NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

Effects of Spectral Error in 

Efficiency Measurements of 

GaInAs-Based Concentrator 

Solar Cells

C.R. Osterwald, M.W. Wanlass, T. Moriarty, 

M.A. Steiner, and K.A. Emery

Technical Report

NREL/TP-5200-60748 

March 2014
NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO 80401

303-275-3000 • www.nrel.gov

Effects of Spectral Error in 

Efficiency Measurements of 

GaInAs-Based Concentrator 

Solar Cells

C.R. Osterwald, M.W. Wanlass, T. Moriarty, 

M.A. Steiner, and K.A. Emery

Prepared under Task No. PV13.1010

Technical Report

NREL/TP-5200-60748 

March 2014
NOTICE

This report was prepared as an account of work sponsored by an agency of the United States government. 

Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, 

express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of 

any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately 

owned rights. Reference herein to any specific commercial product, process, or service by trade name, 

trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, 

or favoring by the United States government or any agency thereof. The views and opinions of authors expressed 

herein do not necessarily state or reflect those of the United States government or any agency thereof.

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Available electronically at http://www.osti.gov/scitech

Available for a processing fee to U.S. Department of Energy

and its contractors, in paper, from:

U.S. Department of Energy

Office of Scientific and Technical Information

P.O. Box 62

Oak Ridge, TN 37831-0062

phone: 865.576.8401

fax: 865.576.5728

email: mailto:reports@adonis.osti.gov

Available for sale to the public, in paper, from:

U.S. Department of Commerce

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22161

phone: 800.553.6847

fax: 703.605.6900

email: orders@ntis.fedworld.gov

online ordering: http://www.ntis.gov/help/ordermethods.aspx

Cover Photos: (left to right) photo by Pat Corkery, NREL 16416, photo from SunEdison, NREL 17423, photo by Pat Corkery, NREL 

16560, photo by Dennis Schroeder, NREL 17613, photo by Dean Armstrong, NREL 17436, photo by Pat Corkery, NREL 17721.

Printed on paper containing at least 50% wastepaper, including 10% post consumer waste. 
iii

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Abstract

This technical report documents a particular error in efficiency measurements of triple-absorber

concentrator solar cells caused by incorrect spectral irradiance—specifically, one that occurs 

when the irradiance from unfiltered, pulsed xenon solar simulators into a GaInAs bottom subcell

is too high. For cells designed so that the light-generated photocurrents in the three subcells are 

nearly equal, this condition can cause a large increase in the measured fill factor, which, in turn, 

causes a significant artificial increase in the efficiency. The error is readily apparent when the 

data under concentration are compared to measurements with correctly balanced photocurrents, 

and manifests itself as discontinuities in plots of fill factor and efficiency versus concentration 

ratio. In this work, we simulate the magnitudes and effects of this error with a device-level 

model of two concentrator cell designs, and demonstrate how a new Spectrolab, Inc., Model 460 

Tunable-High Intensity Pulsed Solar Simulator (T-HIPSS) can mitigate the error. Although in 

this work the error has been identified in GaInAs bottom subcells, increasing the photocurrent in 

any subcell will produce similar errors, regardless of the chemical composition.
iv

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Acknowledgment

This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-08-

GO28308 with the National Renewable Energy Laboratory.
v

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

List of Symbols and Acronyms

1-sun total solar irradiance of 1000 Wm-2

A PV device total area

E total solar irradiance

HIPSS high intensity pulsed solar simulator

I-V PV device current versus voltage curve

Isc short-circuit current

FF fill factor

M spectral mismatch parameter

N number of subcells in a multijunction solar cell

n solar cell diode quality factor

NREL National Renewable Energy Laboratory

OSMSS one-sun multisource solar simulator

Pmax maximum power

R photocurrent ratio

PV photovoltaics

QE quantum efficiency

SRC standard reporting conditions

T-HIPSS tunable-high intensity pulsed solar simulator

× concentration ratio

Voc open-circuit voltage

η solar cell power efficiency

ρ solar cell photocurrent
vi

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

List of Figures

Figure 1. Example quantum efficiencies for subcells typically used for group III-V concentrator solar 

cells............................................................................................................................................... 3

Figure 2. Relative spectral irradiance versus wavelength of the ASTM G173 direct reference spectrum 

and the NREL HIPSS for two different PNV settings.................................................................. 5

Figure 3. Open-circuit voltage, fill factor, and efficiency versus concentration ratio for a GaInP/GaAs 

tandem cell (HIPSS data).............................................................................................................. 6

Figure 4. Open-circuit voltage, fill factor, and efficiency versus concentration ratio for a 41%-efficient 

GaInP/GaAs/Ge triple cell (HIPSS data)...................................................................................... 7

Figure 5. Spectral reflectance versus wavelength of the T-HIPSS Model 460 dielectric mirrors. ............... 8

Figure 6. Open-circuit voltage, fill factor, and efficiency versus concentration ratio for a 

