OCT 2 4 19

-7<S/

NBSIR 79-1909

Measurement Techniques for

Solar Cells, Quarterly Report:

April 1 to June 30, 1978

D. E. Sawyer, H. K. Kessler,

and H. A. Schafft

Electron Devices Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

October 1979

Prepared for Department of Energy

Division of Distributed Solar Technology

Advanced Materials R&D Branch

Under Task Order A054-SE of Interagency

Agreement EA-77-01 -6010

NBSIR 79-1909

MEASUREMENT TECHNIQUES FOR

SOLAR CELLS, QUARTERLY REPORT:

April 1 to June 30, 1978

D. E. Sawyer, H. K. Kessler,

and H. A. Schafft

Electron Devices Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

October 1 979

Prepared for Department of Energy

Division of Distributed Solar Technology

Advanced Materials R&D Branch

Under Task Order A054-SE of Interagency

Agreement EA-77-01 -6010

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Luther H. Hodges, Jr.. Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
'

-
TABLE OF CONTENTS

Page

Executive Summary 1

1. Introduction 2

2. Work Performed During Reporting Period 2 2.1 Development of Solar Cell Device and Material Measurement

Techniques 2

2.1.1 Cell Scanning Technique Employing Current-Source

Biasing 2

2. 1.1.1 Description of Technique 2

2. 1.1. 2 Cell Scanning Results 3

2. 1.1. 3 Mathematical Modeling of Solar Cells ... 5 2.1.2 Equipment for Light-Biasing Cells 5

2.1.3 Laser Flying-Spot Scanner Modifications 5

2. 1.3.1 Increase in Scanning Area 5

2. 1.3. 2 Increase in Bandwidth of Cell-Coupling

Network ..... 5

2.2 Workshops and Symposia 8

References 9

Appendix A 10

Appendix B 12

Appendix C 19
PREFACE

This work was conducted as part of the Semiconductor Technology Program

of the National Bureau of Standards (NBS). This program serves to focus

NBS research to enhance the performance, interchangeability, and reliability of integrated circuits and other semiconductor devices including

solar cells through improvements in measurement technology for use in

specifying materials and devices in national and international commerce

and for use by industry in controlling device fabrication processes.

This research leads to carefully evaluated and well-documented test procedures and associated technology. Special emphasis is placed on the

dissemination of the results of the research to the appropriate technical

community. Application of these results by industry will contribute to

higher yields, lower cost, and higher reliability of semiconductor devices. Improved measurement technology also leads to greater economy in

government procurement by providing a common basis for the purchase specifications of government agencies and, in addition, provides a basis for

controlled improvements in fabrication processes and in essential device

characteristics.

The segment of the Semiconductor Technology Program described in this

quarterly report is supported by the Division of Distributed Solar Technology of the Department of Energy (DOE) under DOE Task Order A054-SE of

Interagency Agreement EA-77-A-01-6010. The contract is monitored by Dr.

Donald L. Feucht, Chief of SERI's Advanced Materials R&D Branch. The NBS

point of contact for information on the various task elements of this

project is Dr. David E. Sawyer of the Electron Devices Division in the

NBS Center for Electronics and Electrical Engineering.

Certain commercial equipment, instruments, or materials are identified in

this report in order to adequately specify the experimental procedure.

In no case does such identification imply recommendation or endorsement

by the National Bureau of Standards, nor does it imply that the material

or equipment identified is necessarily the best available for the purpose.

iv
Measurement Techniques for Solar Cells

Quarterly Report

April 1 to June 30, 1978

D. E. Sawyer, H. K. Kessler

and H. A. Schafft

EXECUTIVE SUMMARY

This report covers research performed in the period April

1 to June 30, 1978 on the Program on Solar Cell Measurement

Technique Development and Other Services by the Electron Devices Division of the National Bureau of Standards. The objectives of the program are to assist the Department of Energy

(DOE) thin film photovoltaic effort by developing solar cell

device and material measurement techniques by using the NBSdeveloped laser flying-spot scanner, and by assisting the DOE

in organizing and hosting appropriate workshops and symposia

and providing general consultation and liaison services.

