC DESIGN

A large-area (2.54 mm x 2.54 mm) InfraRed Associates^ HgCdTe (MCT) detector was selected for radiometric

applications. The resistance range of large-area MCT detectors is roughly 15 to 30 ohm at 77 K. The selected one had

a resistance of 24.7 ohm at this temperature. If we consider that the maximum resistance change of the detector for maxim.um optical radiation of 50 mW is about 10%, it follows that a 25 Q detector will have a resistance change of

about 25 p-Q. if a radiant power level of 0.5 |iW has to be measured.

An amplifier unit was matched to the detector by the manufacturer, working on the principles analyzed in Section

2.1. This circuit operated in the voltage mode, where the voltage on the detector resistance was measured. In order to get the maximum signal to noise ratio, the detector required a bias current of 70 mA. If the detector was to be used

with a customer's bias circuitry and amplifier system, they suggested a serial load resistor ten times higher than the detector resistance. This corresponds to the nonlinear connection between the detector voltage and conductance

described in Eq. 12.

In addition to the manufacturer's amplifier unit, we developed another amplifier that made a current mode

measurement, following the analysis in Section 2.2. It was based on an operational amplifier in the standard

configuration to measure short-circuit current at the input, and it included provisions for biasing the detector.

However, the bias current would have produced an unwanted, amplified output voltage, which in most cases would

have saturated the amplifier. To avoid this, a voltage compensation method was used, as shown in Fig. 3.

SPIE Vol. 1 J 10 Imaging Infrared: Scene Simulation, Modeling, and Heal Image Tracking (19891 /

93
Bias

No Bias

t

Detector

Sensitivity

r-WV^

FIGURE 3: Current to Voltage Converter, Simplified Model

Voltage source V-\ is used to bias the detector and corresponds to Vg in the previous discussion. A compensating

voltage 1/2- of opposite polarity, couples to the summation point of the operational amplifier through a variable

resistor, Rq. When switch S1 is in the "No Bias" position, the voltage sources are removed from the circuit and the

amplifer can be zeroed. When S1 is in the "Bias" position, Rq is adjusted for a null output (Vq= 0) when the

detector is in the dark. Both of these adjustments should be performed at the highest amplifier gain (largest value of

Rp) used for subsequent measurements. Once they are made, the output of the amplifier circuit ^0 = ^1%^orD (16)

To make a useful circuit, it is necessary to do the compensation carefully. The voltage sources should be very stable and have low output impedances. The zero adjustments should be checked repeatedly to counteract changes of the

voltage sources and resistors. Because of the high amplification required to detect small changes in Gq , the circuit

should be well shielded and grounded to minimize interference at the output. Additionally, the operational amplifier

must have low noise, low drift, a large gain-bandwidth product, and a large open-loop gain. The gain of the amplifier

should be calibrated repeatedly to make sure that the optical radiation measurements stay consistent over time.

Our actual amplifer circuit had additional features to allow us to make these gain calibrations. A diagram of the

complete circuit is shown in Fig. 4. When switch S2 is in the up position, this circuit is similar to the one shown in Fig. 3. However, when switch S2 is in the down position, two changes are made. First, the negative terminal of the

bias source is connected to a real ground, rather than the virtual ground at the summation point of the operational

amplifier. This maintains the detector as a load across the bias voltage. Secondly, the operational amplifier is connected to measure the bias voltage itself, through a 1000 Q, resistor. If the bias voltage changes, so does the

proportionality factor shown in Eq. 16. To counteract this change, the effective feedback resistance Rp can be changed

with potentiometer P2 such that the transfer gain of the amplifer remains constant. Potentiometer P2 is followed by a buffer amplifier to maintain a uniform output impedance.

To summarize, the adjustment procedure is to: 1) Switch SI to "No Bias", S2 to "Measure", turn S3, the Sensitivity Range, to the highest scale (the 100 kQ

resistor), and set PI for zero output voltage.

2) Leave SI on "No Bias", switch S2 to "Calibrate", change the Sensitivity Range to the lowest scale (the 1000 D.

resistor), and adjust P2 for a -1.990±.002 V output voltage while the detector is in the dark.

3) Change SI to "Bias" and S2 to "Measure", return the Sensitivity Range to the highest scale, and adjust P3 for a null (zero) output voltage while the detector is in the dark.

/ SPIE Vol. 1 1 10 Imaging Infrared: Scene Simulation, Modeling, and Real Image Tracking (1989)

94
CD

CO DC

if) d

CD

C/D

CO

CO

CO

(O

CC DO CQ

O

4^1^

o

w

w

CD DC

o

COo

CD

a

o

O)co

a3 c

>c

o

o

<DO)

C3O>

0) o

-^LUC

LL

SP/f \/o/. / ; ; Imaging Infrared: Scene Simulation. Modeling, and Real Image Tracking (1989) /

95
For biasing and compensation, we used with equal sucess both high charge-capacity alkaline batteries and

electronically controlled, highly stable, ripple and noise free DC calibrators. If a battery is used as a biasing voltage

source (it has minimum noise and ripple), the 70 mA load current may cause a long-term decrease in its output voltage.