GaInP/GaAs/GaInAs triple cell (HIPSS data).............................................................................. 9

Figure 7. Photocurrent ratio versus HIPSS PNV for a GaInP/GaAs/GaInAs triple cell determined with 

isotype reference cells and assuming unity spectral mismatch................................................... 10

Figure 8. Modeled fill factor versus concentration ratio for two different triple cells, GaInP/GaAs/GaInAs 

and GaInP/GaAs/Ge. .................................................................................................................. 11

Figure 9. Short-circuit currant and fill factor versus bottom subcell irradiance for a GaInP/GaAs/GaInAs 

triple cell (OSMSS data)............................................................................................................. 12

Figure 10. Comparison of I-V parameters versus concentration ratio for the triple cell from Fig. 6 (HIPSS 

and T-HIPSS data)...................................................................................................................... 13

Figure 11. Comparison of I-V parameters versus concentration ratio for the triple cell from Fig. 10, 

corrected for spectral imbalance (HIPSS and T-HIPSS data). ................................................... 15
vii

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Table of Contents

List of Symbols and Acronyms................................................................................................v

List of Figures ..........................................................................................................................vi

1 Introduction.........................................................................................................................1

1.1 Multijunction Efficiency Measurements................................................................................... 2

1.2 Concentrator Cell Measurements.............................................................................................. 3

2 Concentrator Efficiency Measurements at NREL..............................................................4

2.1 High Intensity Pulsed Solar Simulator (HIPSS)........................................................................ 4

2.2 Tunable-High Intensity Pulsed Solar Simulator (T-HIPSS)...................................................... 7

3 GaInAs-Based Triple Cells..................................................................................................8

3.1 Effects of Photocurrent Imbalance ............................................................................................ 9

3.2 Excess Irradiance Estimation .................................................................................................. 10

3.3 Fill Factor Discontinuities....................................................................................................... 11

3.4 Comparison of HIPSS and T-HIPSS Data .............................................................................. 12

3.5 Voc Increases Due to Excess Subcell Photocurrents ............................................................... 13

3.6 Empirical Spectral Imbalance Data Correction Procedure...................................................... 14

4 Conclusions.......................................................................................................................15

References ..............................................................................................................................17
1

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

1 Introduction

The electrical performance of solar photovoltaic (PV) cells and modules is strongly affected by 

the incident light, both the overall intensity level (i.e. the total irradiance) and its variation over 

wavelength. Standard measurements of solar PV device performance require that electrical 

efficiency be determined with respect to reference spectral irradiance distributions, which are 

tables of solar irradiance and light wavelength pairs [1,2]. A reference spectrum is one element

of standard reporting conditions (SRC), which also specify the total irradiance and the internal 

PV cell operating temperature. Electrical performance is measured by tracing the currentvoltage (I-V) curve of a device while it is illuminated [3-6].

While these tables, which are generated by computer models, cannot represent how the light 

from the sun changes over time, they are the only consistent basis on which the performance of 

different solar cells can be compared. For modules, performance measurements at SRC are now 

so institutionalized in the PV industry that the power at 25°C, a total irradiance of 1000 Wm-2

and the global reference spectrum [1] is deemed the “peak-watt rating”, even though a module 

will likely never operate under these exact conditions. This total irradiance is defined as 1-sun. 

Power, the product of current and voltage, is highest on the I-V curve at the maximum-power 

point, Pmax, and PV efficiency is defined as:

(1)

In Eq. 1, E is the total irradiance and A is the total area of the device. Three other important I-V 

curve parameters are the short-circuit current (Isc), the open-circuit voltage (Voc), and the fill 

factor (FF), which are related by:

(2)

Determination of efficiency at SRC obviously requires the test device to be illuminated with the 

desired reference spectrum, but exact reproduction of a given solar spectrum is impossible, even 

outdoors in real sunlight. Approximations can be made with solar simulators using Xe arc 

lamps. For cells fabricated with a single semiconductor absorber, such as CdTe or crystalline Si, 

illumination with an incorrect spectrum produces an error in the measured current when the total 

irradiance is measured with a calibrated reference cell. Knowing the relative spectral response 

(or equivalently, the quantum efficiency, QE) of the test device and the simulator spectrum, the 

error can be mitigated using the spectral mismatch parameter, M [3-7].
2

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

1.1 Multijunction Efficiency Measurements

More complicated PV devices have multiple semiconductor subcells stacked on top of each other 

and electrically connected in series1. Light enters the top subcell of these multijunction devices 

and passes through to deeper subcells, minus the light absorbed in higher subcells. The light 

absorbed in each subcell causes the generation of unique internal photocurrents. These 

photocurrents each produce a voltage across the corresponding subcell that add to produce a 

higher voltage as compared to a single absorber device. Because the subcells are seriesconnected, the same current must flow through all the subcells, even if the photocurrents are not 

identical.

Under illumination, each subcell has a particular I-V curve that is a function of its photocurrent. 