A major portion of the program is the development of techniques that use the scanner to reveal solar cell quantities of

interest such as emitter sheet resistance and poor ohmic contact of portions of the metallization to the underlying emitter. The technique proposed last quarter, which employs cell

forward-biasing during scanning to reveal these quantities, was implemented. With an electrical current source to forward bias

the cell, cracks and metallization regions disconnected from

the cell output electrode were readily revealed.

The mathematical analysis work relating laser scanning

results to cell parameters and defects has been extended to

more realistic cell geometries than the one-dimensional case previously treated. This work will be applicable to a wider

range of real-life situations.

Apparatus development work conducted this quarter included: completion of the high-intensity insolation source used for light biasing a cell while it is being scanned, improvement in coupling to the display electronics cells that are simultaneously biased and scanned, and increase of the scanning

area so that 50-mm cells can be scanned in their entirety without repositioning.

The workshop on Stability of (Thin Film) Solar Cells and

Materials was held on May 1 to 3, 1978 at the National Bureau

of Standards, Gaithersburg, Maryland.

1
1 . INTRODUCTION

This report covers work performed in the period April 1 to June 30,

1978 on the Program on Solar Cell Measurement Technique Development and

Other Services by the Electron Devices Division of the National Bureau of

Standards under Task Order A054-SE of Interagency Agreement EA-77-A-01-

6010.

The objectives of the program are to assist the Department of Energy

(DOE) Advanced Materials R&D Branch photovoltaic effort in the following

ways:

1. Development of solar cell device and material measurement techniques using the laser flying-spot scanner that was originally

developed at NBS for use on integrated circuits and discrete

transistors.

2. Assistance to DOE in organizing and hosting appropriate workshops and symposia and providing general consultation and liaison services.

Activities and accomplishments in the various project areas during this

reporting period are described in the following sections.

2. WORK PERFORMED DURING REPORTING PERIOD

2.1 Development of Solar Cell Device and Material Measurement Techniques

2.1.1 Cell Scanning Technique Employing Current-Source Biasing

2.

1.1.1

Description of Technique . The analysis presented in the

previous Quarterly Reports [1,2] shows how one may make use of the distributed nature of a solar cell to determine cell parameters of interest

and to detect various cell faults. This distributed nature is an intrinsic property of all cells and so techniques that are based on the distributed nature of the cells should be applicable to a large number of

cell types and configurations. The first Quarterly Report [1] described

how one might use high frequency (e.g., microwave) modulated light and

the distributed junction capacitance to determine cell quantities. The

second Quarterly report [2] described a much simpler method which uses

the low-frequency conductance of each of the elemental diodes making up

the cell. In this simpler method, the cell is scanned with unmodulated

light as it is forward biased. It was suggested [2] that biasing could

be provided either by shining light on the cell (and calculations were given to allow one to estimate the required light intensity) or by using

an external (electrical) current source. During the present reporting

period, several types of p-n junction solar cells were scanned while so forward biased. Although scanning results obtained with an external

source may not be identical to those obtained with light-biasing for the same (internal) current value, it was found that an external currentsource provided a very convenient way of assessing cell fabrication and

service-connected defects.

2
2. 1.1.2 Cell Scanning Results . The highlights of cell defectdetection experiments performed during the present reporting period were

given in a late-news paper delivered at the 13th Photovoltaic Specialists

Conference, Washington, D.C. The abstract of this paper is included in

Appendix A of this report. A more complete discussion of the results is

presented below.

2.1. 1.2.1 Metallization Integrity . The upper sketch and photographs in Appendix A are for one of the first cells scanned while energized from a current source. A pair of metallization breaks detected by

means of an optical microscope are shown by circles in the sketch. The

surrounding shaded rectangle shows the area scanned. Because of the

electrical redundancy in connecting the fine (50—pm) herringbone metallization grid lines in the central portion of the cell to the wider