While the calibration of the amplifier transfer gain gives stability to the measuring circuit, it does not eliminate the

bias-current dependent change in the detector responsivity. When a battery is used for biasing, the small changes in the

bias voltage must be regarded as a potential source of error, which can be estimated using data provided by the detector

manufacturer.

There is one more electronic detail concerning the measurement of optical radiation. In practice, the signal on the

photodetector is chopped. The output of the amplifer circuit is detected by a "Lock-In Amplifier," which provides

greater noise rejection than would a DC measurement, alone. Care must be taken that the amplifer has a sufficient

bandwidth. In Fig. 5, we show a block diagram of the electronic instrumentation used for our measurements.

4. STABILITY

The use of this circuit for detector studies is beyond the scope of this paper. However, we would like to report

that the radiometer operated stably over an extended period of time.

A tungsten strip lamp, fed from a highly stable DC current source and operating at about 100 °C, was imaged onto

the MCT detector using a spherical mirror and an aperture 2 mm in diameter. The radiation was chopped at 13 Hz.

The roll-off frequency of the low pass filter on the lock-in amplifier was set two decades lower. The sensitivity of

the current to voltage converter was 10^ Volts/Amp (the 100 kQ feedback resistor).

Over the course of 122 minutes, 1269 voltage measurements were made at the output of the lock-in amplifier.

These voltages held in the range between 9.078 and 9.173, with an average of 9.132. The standard deviation was

0.017 V, which corresponds to 0.19%.

Fig. 6 shows what happened after this data was taken. As the quantity of liquid nitrogen decreased in the dewer,

the detector resistance changed, causing the compensation voltage and the bias voltage to be out of balance. However,

when the dewer was refilled and the electronic adjustment procedure followed, the output readings matched the

previous ones.

5. ACKNOWLEDGEMENTS

The authors thank Robert D. Saunders for participating in the stability measurements and Jonathan E. Hardis for help in preparing the manuscript.

6. REFERENCES

1. E. L. Dereniak and D. G. Crowe, Optical Radiation Detectors, p. 94, John Wiley & Sons (1984).

2. Commercial products - materials and instruments - are identified in this document for the sole purpose of

adequately describing experimental or test procedures. In no event does such identification imply recommendation or endorsement by the National Institute of Standards and Technology of a particular product, nor does it imply that a named material or instrument is necessarily the best available for the purpose it serves.

3. Infrared Components Brochure, Edition 17, p. 58, Santa Barbara Research Center, Goleta, CA (1983).

4. Technical Data Book, HgCdTe Instruction Manual, p. 2, InfraRed Associates, Inc., Cranberry, NJ (1985).

5. E. L. Dereniak and D. G. Crowe, ibid., p. 92.

6. Linear and Conversion Applications Handbook, pp. 240-241, Precision Monolithics, Inc., Saiftta Clara, CA

(1986).

/ SPIE Vol. 1110 Imaging Infrared: Scene Simulation. Modeling, and Real Image Tracking (1989)

96
Compensation

Voltage

CurrentA^oltage

Converter

Virtual Ground

Photoconductive

Detector

Locl<-in

Amplifier

Oscilloscope

Digital

Voltmeter

FIGURE 5: Block Diagram of Photoconductive Detector Radiometer

10-1

<

OI—

CO

O

8-

6-

0-

Detector heats up,

HgCdTe Radiometer

June 22, 1988

Bias

Compensation

Reset

Liquid N Added

100 200

TIME [min]

300

FIGURE 6: Detector Stability

SP/E Vol. J 1W Imaging Infrared: Scene Simulation. Modeling, and Real Image Tracking (1989/ /

97

Photocurrent measurement of PC and PV HgCdTe detectors.

George P. Eppeldauer' and Robert J. Martin^

'National Institute of Standards and Technology

Gaithersburg, Maryland 20899

^Analog/Digital Integrated Circuits, Inc. Longwood, Florida 32750

Abstract

Novel preamplifiers for working standard photoconductive (PC) and photovoltaic (PV)

HgCdTe detectors have been developed to maintain the spectral responsivity scale of the

National Institute of Standards and Technology (NIST) in the wavelength range of 5 |im

to 20 fim. The linear PC mode preamplifier does not need any compensating source to zero the effect of the detector bias current for the preamplifier output. The impedance

multiplication concept with a positive feedback buffer amplifier was analyzed and

utilized in a bootstrap transimpedance amplifer to measure photocurrent of a 200 Q shunt

resistance photodiode with a maximum signal gain of 10^ V/A. In spite of the high

performance lock-in used as a second-stage signal-amplifier, the signal-to-noise ratio had

to be optimized for the output of the photocurrent preamplifiers. Noise and drift were

equalized for the output of the PV mode preamplifier. The signal gain errors were

calculated to determine the signal frequency range where photocurrent-to-voltage

conversion can be performed with very low uncertainties. For the design of both PC and

PV detector preamplifiers, the most important gain equations are described.