However, independent measurement of these I-V curves is not possible because a multijunction 

solar cell has just two electrical terminals. The subcell internal I-V characteristics combine in a 

non-intuitive way to form the I-V curve of the solar cell that can be externally measured [8]. As 

a result, spectral content of light applied to multijunction devices affects not only the current but 

also the voltage and the shape (i.e. the fill factor, FF) of the measured I-V curve [9]. Thus, in 

order to accurately measure the performance of a multijunction device, it must be illuminated 

with light such that the photocurrents (ρ) correspond to those that would be produced by the 

reference spectrum. In general, photocurrent balancing (or tuning) must be done with a 

spectrally adjustable solar simulator [10-15].

Forming the ratios of the photocurrents (R) of every subcell with all other subcells is a way to 

map the photocurrent balance for any given spectrum. The R values correspond to the ratios of 

the effective irradiances impinging the subcells. The number of ratios needed is the mathematical 

combination of N subcells taken 2 at a time, or:

1, 3, 6, 10, 15..., for N = 2, 3, 4, 5, 6... (3)

An iterative adjustment procedure can be used in which photocurrent ratios are measured with 

calibrated reference cells that correspond to each subcell (also known as isotype reference cells) 

and the simulator spectrum is measured with an instrument called a spectroradiometer or 

spectrometer. Because the subcell photocurrents cannot be measured directly, they are instead 

inferred from the reference cell Isc values, modified by the spectral mismatch [14,15]. The ratios 

of the inferred photocurrents are compared, the spectrum is altered, and the process repeated 

until all ratios are sufficiently close to one.

Ideally, to facilitate the iterative procedure, the number of adjustable simulator parameters 

needed for testing any given multijunction device should be equal to N, with each parameter 

corresponding to the spectral regions of the individual subcells. If an adjustment alters the 

photocurrents of multiple subcells, the iteration is more difficult because more photocurrent 

ratios are changed.

 

1 The word “junction” is commonly used to refer to one portion of a multijunction solar cell that absorbs a particular 

wavelength region. Because the series connections between the absorbers use semiconductor devices called 

tunneling p-n junctions, in this report we instead refer to the individual absorbers as “subcells” to avoid confusion.
3

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Spectral tuning was first used for amorphous-Si cells with two and three subcells [10,11], and 

then later for high-efficiency group III-V solar cells [12], especially the GaInP/GaAs/Ge triple

scheme [14]. For reference, Fig. 1 shows quantum efficiency (QE) versus wavelength plots that 

are representative of the subcells discussed in this report. For a single-absorber solar cell, Isc is 

equal to a convolution over wavelength of its QE and the incident spectrum [3,4,7].

Figure 1. Example quantum efficiencies for subcells typically used for group III-V concentrator 

solar cells.

At NREL, multijunction performance measurements at SRC were first done in a Spectrolab, Inc. 

model X-25 Xe-arc simulator retrofitted with optical filters and apertures to subtract light in 

specific spectral regions. The iterative adjustment procedure could be quite tedious and timeconsuming, often requiring a whole day, and is intractable for devices with more than three 

subcells [14]. 

In 2011 the X-25 procedure was replaced with a new instrument called the one-sun multisource 

solar simulator (OSMSS) that features nine separate light sources covering different wavelength 

regions. All nine sources can be independently adjusted from zero to 150% of 1-sun levels, and 

the spectral adjustment is completely automated [16]. The OSMSS has successfully measured 

devices with as many as six subcells.

1.2 Concentrator Cell Measurements

Concentrator cells take advantage of how solar cell efficiency increases as sunlight is focused 

onto smaller areas. As the total irradiance on a cell is increased, the current scales roughly 

linearly while the voltage increases logarithmically. The efficiency (proportional to voltage 

times current, see Eq. 1) also increases approximately logarithmically until losses (especially 

series resistance) cause it to decrease at higher concentration. Thus, a plot of efficiency versus 

irradiance will show a peak value at some value of irradiance. 

Standard reporting conditions for concentrator cells are defined as the ASTM G173 direct 

reference spectrum [1], scaled to the desired concentration, and a cell temperature of 25°C. 

Although the G173 direct spectrum has a total irradiance of 900 Wm-2

, 1-sun is still defined as 

1000 Wm-2

, which effectively scales the spectrum by 10:9 independently of wavelength [6,14]. 
4

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Concentration is determined by assuming Isc is directly proportional to irradiance (slight 

deviations from this assumption are neglected here). Isc is measured at 1-sun and again under 

concentrated light; the ratio of the two is the concentration ratio, ×. Sunlight concentrated to 

150×, for example, corresponds to 150 kWm-2. Different cell designs have varying peak 

concentrations; the practical maximum concentration is about 2000×.

An important problem with efficiency measurements at SRC of concentrator cells is that the high 

irradiance levels cause heating, high enough to melt metallic materials. In a real system this 

means the design must include means to limit cell temperatures to acceptable levels using 

passive or active cooling. Indoor laboratory testing at SRC with the relatively cold temperature 

of 25°C dictates that temperature mitigation be done by restricting the illumination time using 

pulsed light sources. Commercial simulators have flash durations of a few milliseconds, so that 

if a test cell is mounted on a temperature-controlled block with good heat conduction, the 

temperature rise during the flash will be negligible.