(280-pm) metallization splines, two breaks in a fine line are required to

disconnect any appreciable length of fine-line metallization from the

cell output electrode. On the left is a photomicrograph of the line

breaks indicated in the central sketch. On the right are two photographs

of the display screen of the laser scanner. The display presentation is

a mix of y-axis and z-axis display modes, i.e., an increase in photoresponse simultaneously produces a larger upward deflection of a horizontal

scan line and an increase in screen brightness. The upper of the two

photographs shows the photoresponse with no applied cell current; the

lower shows the photoresponse with an applied current of 126 mA, which

corresponds to a value of about 80 percent of the cell's short-circuit

output current were it exposed to AMI insolation. The metallization

breaks are not detected at zero bias but are readily observed with

forward bias by the lowered photoresponse in their vicinity. The breaks

appear to be the only metallization defects in the scanned area. The

metallization which is continuous to the splines appears to make uniform

electrical contact to the underlying emitter, as evidenced by the photoresponse attaining a maximum adjacent to the metallization. Even though

scanning was performed with a spot of light, the general shape of the

photoresponse versus position away from the broken metallization region

is in qualitative agreement with the results predicted by a line-scan

analysis [2] and by the mathematical results presented in Appendix B.

Other portions of the cell having disconnected metallization regions were

laser-scanned with results similar to those reported above.

The results obtained in these experiments suggest several ideas:

1. In order for photoresponse at the edge of a metallization stripe

to achieve a common, maximum value, the metallization must be continuous

to the output lead and must make a uniform ohmic contact to the underlying semiconductor. These are precisely the "bottom line" requirements

for effective metallization, and so the scanning technique described

should provide a test for metallization efficacy.

2. Metallization-efficacy testing can be done under production line

conditions by unskilled personnel. With the equipment set up for a particular cell type and using the intensity-modulation display mode, one

3
only requires that the operator note if a dark line (shadow of the

metallization stripe) runs through the center of a dark region, and no knowledge of devices or fabrication processes is required.

3. By dividing the scanning response under bias with the zero-bias

response on a spatial point-by-point basis, the fabrication and servicerelated loss mechanisms should be even easier to perceive and measure.

The eye can make comparisons of this sort to some extent , but it would be

better to use a computer.

4. Electron-beam instruments such as the scanning electron microscope (in the electron-beam-induced-current mode) might also be used in

the same manner as was done with light. Most of these instruments appear

to be designed to image small areas at high magnification, and hence, devices the size of working solar cells may require appreciable repositioning for their entire area to be scanned.

2.1. 1.2.2 Crack Detection. The biased-cell scanning technique was also used to locate cracks in solar cells. This is an important application because cracks have been known to cause cell arrays to fail, sometimes dramatically, with electric arcs and flames produced at the crack

[3J. If the cell surface is smooth and the crack is sufficiently wide,

the crack may be detected under favorable conditions by its scattered

light during optical inspection. If the surface is not smooth, cracks

wide enough to stand out against a smooth surface may be lost in the surface texture and go undetected. The NBS-developed method makes use of

the fact that the semiconductor electrical conductivity is discontinuous

across the crack. By using this method, one might expect to detect

cracks which are too fine to be revealed by optical inspection techniques. With the cell forward biased, one sees a change in the cell's

photoresponse as one scans across the crack. Experimentally, one sometimes sees this manifested as a slope change and sometimes by an amplitude change in the photoresponse scan. A crack between a pair of metallization grids should not influence the photoresponse outside that re- gion. Occasionally it does, and some areas of the cells delineated by

cracks may exhibit a lowered scanning response everywhere. This could be

due to differences in resistances between the cell output electrodes and

the various semiconductor regions contacted.

The lower half of the figure sheet in Appendix A illustrates both

the slope-change (left) and amplitude-change (right) possibilities discussed above of a cell purchased commercially. The crack location of

this 4-in. diameter cell was confirmed by optical inspection (cracks in

other cells not discernible to the eye were scanned subsequently and located with the forward-biased scanning techniques). In the display photographs, several surface features can be seen that are not cracks but

show similar zero-bias scanning signatures. These features appear to be

benign and are probably due to scratches, dislocation lines, or the presence of unwanted material. Since cell cracks (when they are wide enough

to produce photoresponse perturbations without the cell being biased) and

these blemishes can yield the same zero-bias scanning signature, the

harmless features could be mistakenly labeled as cracks and the cell re4
jected needlessly. Alternatively, a true crack might be mistaken as a benign cosmetic blemish. The sets of photographs demonstrate that separation of these classes can be accomplished with forward-bias scanning.