Measurement results on signal ranges and noise performance are discussed.

1. Introduction

HgCdTe detectors are widely used for low-level optical radiation measurements in the

infrared (IR) range. Working standard HgCdTe radiometers have been developed and

calibrated against a transfer standard cryogenic bolometer [1]. The working standards

hold the IR spectral responsivity scale and test detectors are calibrated against them. The

expectation from the working standards is to propagate and maintain the 0.8 % (coverage

factor ^=1) standard relative uncertainty of the IR spectral responsivity scale with the

smallest possible uncertainty increase. One of the most important requirements for

working standards development was to produce linear operation in a wide radiant power

range. Linear response can be obtained from both photovoltaic (PV) and

photoconductive (PC) type devices if the detector short circuit current is measured [2].

HgCdTe detectors have low resistance-area (RA) product resulting in small detector99
resistance and high gain for the preamplifier input voltage-noise, even for small area

detectors. It is an important design consideration to produce high sensitivity by keeping

the voltage-noise gain low. Also, the spatial response non-uniformity of HgCdTe

detectors is poor because of the difficulties associated with producing homogeneous

material. For accurate measurements, it is necessary to overfill these detectors with a uniform field of radiation to average out high response non-uniformities. However, the

signal loss can be significant in the overfilled (irradiance) measurement mode. Again,

high sensitivity is necessary to measure the decreased radiant flux on the detector in this

measurement mode. At low signal frequencies, the 1// noise of HgCdTe detectors can be

orders of magnitude larger than the noise from the background. It is important to keep

the chopping frequency close to the l//noise elbow. As the elbow frequency depends on

the bias voltage, biasing of PV detectors should be avoided in high sensitivity

applications.

PV HgCdTe detectors can be used for optical radiation measurements from about 5 jam to 12 |im. At present, the optically sensitive diameter of these detectors is 2 mm or less. The shunt resistance of these devices is a few-hundred ohm and the capacitance is close

to 1 nF for a 2 mm detector. The PV devices are linear only if the short-circuit current of

the detector is measured. Photodiodes have smaller noise than PC detectors because the

dominating photodiode shot-noise is much smaller than the generation-recombination

noise of PC detectors. Bootstrapped preamplifiers have been reported [3, 4] that can keep

the voltage drop on the photodiode very low resulting in an increased shunt resistance

and better short circuit for the photodiode. The increased shunt resistance will result in

smaller closed-loop voltage-gain and higher loop gain [5]. The smaller closed-loop

voltage-gain produces lower voltage noise and voltage drift amplifications. The higher

loop gain will decrease the uncertainty of the current-to-voltage conversion. Analysis

and application of the bootstrap method for PV HgCdTe detectors is discussed below.

PC HgCdTe detectors can be used for longer wavelengths than PV detectors. We have

used the PC HgCdTe detectors up to 20 |im, which is the long wavelength limit of the

NIST IR spectral responsivity scale. PC detectors are operated with a dc bias current to sense the photogenerated conductance change, which is proportional to the radiant flux

(power) on the detector. In a traditional biasing and measuring circuit, a dc source is connected to the detector through a load-resistor connected in series. The voltage change

is measured across the detector while the high load-resistance keeps the bias current

constant. It was shown in our earlier work [2] that the voltage measured on the detector

is a nonlmear function of the conductance change. To eliminate this response nonlinearity, a current measuring PC HgCdTe radiometer was developed [2]. This

radiometer needed frequent zeroing to eliminate output voltage saturation caused by the

100
non-stable dc compensation of the biasing source. The main concern of the new hnear

preamphfier design, described here, was to ehminate the need for output dc voltage

compensations.

2. PC HgCdTe detector and preamplifier

The tested PC HgCdTe detectors had active areas of 3 mm x 3 mm or 4 mm x 4 mm. No

cut-lines were fabricated in the detector centers to avoid large and sudden changes in the

spatial response uniformity. In most commercial PC HgCdTe detectors, the detector

segments, isolated by cutlines, ai^e connected in series to increase the resultant resistance

of the detector. The tested cutline-free detectors had very low cold (77 K) resistances,

ranging from 15 ^ to 22 fit. A dc bias current of about 50 mA was needed for a detector

to obtain a high enough detector responsivity. The test detector responsivities were vei-y

different. They ranged from a few VAV to 122 VAV when the broadband radiation of a ceramic glower was measured. The detector responsivity tests were made against

pyroelectric detector standards of spectrally constant responsivity.