2 Concentrator Efficiency Measurements at NREL

The NREL PV Cell and Module Performance Characterization Group has used two different 

commercial solar simulators for concentrator efficiency measurements with respect to SRC; 

these measurement systems are now described.

2.1 High Intensity Pulsed Solar Simulator (HIPSS)

NREL has used a Spectrolab, Inc. HIPSS for concentrator performance measurements since 1996

[14,17]. It features two long-arc Xe flash lamps with a total illumination time of 3 milliseconds; 

parabolic reflectors focus the light onto the test plane, which is about 1 meter below the lamps. 

A power supply called a pulse-forming network (PFN) charges a large capacitor to a setpoint of 

several thousand volts, then a high-voltage trigger initiates the flash discharge in the lamps. 

Spectrolab terms the trigger setpoint voltage divided by 10 the pulse network voltage (PNV). 

The flash irradiance is varied with the PNV and with adjustable slits in front of the lamps. To 

keep the lamp temperature constant, and thus also the spectral irradiance, the time between 

flashes should be a minimum of 1 to 2 minutes.

After an initial rise time, the irradiance is relatively stable for about 1 ms during which time the 

I-V curve is swept. An analog electronic load traces the I-V curve but can only sweep in one 

direction, from Isc to Voc. For unknown reasons, the load can oscillate when sweeping I-V

curves on some cells, sometimes to a level where it is completely unable to sweep an I-V curve. 

The analog-to-digital converters for the current and voltage measurements are only 12-bit, which 

limits the resolution to 1 out of 4096. Another limitation of the HIPSS is a tendency to give 

unreliable data for concentration ratios below 10×.

The spectral irradiance of a flash depends on the PNV setting; as the lamp voltage increases the 

temperature of the Xe plasma increases. This has the affect of shifting the spectral irradiance 

toward shorter wavelengths less than 700 nm in the visible and ultraviolet regions. 

Accurate measurements of the HIPSS’s spectral irradiance have been problematic because of a 

lack of suitable spectroradiometers. A system was developed at NREL that measures spectral 

irradiance during a flash at a fixed wavelength [17]; because of this limitation, acquisition of an 
5

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

entire spectrum requires many flashes and many hours of time. Thus, obtaining spectra for more 

than two PNV values is impractical. Figure 2 compares two measured HIPSS spectra, at different 

PNV values, against the direct reference spectrum.

Figure 2. Relative spectral irradiance versus wavelength of the ASTM G173 direct reference 

spectrum and the NREL HIPSS for two different PNV settings.

The PNV is the only parameter available for adjusting the spectrum, and the lack of suitable 

spectral measurements precludes use of the iterative spectral adjustment procedure described

previously. Despite these drawbacks, the HIPSS was the only available option for concentrator 

I-V measurements. For tandem cells such as GaInP/GaAs, the ratio of the GaInP top subcell

photocurrent to that of the GaAs bottom subcell can be adjusted by changing the PNV. By 

assuming the spectrum changes linearly with PNV, a calculation was devised to select a suitable

PNV based on the two measured spectra and the measured quantum efficiencies (QE) of the two 

junctions. The procedure adopted was:

• Measure the QE of each subcell [9-11,15]

• Calibrate the 1-sun Isc of the cell in the X-25 using the iterative spectral adjustment

• Determine the HIPSS PNV setting to balance the top and bottom photocurrents

• Flash the cell repeatedly under the HIPSS; measure I-V curves as the irradiance is varied

• Divide the Isc for each flash by the 1-sun Isc

• Calculate the irradiance and concentration ratio

• Plot the I-V parameters versus log (concentration ratio) and locate the peak efficiency.

Figure 3 is an example of HIPSS data for a GaInP/GaAs tandem that includes the 1-sun I-V data 

point, which was measured with the X-25 spectrally adjusted according to the QEs of the two 

subcells. Because GaAs does not absorb wavelengths greater than 900 nm (compare Figs. 1 and 

2), the simulator spectrum in the near infrared (IR) region is irrelevant. Each data point 

represents a separate flash and I-V curve. Note how all three curves match with the 1-sun 

values, and how the Voc increases logarithmically.
6

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 3. Open-circuit voltage, fill factor, and efficiency versus concentration ratio for a 

GaInP/GaAs tandem cell (HIPSS data).

This procedure was extended to GaInP/GaAs/Ge triple devices by considering the nature of the 

bottom Ge subcell, which absorbs light out to 1800 nm in the infrared and produces

photocurrents that are 30-40% higher than the top and middle subcells. From this, two 

assumptions were made: 1) the external current through the entire cell under illumination will 

likely be limited by either the top or middle subcell, and 2) the exact photocurrent level in the 

bottom subcell is less important. Thus, the large number of Xe emission lines in the 800-

1000 nm wavelength region of the HIPSS (Fig. 2) probably would not adversely affect results.