2. 1.1. 3 Mathematical Modeling of Solar Cells. To support the laser

scanning work, K. Lehovec and A. Fedotowsky, under subcontract at the

University of Southern California, are performing mathematical modeling

of cells containing defects such as regions of open metallization and

cracks. Initial modeling work completed this reporting period. appears in

Appendix B.

2.1.2 Equipment for Light-Biasing Cells

The program needs an illuminator to bias cells optically while they are scanned. Effective insolation levels of 20 suns AMI are desired.

The light output must be free from modulation produced either by the lamp

power-supply or by lamp internal processes. An illuminator has been designed and constructed to satisfy these criteria. A photograph of this

illuminator with the top cover removed is shown in figure 1. The light source is a 60-W quartz-halogen incandescent lamp. The illuminator uses four groups of heat filters and condensing and focusing lenses arranged

symmetrically around the long axis of the lamp. This arrangement, which

captures almost all of the light available, is designed so that the light

is focused onto the receiving ends of four flexible fiber-optic pipes

which direct the light to the cell area being scanned. A muffin-type fan

mounted below the bottom plate cools the lenses and filters. A small

silicon solar cell, mounted inside the illuminator, powers the external

meter shown to monitor the light from the lamp. This circuit permits one

to easily adjust the lamp power source for a given light output at the

ends of the fiber-optic pipes. Figure 2 shows the laser scanner being

used with the illuminator.

2.1.3 Laser Flying-Spot Scanner Modifications

2. 1.3.1 Increase in Scanning Area. Increasing the cell size that can be scanned at one setting of the equipment is a continuing activity.

Before the beginning of the solar cell program, the scan excursion was limited to about 3 mm by the optical parts available for the particular

microscope used for the scanner optics. By removing lenses and replacing

the original microscope lenses with lenses purchased from other sources,

the scan excursion was increased to 11.5 mm, and the working distance

(objective lens to specimen distance) was increased to permit the inclusion of the optical-bias fiber-optic pipes described in section 2.1.2.

Additional increases in scan area and working distance were achieved by

replacing the entire microscope optical system with a 35-mm camera lens

having a focal length of 55 mm. The maximum scan excursion is now 50 mm with a spot resolution of about 25 pm. This resolution is adequate to

resolve the finest metallization grids found on nonconcentrator solar

cells

2. 1.3.2 Increase in Bandwidth of Cell-Coupling Network. It is

necessary to couple forward-biased cells to the scanner display elec5
Figure 1. The high- intensity light source with the top cover removed.

6
Figure 2. The high- intensity light source being used with the laser

scanner.

7
tronics by a means that ensures that the cell sees a low impedance, nec- essary [ 2 J to maintain the scanned cell signal-to-noise ratio and to

minimize the effects of the cell's capacitance at the maximum permissible

scanning rate. The coupling found to be most satisfactory to date is a transformer in conjunction with a large-value dc blocking capacitor.

Further improvements have been achieved in bandwidth, and hence in

display-screen detail, by increasing the capacitance of the blocking

capacitor from 9,000 yF to 27,000 yF, and by replacing the coupling

transformer with a more suitable one. The bandwidth for the combination

is now 5 Hz to 13 kHz (3-dB points); this bandwidth yields adequate

display-screen definition.

2.2 Workshops and Symposia

A workshop on the Stability of (Thin Film) Solar Cells and Materials

was conducted at the National Bureau of Standards on May 1 to 3, 1978 as part of the Department of Energy's National Photovoltaic Program. The

workshop program is included as Appendix C. The workshop addressed many

of the obstacles to achieving stability and long life of terrestrial

solar cell devices using forefront technology. The following three

groups of exploratory solar cell materials and concepts were considered:

(1) CU 2 S/ [CdZn]S, Cu-ternaries/ CdS , InP/CdS, and amorphous Si, (2)

polycrystalline, MIS, and conducting oxide Si, and (3) polycrystalline

and AMOS (antireflection-coated metal-oxide-semiconductor) GaAs.