The preamplifier was constructed from ten current-to-voltage converters connected in

parallel as shown in the schematic of Fig. 1 . Only three of the ten amplifiers are shown

in this drawing. The ten current-to-voltage converters produced 10 * 5 (50) mA dc

current to bias the PC detector. The voltage drop on the detector was determined by the

bias voltage V^ connected to the non-inverting inputs of the operational amplifiers. The

dc bias current requirement and the cold dc resistance of an individual detector

determined the feedback resistor value for the operational amplifiers. The same feedback

resistor value, i?i=/?2=/?io=1875 Q, was used in all of the ten parallel-connected

amplifiers. The Ra=l5 Q. corresponds to ten 150 ^ resistors connected in parallel,

producing smaller feedback attenuation (from the operational amplifier output to its input) in each individual current-to-voltage converter. At low frequencies, the feedback

network attenuation in each amplifier is 13.5 =(150+1875) Q. / 150 Q. The loop gain,

which is the product of the feedback attenuation and the amplifier open-loop-gain, is close to 10^ for the applied AD797 [6] amplifiers. Large loop gains result in high

accuracy current-to-voltage conversion [5]. Note that each amplifier needs an offset

equalizing resistor (not shown in the figure) connected in series to the non-inverting

input. This resistor is needed to allow the error current of each amplifier to prevent

excess output voltage effect. A value of 10 Q. was used to compromise offset error versus gain error. The ac (10 Hz) signals from the ten channels of the preamplifier were combined with a sum-amplifier after the dc voltages at the outputs of the individual

amplifiers were de-coupled. The low frequency roll-off point of the signal gain curve

101
was tuned to 0.3 Hz by using serially connected 10 kQ resistor and 47 |jF capacitor for

each channel.

As the conductance of the detector varies, there is a proportional variation in the output

voltage of each preamplifier and in the variation of the summation amplifier. The

conductance of the detector Gj varies only a small amount about the dc operating point.

This incremental conductance change follows the rate of the radiation-chopper. As the

measured change in the detector-current is proportional to the change of the detector

conductance [2], the equivalent transfer resistance gain is found by taking the derivative

of the output voltage V„ with respect to the detector conductance G^:

dVJdG, = -V^RfRj/R, [V/S] (1)

R^=^5Q RtI = 1 875 n

'^'^.^^ flji =1 ki2 Rf=^ kQ

[

-'VS/*—

Vv.

1^

^ f—^^^^^

47 mF -NA/»

9—1( '\A/»--jf?j2=10 kQ

R-^.,Q=1875i2 ^"^^^

<( ^

<f f

flj10=10kfll

Fig. 1. Multiple amplifier current-to-voltage converter for the PC HgCdTe detector.

where V^ is the output voltage in V,

Rf is the feedback resistor in the summing amplifier in Q,

/?i is the input summing resistor of the summing amplifier in Q.,

Vb is the bias voltage in V,

Rj is the transfer (feedback) resistance of one of the input stages in Q, and

Gd=l//?d is the conductance of the detector in S

102
Because of the summing operation, the transfer resistance (current-to-voltage gain) is independent of the number of amplifiers used.

The advantage of this preamplifier design is that the dc output voltages of the individual

operational amplifiers do not go into saturation and no compensating source is needed at the input. A compensating voltage source could produce large (and dominating) noise

and also repeated compensations for zeroing the output voltage might be necessary.

From preamplifier output noise measurements (without the detector at the input) and the

nominal 125 V/V preamplifier voltage-gain (calculated from Eq. 1 for a 15 Q detector

resistance), an input noise of 0.6 nV/Hz^'^ was obtained. This noise is comparable to the

0.5 nV/Hz^'^ Johnson noise of the 15 Q detector resistance.

The 0.6 nV/Hz^'^ input voltage noise corresponds to a noise equivalent power (NEP) of

40 pW/Hz''^ for a detector responsivity (without the preamplifier voltage-gain) of 16

VAV. This responsivity was measured on a typical test detector at 50 mA bias current

and 10 Hz chopping frequency. The measured NEP was one order of magnitude larger,

0.34 nW/Hz^'^. The large noise was caused by the generation-recombination (G-R) noise

of the biased PC HgCdTe detector. The calculated G-R current noise for 1 Hz bandwidth

is: /oR=(2gq/,Ay)^^ = 0.57nA

where /^ is the detector current, in our case 0.05 A,

q is the electron charge, 1.6 * 10"'^ C,

g is the photoconductive gain (typically about 20 electrons per electron), and

A/is the electrical bandwidth in Hz.

Using the NEP=0.34 nW/Hz''' and the detector area A=0.16 cm', a Z)*=A''YNEP = 10^

cm Hz^'^AV was calculated. The same detector was tested at a bias current of 10 mA

where the detector responsivity decreased to 3.7 VAV.

At 50 mA bias, the resultant radiant power-to-voltage gain for the preamplifier output is 16 VAV * 125 VA/ = 2000 VAV. The current-to- voltage gain is 1875 V/A. Accordingly,

the power-to-current gain is about 1.1 AAV. From these gains and the measured 0.34 nW

noise, a photoconductive gain of only 13 (from /gr= 0.37 nA) is obtained.