An example HIPSS measurement of a Ge-based triple cell is Fig. 4, in which the efficiency peaks 

at 41% when the concentration ratio is about 300×. The top-middle R was adjusted via the PNV 

setting of the simulator and the 1-sun measured with the X-25, as discussed above. Here again 

the Voc increases logarithmically from the 1-sun point through about two decades of 

concentration ratio. Without the ability to adjust the spectral irradiance under concentration,

verification of the PNV selection procedure has not been possible.
7

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 4. Open-circuit voltage, fill factor, and efficiency versus concentration ratio for a 41%-

efficient GaInP/GaAs/Ge triple cell (HIPSS data).

2.2 Tunable-High Intensity Pulsed Solar Simulator (T-HIPSS)

The lack of a simulator with adjustable spectral content was certainly realized as a severe 

limitation for accurate concentrator cell measurements, and in 2008 NREL entered into a 

contract with Spectrolab to develop a suitable instrument. The defined requirements were quite 

ambitious, and included: 1) independent spectral adjustment in six wavelength bands from 400 to 

1800 nm, 2) complete spectral irradiance measurement during a single flash, and 3) improved 

instrumentation for I-V curve measurements. Spectrolab’s proposal was to develop an improved 

version of their existing Model 420 tunable-high intensity pulsed solar simulator (T-HIPSS) that 

would be coupled with a high-speed spectrometer (which was not available at the time) and 

completely new instrumentation (the Model 420 T-HIPSS has the same analog instrumentation 

as the HIPSS).

In 2013 Spectrolab completed development and delivered the Model 460 T-HIPSS; the 

instrument has now replaced the HIPSS for all standard concentrator cell efficiency 

measurements at NREL. The T-HIPSS still uses a PFN, but has a single Xe bulb design instead 

of the two-bulb HIPSS, and 14 discrete thin-film dielectric mirrors replace the parabolic 

reflectors. Spectral adjustment is accomplished with computer-controlled shutters that cover the

mirrors, thus giving the ability to subtract light in six different wavelength bands (Fig. 5).
8

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 5. Spectral reflectance versus wavelength of the T-HIPSS Model 460 dielectric mirrors.

Other important features of the T-HIPSS include the state-of-the-art Avantes spectrometer, highspeed 16-bit analog-to-digital conversion, and programmable electronic loads that are able to 

sweep I-V curves in both directions. The loads are also well suited for measuring current at a 

fixed voltage, and can measure no-load Voc.

3 GaInAs-Based Triple Cells 

Development of improved concentrator cells has continued with the goal of ever-increasing 

efficiencies, which has increased the need for accurate measurements. The GaInP/GaAs/Ge 

structure has shown excellent results, 41% or greater for concentrator applications, and has 

supplanted Si for space power applications (in non-concentrating forms). Its theoretical 

efficiency limits, however, have dictated that research and development be directed toward 

replacing the Ge bottom subcell with a subcell having a more optimally current-matched ~1-eV 

bandgap. Several effective ways have been demonstrated to accomplish this, including the use of

bottom subcells based on GaInAs-based compound semiconductors.

2

 

From the performance measurements point-of-view, the most significant feature of these newer 

cells is that the photocurrents in all three subcells can be very close to each other. With its wider 

bandgap, GaInAs absorbs less light than Ge subcells (see Fig. 1) and therefore generates less 

current. However, such cells invalidate the assumptions made for HIPSS measurements that 

allowed for spectral adjustment based on the lamp voltage alone. If the photocurrent ratios

deviate significantly from unity, additional error should be expected.

 

2 The exact compositions of these semiconductors are unimportant for the purposes of this report.
9

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

3.1 Effects of Photocurrent Imbalance

By 2010 a significant number of GaInP/GaAs/GaInAs cells were being submitted to the Cell and 

Module Performance Characterization Group for concentrator measurement, and Fig. 6 is an 

example of HIPSS data. At first glance these data seem reasonable, but comparison with Figs. 3 

and 4 shows an important difference—extrapolation of the trends down to 1× do not match the 

same values of Voc, FF, and η as measured in the spectrally adjusted X-25. A ~3% relative 

discontinuity in η is evident, the Voc is offset by 37 mV, and the FF is higher by 1 percentage 

point.

Figure 6. Open-circuit voltage, fill factor, and efficiency versus concentration ratio for a 

GaInP/GaAs/GaInAs triple cell (HIPSS data).
10

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

3.2 Excess Irradiance Estimation

Without measurements of the HIPSS spectral irradiance it is not possible to know the exact 

photocurrent ratios for Fig. 6, but the excess Voc is an important clue to understanding what is 

happening. At open-circuit, no current is flowing through the cell’s external leads and the 

voltage across the leads is simply the sum of the three subcells. For this cell at 1-sun, the 

individual subcell contributions to the overall Voc are: GaInP: 1.440 V, GaAs: 1.020 V, and 

GaInAs: 0.640 V. If the middle-top R is equal to 1, any voltage increase will be the result of 

extra photocurrent in the bottom subcell at wavelengths between 900 and 1300 nm (see Figs. 1 

and 2). 