For the NEP equal to 0.34 nW/Hz^'^ the output noise voltage of the preamplifier is 0.68

|iV at a bandwidth of 1 Hz. The signal dynamic range, for a minimum signal-to-noise

103
ratio of 100, will be from about 68 |aV to 5 V (at the preamplifier output), which

corresponds to a radiant power range of 34 nW to 2.5 mW. This is a dynamic range of

close to five decades for radiant power measurements with 1% (coverage factor ^=1)

relative uncertainty.

3. PV HgCdTe detector and preamplifier

Instead of applying a bias voltage for the photodiode, we chose the bootstrap method to increase the shunt resistance of our PV HgCdTe detector. The shunt resistance increase was necessary to achieve high signal gains and to obtain low output noise for the

preamplifier. The term bootstrapping refers to the use of an amplifier to increase the

apparent impedance using near unity gain positive feedback [3,4]. Large area photon

detectors may have relatively large capacitance and low shunt resistance. One method of

dealing with this relatively low impedance is to use a near unity gain buffer amplifier to increase the effective equivalent impedance of the detector.

3.1. Bootstrap impedance multiplication circuit

The impedance multiplication circuit, using the unity gain buffer amplifier, is shown in

Fig. 2. The unity gain buffer is implemented with an operational amplifier OA. To

demonstrate the impedance multiplication concept, a I V ac voltage source was

connected to the input in a circuit simulation.

INPUT

OUTPUT

out —VW-'

Cd =1 nF

Fig. 2. Computer simulation circuit to demonstrate the impedance multiplication concept.

104
The effective equivalent input impedance which will be connected to the input of a second stage transfer resistance amplifier (not shown in Fig. 2) will be determined first. The input current can be calculated from Kirchoff's and Ohm's laws:

Us)=Y, (VM-V^M) [A] (2)

where Y^=Ga+C^s is the detector admittance,

Gd=l//?d is the conductance of the detector in S,

Q is the junction capacitance of the detector in F,

s is frequency in the steady state frequency domain in rad/s or s=j2nf, and

/is frequency in Hertz with j=(-l)^'^

IJ^s) is the input current in A,

Vi^(s) is the input voltage in V, and

V^^fis) is the amplifier output voltage in V.

The closed loop voltage gain of the operational amplifier can be defined in terms of the

open loop voltage gain as:

= [VA^] (3)

V.,,(s) A(s)+1

where A(s) is the open loop gain of the operational amplifier in VA'^.

The equivalent input impedance is defined as the ratio of the input voltage to the input

current. Further, in order to eliminate the output voltage, equation (2) is written in the

following form:

IM=V.Js){l-V,Js)/V-Js))Y, [A] (4)

Inserting equation (3) into equation (4) becomes

IM=VJs)(l-A{s)/(A(s)+l))Y, [A] (5)

Simplifying equation (5) and taking the voltage to current ratio, the equivalent impedance

may be expressed as:

Z.Js)=(A{s)+\)Z, m (6)

105
where the detector impedance 2^= l/Y^.

Assume that the general form of A(s) may be expressed by a finite gain and a dominant

pole [5], then:

A(s)=AJ(zs+l) [YfV] (7)

where A^ is the dc open loop voltage gain in V/V, and

T is the time constant of the dominant pole of the amplifier in s.

Inserting equation (7) into equation (6), the general form of the equivalent input

impedance is written as follows:

R;„(l+S/CDj

ZM = m (8)

(Ts+l)(R,Qs+l)

where R,^ = R^iA^+l) in Q,

co^ = (Ao+l)/Tin rad/s and is commonly called the unity gain bandwidth product

for the operational amplifier.

A typical operational amplifier would have an open loop gain of 400 V/mV and a dominant time constant of 16 ms. In the computer simulation, a Ik^ shunt resistance and

a 1 nF capacitor along with a standard operational amplifier was used to demonstrate the

multiplication of impedance concept. The simulation results are shown in Fig. 3.

10° 101 102 103 10^ 105 106 ''[Hz}

Fig. 3. The equivalent input impedance calculated for a

106
1 kO. shunt resistance and a 1 nF junction capacitance.

For this example, at low frequencies the equivalent impedance is resistive and approaches

400 MQ. There is a break point at 10 Hz and the impedance becomes capacitive over the

band from 10 Hz to 1 MHz.

3.2. Bootstrap transimpedance amplifier, signal gain

If we combine the bootstrap impedance multiplier circuit with a transimpedance

amplifier, an improved performance current-to-voltage converter can be realized (Fig. 4).

The feedback network of the second operational amplifer 0A2 consists of a feedback

capacitor Cj connected in parallel with the feedback resistor Rj. The photocurrent L,^ from the photodiode P is converted into an output voltage Vq. The equivalent transfer

function of the combined circuit has to be determined to obtain the signal gain. An

equivalent circuit is shown in Fig. 5 for nodes a, b, and c.

Cj

1 f II

yv yv XV

N/ 9

Uf\\

^ f (^ 9

(

i—

i ^0

i—

Fig. 4. Bootstrap transimpedance amplifier.

The node-voltages [7], shown with voltage sources (circles), are referenced to the

common and expressed from the output voltage Vq. The voltage polarities are shown

with both signs and arrows. The input voltage of the operational amplifier 0A2 is on node b and it is equal to VV^2- This voltage is multiplied by the gain of the buffer

amplifier (shown by Eq. 3). The output voltage of the operational amplifier OAl on node

a will be A^Vg /(Ai+1)A2. The input current I^^ is represented by a current source (double

107
circle). It can be calculated from the node-voltage equation using Kirchoff s current law

[7] for node b:

'in <0>

][

^\/\/v b

''T'N/V^

Qii: ^T>'2

+

COMMON

Fig. 5. Three-node equivalent circuit of the combined transimpedance amplifier.

iM =

v^o(^)A v,{s)

(Aj + 1)^2 ^2

^^.w

A2

_\_ [A] (9)

Both Vq (s) and/j„(5') are frequency dependent. After simplifying and collecting terms, the

output voltage to input current ratio (signal gain) can be written as:

Kis) -RjRfG^ + sRj-Cj

^in (^) 1 + sR^Ct- + —(1 + sR^Cr +

"r-j ' --r--rf ^) m (10)

where ^^(s) is the output voltage of 0A2 in V,

/i„(s) is the input current from the PV detector (photodiode) in A,

A2(s) is the open loop gain of OA2 in VA'^,

Ai(s) is the open loop gain of the bootstrap operational amplifier OAl in V/V,

R^ is the shunt resistance of the photodiode, and

Q is the junction capacitance of the photodiode.

For high gain operational amplifiers, the transfer function in Eq. 10 becomes equal to -Rj

which is the low frequency (dc) current-to-voltage gain of the combined transimpedance

amplifier. The denominator describes the frequency dependent error of the photocurrent108
to-voltage conversion. The error voltage curves of the signal conversion (gain) as calculated for the summing junction of the 0A2 for an output signal of Vq=1W are shown

in Fig. 6. The combined circuit used in this computer simulation is shown in Fig. 7. The

error voltage curves were calculated for a detector resistance of 200 Q and feedback

resistors from 1 klQ to lOOM^. The transfer resistance curves, shown in Fig. 8, were

calculated with feedback resistors up to IMQ only.

at

(a

o

UJ

Frequency [Hz]

Fig. 6. Error voltages (referenced to Vo=lY) of the the bootstrap transimpedance

amplifier for a shunt resistance of 200 Q. and feedback resistors of 1 kQ to 1 M^.

The error voltage is reciprocal of the loop gain which is, at low frequencies, roughly

equal to the open loop gain (4 x 10^) of 0A2. This is the result of the close to unity

feedback attenuation at low frequencies, caused by the detector impedance multiplication.

R^= 200 ka Cp= 0.51 pF

^A/v

n

1 kQ

lOkQ

lOOkQ

1MQ

A/W

A/W

Fig. 7. Computer simulation circuit for a bootstrap transfer resistance amplifier.

109
The maximum signal current can be measured when the output signal is 1 V and the

feedback resistance is 1 k^. This corresponds to a maximum photocurrent of 1 mA. The

output signal maximum is determined by the largest full-scale signal of the lockin

amplifier input where the output signal is connected. The relatively wide range of transfer

resistance is one of the advantages of active impedance compensation. Note that R^ and Q

have been added to OA2 to provide voltage gain (gain peaking) compensation [5].

Transfer resistance

10"=

10^

10^=

Q]

A

\

\

1 , rS ^- 10° lO"" 102 10^ 10^ 10= R 7 ''[Hz] 10^ lO'^

Fig. 8. Transfer resistance (signal gain) of the bootstrap transimpedance amplifier

with feedback resistor selections from 1 k^ to 1 MQ.

3.3. Output noise

The output voltage as a power spectral density in volts squared per hertz can be written

as:

(/?TG,^„,*A,/(Ai+l))^+(e„2(l+^TGy(A,+l)))^+4kT/?x+(i^Tini)'+0^T4i)'+2q/,i?T fZ),- \2 , /D ,• \2 ,

l + sRj.C^+ —(1 + sRj^Cj + Aj+l

(11)

where e^^^^ is the equivalent output noise voltage density in V/Hz"^

k is the Boltzmann's Constant (1.38*10"^^ Joules/K),

T is the absolute temperature in K,

^ni is the noise voltage density of the bootstrap amplifier in V/Hz^'^,

e^2 is the noise voltage density of the transfer resistance amplifier in V/Hz^'^,

110
/„! is the equivalent input noise current density of the bootstrap amplifier in

A/Hz^'',

i^2 is the equivalent input noise current density of the transfer resistance amplifier

in A/Ez"\

/j is the average detector current and includes the dark leakage current in A, and

q is the electron charge equal to 1.602*10"'^ Coulombs/electron.

The amplifier gains are taken at the frequency of interest and are in general complex.

For low enough frequencies and high enough amplifier open loop gains, and where the

input current noise of the operational amplifiers may be neglected, Eq. 1 1 simplifies to:

e.oJ = (RrG,ej' + (eM+GaRT/A,)f+4kTR,+2qI,R,' [ W'/Hz] (12)

In Eq. 12 the denominator error drops out.