Photocurrent ratios can be quantified without spectral irradiance if the is spectral mismatches 

between isotype cells and their corresponding subcells are assumed to be unity (true if they have 

identical QEs). Figure 7 shows the results of measuring isotype Isc ratios as the HIPSS PNV was 

varied through its entire range, where the vertical arrow shows the PNV at which the middle-top

R is unity, PNV=372, and the horizontal arrow shows the ratios associated with the bottom at 

this condition, which are 1.34 (the bottom-top and bottom-middle ratios are always equal when 

the middle-top is unity because of how the ratios are defined).

Figure 7. Photocurrent ratio versus HIPSS PNV for a GaInP/GaAs/GaInAs triple cell determined 

with isotype reference cells and assuming unity spectral mismatch.

Figure 7 also demonstrates that for any value of PNV, the HIPSS spectral irradiance is such that 

the bottom subcell will always generate photocurrents that are artificially high, regardless of the 

middle-top R.
11

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

3.3 Fill Factor Discontinuities

To demonstrate the effects of excess bottom irradiance, a numeric model was used to generate 

FF versus concentration for GaInAs- and Ge-based bottom subcells. The top and middle 

subcells were GaInP and GaAs with diode ideality factors (n) equal to one, and the bottom 

subcell ideality factors were two in both cases. A series resistance was chosen to simulate a 

reasonable roll-off at high concentration. These calculations are plotted in Fig. 8, where the solid 

curves correspond to photocurrents balanced with the direct reference spectrum, while the 

dashed curves have a 30% excess photocurrent in the bottom subcells to simulate the HIPSS 

measurement conditions.

Figure 8. Modeled fill factor versus concentration ratio for two different triple cells, 

GaInP/GaAs/GaInAs and GaInP/GaAs/Ge.

This work demonstrates that: 1) FF versus concentration is predicted to be a smooth curve 

without discontinuities, 2) the discontinuities observed in GaInAs-based triple cells between the 

X-25 and HIPSS measurements can be reasonably explained by incorrect spectral irradiance, and 

3) the effects of excess bottom-subcell photocurrents are much stronger in GaInAs bottom 

subcells compared with Ge subcells.

By taking advantage of the OSMSS’s spectral adjustment capabilities, it is possible to measure 

how the FF varies with the excess irradiance. First, the simulator was adjusted to the reference 

spectrum at 1-sun for a GaInP/GaAs/GaInAs cell similar to the cell from which Fig. 6 was 

generated. Next, the OSMSS light source corresponding to the bottom subcell was varied from 

70% to 140% and the I-V curve measured at each value. These data are plotted in Fig. 9. Note 

that as the bottom subcell increases above 100% the FF increases monotonically. Also, the Isc is

constant in this region, indicating either the top or middle is the limiting subcell, while the 

bottom subcell limits Isc when its irradiance is reduced below 100%.
12

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 9. Short-circuit currant and fill factor versus bottom subcell irradiance for a 

GaInP/GaAs/GaInAs triple cell (OSMSS data).

3.4 Comparison of HIPSS and T-HIPSS Data

With the T-HIPSS, it is now possible to adjust the spectral irradiance so that the R values are

within 1.00 ± 0.01 for triple cells and compare the I-V parameters against HIPSS data in which 

the bottom subcell is overdriven. In Fig. 10, the HIPSS data from Fig. 6 is compared with two 

separate T-HIPSS measurements on the same GaInP/GaAs/GaInAs cell; for one data set the 

spectral irradiance was adjusted until all three R-values were within ±0.004 of unity, and for the 

second set light to the bottom subcell was increased until the bottom-top and bottom-middle R

values were 1.45. Thus, this second set simulates light conditions in the HIPSS by overdriving 

the bottom subcell with 45% extra irradiance. It is evident that the T-HIPSS tuned data set 

agrees quite well with the OSMSS data when the trends are extrapolated down to 1-sun, while 

the other two sets show large offsets for the FF and η.
13

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 10. Comparison of I-V parameters versus concentration ratio for the triple cell from Fig. 6

(HIPSS and T-HIPSS data).

3.5 Voc Increases Due to Excess Subcell Photocurrents

Close examination of the T-HIPSS Voc data in Fig. 10 reveals a constant offset of +10 mV from 

the tuned to the +45% excess bottom subcell conditions over the entire range of concentrations. 

From solar cell theory, a change of Voc caused by a change of photocurrent in a single cell at 

25°C can be expressed as [18]:

(4)

Note that this change depends only on the diode quality factor and the photocurrent ratio, and 

isn’t related to the bandgap. For a multijunction cell, the total change will be the sum from each 

subcell:
14

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

(5)

When only the bottom subcell irradiance is changed, Eq. 5 reduces back to Eq. 4. With ∆Voc and 

R known, solving for the diode quality factor gives n = 1.047, a quite reasonable value.