Equation 12 shows that the noise of the transfer resistance amplifier will in general be

small compared to the voltage noise of the impedance feedback amplifier by virtue of the

relatively large gain of this bootstrap operation. Clearly, for a large diode conductance,

the noise of the bootstrap amplifier dominates. To avoid amplifier noise domination, the

noise of the bootstrap amplifier's voltage noise density must be less than or equal to the

detector noise. Care should be taken because the 1// amplifier voltage noise, at very low

(dc) frequencies, can be much larger than the detector noise.

The measured PV HgCdTe detector noise was 40 pA/Hz''^ at 25 Hz. This shot-noisedominated PV detector noise is about an order-of-magnitude smaller than the G-R-noisedominated PC HgCdTe detector noise in Section 2. In order to match the amplifier noise

to this detector noise, operational amplifiers OPA627 and 637 (as shown in Fig. 7) were

used in the computer model. Figure 9 illustrates the output noise versus frequency

characteristics of the bootstrap transimpedance amplifier for 7^^=200 Q. The 0A2

feedback resistors were selected in the simulator program between 1 kQ and 1 Mi2 in

decadic steps.

When the feedback resistor is increased to /?-r=100 M^ the output voltage noise density

will be close to 4 mV. This corresponds to a minimum signal current of 40 pA which is equal to about 25 pW at a wavelength of 9 pm as calculated from the 1.6 AAV

111
CMI

ZL

0)

(0O

c

0)Di

-^Q.

o

100

0.01

loO

— A

/?T-=100ki2

f?j=10k^

f?T=1kQ

10-= 10^

Frequency [Hz]

10^ 10^

Fig. 9. Output voltage noise density of the bootstrap transimpedance amplifier (shown in

Fig. 7) for a detector shunt resistance of 200 Q. and various transfer resistance values.

responsivity of the PV detector. With the described operational amplifier selection, the

amplifier noise and the detector noise were equalized at the highest signal gain of 10^

V/A. For a measurement relative uncertainty of 1 % (^=1) a signal range from about 4

nA to 1 mA could be achieved with the described component selections. As calculated

from the 1.6 AAV responsivity, the 4 nA detector current corresponds to a radiant power

of about 2.5 nW at the 9 [nn peak responsivity of the 2 mm diameter PV HgCdTe

detector.

3.4. Output offset and drift.

The output offset voltage and its thermal drift is another concern if very large transfer

resistance values are used. The output offset voltage, in terms of the input offset voltage,

is:

V' outos=

-R.,G,V,,,*AAA, +l) +V,M+RtGMi+ ^)) +(/Bl+/B2+/dark)^T

1 + sR^Cr + —(1 + sILCr +

^^^' ^

'^"^^^

[V] (13)

where Voutos is the output offset voltage in V,

Vosi is the input offset voltage of the bootstrap amplifier in V,

Vos2 is the input offset voltage of the transfer resistance amplifier in V,

112
/bi is the input bias current of the bootstrap amphfier in A,

/b2 is the input bias current of the transfer resistance amphfier in A, and

/^ark is the dark current of the detector in A. (Usually, the dark current of an

unbiased photovoltaic detector is zero.)

To evaluate a high offset voltage sensitivity case, we consider a 200 Q detector with a 100 MQ transfer resistance. Only 1 pV input offset voltage can produce 0.5 V output

voltage. This observation is against intuition as both amplifiers provide equivalent open

loop gain. In addition, a drift of 1 pV/K will produce a 0.5 V/K output drift. If such a system is desired for dc signal measurements then the amplifiers must be under

temperature control and precise offset voltage trim has to be implemented. For ac (chopped radiation) measurements, the temperature control for the amplifiers may not be

necessary but the offset trimming is still important to avoid saturation of the output

voltage of the transfer resistance amplifier. Practical amplifiers are hmited to one or two

pV/K drift.

Care should be taken when high signal gains (transfer resistances) are selected because

the very high feedback resistor and a very small detector shunt resistance can produce a very high closed loop voltage gain. The closed loop voltage gain, calculated as the

inverse attenuation produced by the feedback network , can not be larger than the open

loop gain of the transfer resistance amplifier. From this restriction and the noise gain

considerations in Section 3.3, the practical limit of the feedback resistor for a 200 Q.

detector shunt resistance will be about 100 MQ. This feedback network gives a closedloop voltage gain of 5 x 10^ roughly equal to the open-loop voltage gain.

4. Conclusion

Because room temperature thermopiles and pyroelectric detectors do not have high

enough sensitivities to measure weak signals from monochromators, HgCuTe detectors were selected as working standards for the 5 pm to 20 pm wavelength range. The high

sensitivity and low uncertainty requirements for spectral responsivity measurements

made it necessary to design linear and low noise photocurrent meters for both

photoconductive (PC) and photovoltaic (PV) HgCdTe detectors. Using the results of the

circuit analysis described here, high signal responsivities and low output noise can be

achieved for the output of the preamplifiers even if very low detector resistances are

applied.

PC detectors were used for the longer wavelength range where the detectors were biased

with a dc current of 50 mA. A novel preamplifier was developed where the 50 mA bias

113
was produced from ten current-to-voltage converters connected in parallel. The

advantage of this preamplifier design was that the dc output voltages of the individual

operational amplifiers did not go into saturation and no compensating voltage source was

used at the input. Accordingly, repeated compensations were not needed and the

dominating noise of the compensating source was eliminated. The input voltage noise of

the parallel connected converters corresponded to an NEP of 40 pW/Hz''^. The cold

resistance of the cut-line free 3 mm by 3 mm detector was 15 Q. and the signal

responsivity was 16 W/W. The measured NEP was an order of magnitude larger,

dominated by the G-R noise of the current-biased PC detector. A radiant power range of

34 nW to 2.5 mW can be measured by this PC HgCdTe detector current meter with a

relative standard uncertainty of 1 % (coverage factor k=l).

Bootstrapping transimpedance amplifiers were designed and implemented to increase the

equivalent impedance of PV HgCdTe detectors. The impedance multiplication concept

has been analyzed and the equivalent input resistance has been computed versus frequency. For a detector shunt resistance of 1 kQ and a junction capacitance of 1 nF, the

equivalent impedance was resistive and approached 400 MQ up to 10 Hz. When this

impedance multiplier was applied for a 200 Q. and 1 nF impedance of a PV HgCdTe

detector, and it was combined with a transfer resistance amplifier, a range of transfer

resistances from 1 k^ to 100 MQ could be implemented. The relatively wide range of

transfer resistance is one of the advantages of active impedance compensation. The

frequency dependent transimpedance (signal) gain of the bootstrap current-to-voltage

converter was determined. The maximum 100 M^ transfer resistance was dominated by

the voltage gain for the input drift of the bootstrap amplifier. Also, this highest transfer

resistance multiplied by the high detector conductance produced a high voltage gain for

the input voltage noise of the bootstrap amplifier resulting in a noise equivalent

photocurrent roughly equal to the PV HgCdTe detector noise current of 40 pA/Hz^'^.

This noise current was measured on the PV HgCdTe detector used in our PV HgCdTe

radiometer and it was about an order of magnitude smaller than the measured G-R noise

of the current-biased PC HgCdTe detector. With a relative uncertainty of 1 % (^=1),

signals from 4 nA to 1 mA could be measured with the PV HgCdTe radiometer. The 4

nA detector current corresponds to a radiant power of 2.5 nW at the 9 jjm peak

responsivity (1.6 AAV) of the 2 mm diameter detector. The frequency dependent error voltage of the photocurrent-to-voltage conversion was determined.

The described frequency dependent gain equations and photocurrent measurement

considerations can be applied to other PV and PC detectors as well. Such other devices

are Ge, extended-InGaAs, InSb, and InAs photodiodes, and PbS or PbSe PC detectors.

114
5. References

1. A.L. Migdall and G.P. Eppeldauer, Spectroradiometric Detector Measurements: Part

in -Infrared Detectors, NIST Special Publication 250-42, 1998.

2. G. Eppeldauer and L. Novak, Linear HgCdTe radiometer, SPIE Proc. Vol. 1110,

Edited by A.J. Ruber, M.J. Triplett, and J.R. Wolverton, 267-273 (1989).

3. J. Graeme, Photodiode Amplifiers, McGraw-Hill, New York, p. 77 (1996).

4. J.P. Makai, J.J. Makai, and J. Balazs, Noise characteristics of bootstrapped

photovoltaic and photoconductive detectors, SPIE Proc. Edited by S.M. Goodnick, W.F.

Kailey, R.E. Longshore, and Y-H Zhang, Vol. 3794, 108-1 14 (1999).

5. G. Eppeldauer, Chopped Radiation Measurements With Large Area Si Photodiodes,

J. Res. Natl. Inst. Stand. Technol. 103 (2),. p. 153-162 (1998).

6. Identification of commercial equipment to specify adequately an experimental

problem does not imply recommendation or endorsement by the National Institute of

Standards and Technology nor does it imply that the equipment identified is necessarily

the best available for the purpose.

7. J.W. Nilsson, Electric Circuits, 3"^ Edition, Addison Wesley Publishing Company,

Inc., USA, 1990.

About the Authors:

George P. Eppeldauer is a Ph.D. Electronics Engineer in the Optical Technology Division

of the NIST Physics Laboratory. The National Institute of Standards and Technology is an agency of the Technology Administration, U.S. Department of Commerce.

Robert James Martin is a Florida Registered Ph.D. Electronics Engineer at Analog Digital

Integrated Circuits (ADIC) Inc. in Longwood, Florida. ADIC is a small company that

specializes in analog discrete and integrated circuit design.

AU.S. GOVERNMENT PRIhTTING OFFICE: 2001-472-068/46003 115



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