It has been assumed that the spectral conditions in the HIPSS are such that the middle-top subcell 

R is correct, but this may not true. If this ratio is incorrect, then according the Eq. 5, the Voc

offset will include a contribution from the second subcell. Because the HIPSS FF and η in 

Fig. 10 are both higher than the T-HIPSS +45% bottom subcell curves, the HIPSS spectral 

conditions are likely farther away.

Looking at the Voc plots in Fig. 10 again, three separate regions can be discerned. Above about 

200×, the rate of change of Voc with concentration is reduced, reaching a drop of about 20 mV at 

1100×. This drop is likely caused by cell heating during the flash I-V measurement. Between 

10× and 100× the increase with concentration is logarithmic, and a curve fit in this range 

indicates the n factor sum (see Eq. 5) is 3.30. Below 10× the change is still logarithmic, but the n

factor sum has increased to 3.94.

3.6 Empirical Spectral Imbalance Data Correction Procedure

Figure 10 suggests the possibility of correcting concentrator performance data for the effects of a 

non-adjustable solar simulator, if a 1-sun data point obtained with a spectrally adjustable 

simulator is available. By assuming the shapes of the curves do not vary with spectral irradiance, 

constant offsets are subtracted from Voc and η data; the offsets are calculated from logarithmic 

extrapolation down to 1-sun and subtracted from the 1-sun data points. Fill factors 

corresponding to the corrected Voc and η data can then be calculated.

By applying the procedure to the HIPSS and T-HIPSS +45% bottom data in Fig. 10, the results 

can then be directly compared with the T-HIPSS tuned data; this comparison is shown in Fig. 11. 

The procedure used was:

• Calculate ∆Voc. For the T-HIPSS we take advantage of the tuned data and apply the 

constant -10 mV offset, as discussed above. The HIPSS data, however, lacks data points 

below 4×, and extrapolating a logarithmic fit over the 4× to 30× range down to 1-sun 

gives a ∆Voc of -38 mV. Because this offset would overcorrect and introduce error, no 

∆Voc was applied to the HIPSS data.

• Calculate ∆η. These were done over the 2× to 40× range and gave -1.10% for the HIPSS 

data, and -0.86% for the T-HIPSS +45% bottom data.

• Calculate and for each data point.

• Calculate the FF that corresponds to the corrected Voc and η: .

The results of the data corrections are shown in Fig. 11.
15

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 11. Comparison of I-V parameters versus concentration ratio for the triple cell from Fig. 10, 

corrected for spectral imbalance (HIPSS and T-HIPSS data).

4 Conclusions

Although it has been known for many years that accurate efficiency measurements of 

multijunction solar cells to SRC require spectrally adjustable solar simulation, extension of these 

measurement principles to high-efficiency concentrator cells has been hindered by the lack of 

capable I-V measurement systems. Specifically, high-speed acquisition of spectral irradiance 

data and independent spectral adjustment in sufficient wavelength bands for high intensity pulsed 

Xe simulators have not been available. 

In general, the spectral content of unfiltered Xe flash lamps for IR wavelengths greater than 

900 nm is too high due to the Xe emission lines. Measurement of GaInP/GaAs/Ge triple cells has

been possible using such simulators, however, because the Ge bottom photocurrents were much 

higher than those of the top and middle subcells. Using this technique for Ge-based cells has 

been validated.
16

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Newer triple cell designs with bottom subcells that respond to a narrower wavelength range are 

therefore much more sensitive to excess irradiance. The internal I-V characteristics of recent

high-efficiency GaInP/GaAs/GaInAs cells combine to produce external I-V curves with inflated

fill factors when illuminated with a raw Xe spectrum. This propagates as an error in the 

measured efficiency that is always too high.

A good rule-of-thumb based on our work is that any concentrator SRC efficiency measurement

of a triple cell, in which the subcell photocurrents are comparable in magnitude, uses unfiltered 

Xe simulator illumination, and the fill factor exceeds 88 to 89% at high concentration, should be 

flagged and suspected of having excess bottom-subcell irradiance.

Lastly, this error can be avoided with proper spectrally adjustable measurement systems, such as 

the Spectrolab T-HIPSS and the OSMSS. If a spectrally adjustable concentrator simulator is not 

available, a correction procedure based on logarithmic extrapolation can be used to mitigate the 

effects of excess subcell irradiance, provided that a 1-sun data point from an adjustable simulator 

is available. This empirical correction can lose validity if the uncorrected I-V performance data 

do not include sufficient data points at low concentration.

While the error has been identified in GaInP/GaAs/GaInAs triple cells measured with unfiltered 

Xe-arc lamps, it should be emphasized that similar errors can arise whenever the photocurrent in 

a single subcell is artificially increased, regardless of the subcell’s bandgap or semiconductor 

composition. Figure 8 demonstrates that it also occurs in Ge-based cells, although to a lesser 

degree. Increasing the photocurrent in a GaAs middle cell, for example, will also increase the 

measured efficiency.
17

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

References

[1] ASTM G 173–12 (2012). “Standard Tables for Reference Solar Spectral Irradiances: Direct 

Normal and Hemispherical on 37° Tilted Surface.” Annual Book of ASTM Standards (14.04). 

West Conshohocken, PA: ASTM International.

[2] ASTM E 490–06 (2006). “Solar Constant and Air Mass Zero Solar Spectral Irradiance 

Tables.” Annual Book of ASTM Standards (15.03). West Conshohocken, PA: ASTM 

International.

[3] Osterwald, C.R. (1986) “Translation of Device Performance Measurements to Reference 

Conditions.” Solar Cells (18); pp. 269–279.

[4] Emery, K.A. (1986) “Solar Simulators and I-V Measurement Methods.” Solar Cells (18); pp. 

251–260.

[5] ASTM E 948–09 (2009). “Standard Test Method for Electrical Performance of Photovoltaic 

Cells Using Reference Cells Under Simulated Sunlight.” Annual Book of ASTM Standards

(12.02). West Conshohocken, PA: ASTM International.

[6] Emery, K. (2011). “Measurement and Characterization of Solar Cells and Modules.”

Handbook of PV Sci. and Eng., 2nd Ed. (7). Ch. 18; pp. 797-840. John Wiley & Sons, W. Sussex, 

UK, ISBN -0-470-72169-8.

[7] ASTM E 973–10 (2010). “Standard Test Method for Determination of the Spectral Mismatch 

Parameter Between a Photovoltaic Device and a Photovoltaic Reference Cell.” Annual Book of 

ASTM Standards (12.02). West Conshohocken, PA: ASTM International.

[8] Wanlass, M.W.; Albin, D.S. (2004). “Rigorous Analysis of Series-Connected, Multi-Bandgap, 

Tandem Thermophotovoltaic (TPV) Energy Converters.” Proc. 6th Conf. on Thermophotovoltaic Gen. of 

Electricity, Freiburg, Germany; AIP Conference Proceedings (738); pp. 462-470.

[9] McMahon, W.E.; Emery, K.E.; Friedman, D.J.; Ottoson, L.; Young, M.S.; Ward, J.S.; 

Kramer, C.M.; Duda, A.; Kurtz, S. (2008). “Fill Factor as a Probe of Current-Matching for 

GaInP2/GaAs Tandem Cells in a Concentrator System During Outdoor Operation.” Prog. in PV: 

Res. Appl. (16); pp. 213-224.

[10] Burdick, J.; Glatfelter, T. (1986) “Spectral Response and I-V Measurements of Tandem 

Amorphous-Silicon Alloy Solar Cells.” Solar Cells (18); pp. 310–314.

[11] Emery, K.A.; Osterwald, C.R.; Glatfelter, T.; Burdick, J.; Virshup G., (1988). “A 

Comparison of the Errors in Determining the Efficiency of Multijunction Solar Cells by Various 

Methods.” Solar Cells (24); pp. 371-380.

[12] Virshup G.F. (1990). “Measurement Techniques for Multijunction Solar Cells.” Proc. 21st

IEEE PV Spec. Conf., Kissimimee, FL; pp.1249-1255.
18

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

[13] Nagamine, F.; Shimokawa, R.; Suzuki, M.; Abe, T. (1993). “New Solar Simulator for 

Multi-Junction Solar Cell Measurements.” Proc. 23rd IEEE PV Spec. Conf., Louisville, KY; pp. 

686-690.

[14] Emery, K.; Meusel, M.; Beckert, R.; Dimroth, F.; Bett, A.; Warta, W. (2000) “Procedures 

for Evaluating Multijunction Concentrators,” Proc. 28th IEEE Photovoltaic Specialists Conf., 

Anchorage, AL; pp. 1126-1130.

[15] ASTM E 2236–10 (2010). “Standard Test Methods for Measurement of Electrical 

Performance and Spectral Response of Nonconcentrator Multijunction Photovoltaic Cells and 

Modules.” Annual Book of ASTM Standards (12.02). West Conshohocken, PA: ASTM 

International.

[16] Moriarty, T.; Jablonski, J,; Emery, K. (2012). “Algorithm for Building a Spectrum for 

NREL One-Sun Multi-Source Simulator.” Proc. 38th IEEE Photovoltaic Specialists Conf.,

Austin, TX.

[17] Kiehl, J.; Emery, K.; Andreas, A. (2004). “Testing Concentrator Cells: Spectral 

Considerations of a Flash Lamp System,” Proc. 19th Euro. PV Sol. Energy Conf. and Exhibition, 

Paris France; 5BV.2.11.

[18] Green, M.A. (1995),“Silicon Solar Cells: Advanced Principles and Practice.” Univ. of New 

South Wales, Sydney, Australia.