Researchers in the field reviewed modes and mechanisms for failure

and degradation of these systems and the status of present reliability

testing. Speakers from related device technologies discussed measurement

and test approaches that have been used to achieve high device reliability. Two talks were of particular interest. One described a technique

for detecting changes in the physics of failure with increasing severity

of a stress parameter to establish the maximum possible acceleration factor for a given failure. The other described a technique for uncoupling

different failure mechanisms by an analysis of failure rate data.

Discussions in the working groups of the workshop led to the identification of a number of needs that require attention before meaningful

headway can be made in the achievement and quantification of stability

and long life for solar cells developed using forefront materials and

device technologies.

The main conclusion reached by the 102 scientists and engineers who

attended the workshop was that more research needs to be conducted in

this forefront technology. In particular, they identified the need to

study the chemical, mechanical, and physical compatibility of the various

materials used in these solar cell devices and the influence of compatibility on device characteristics. Also expressed was the need for the

development of performance and measurement standards for use in characterizing these devices. Finally, the need for adequate device manufacturing process controls and adequately described test procedures and

data was underscored as a prerequisite for meaningful headway in the

quantification of solar cell stability and long life.

8
REFERENCES

Sawyer, D. E. , Kessler, H. K., and Schafft, H. A., Measurement

Techniques for Solar Cells, Quarterly Report, September 15 to

December 31, 1977, NBSIR 78-1488 (July 1978).

Sawyer, D. E., Kessler, H. K., and Schafft, H. A., Measurement

Techniques for Solar Cells, Quarterly Report, January 1 to March 31,

1978, NBSIR 78-1513 (September 1978).

Ross, R. G., private communication.

9
APPENDIX A

A Technique for Using an Optical Scanner

to Reveal Solar Cell Defects*^

David E. Sawyer

Electron Devices Division

National Bureau of Standards

Washington, D.C. 20234

(301) 921-3621

Except for grossly deficient solar cells, most of the previous attempts to use an optical-spot scanner to reveal cell defects such as cracks and poor metallization have not been very successful. In the work

reported here, the cell is forward biased while scanning with the optical

spot. Under these conditions, one makes use of the cell's distributed

nature, an intrinsic property shared by all solar cells, to readily re- veal such defects. The low-frequency small-signal equivalent circuit of

the biased and scanned cell is a three-dimensional resistive array, and

the light spot is represented by a current generator moving within the

array as the spot scans the cell. The array components are normally made

up of the cell "emitter" sheet resistance and the distributed resistance

for the p-n junction. This distributed resistance is the local slope of

the voltage current for each increment in cell area. A simplified, twodimensional analysis of this array predicts that cracks and regions of

poor metallization can be pinpointed while scanning the cell if it is

adequately forward biased. This predicted behavior has been confirmed by

measurements made on cells with known defects. Measurements have been

made on silicon flat plate and gallium arsenide concentrator cells using

forward-bias current somewhat less than those which would flow with the

cells exposed to their normal insolation levels. The technique is nondamaging; it requires no electrical contacts to the cell other than those

already present, and it can be used on encapsulated or unencapsulated

cells in almost any laboratory or test environment.

£ This work was supported by DOE's Advanced Materials R&D Branch under

Task Order A054-SE of the Interagency Agreement EA-77-A-01-6010.

t Contribution of the National Bureau of Standards, not subject to copyright.

10
aEULLUAummiEfifiin

0,9 A DC BIAS 291

Am CELL CURRENT

0,9 A DC BIAS 292

AMI CELL CURRENT

11
APPENDIX B

Light Beam Probing of Solar Cells

K. Lehovec and A. Fedotowsky

Department of Electrical Engineering

University of Southern California

Los Angeles, California 90007

B.l. Introduction

D. Sawyer and coworkers at NBS are scanning solar cells by a modulated light spot as a means to locate and identify cell faults by inspection of the cell output pattern. Our aim is the modeling of various

faults and the computation of the resulting output patterns. Comparison

of the computed patterns with observations will assist in identifying the

faults in experimental cells.

The solar cell will be modeled by a two-dimensional distributed network of diodes connected by semiconductor sheets having sheet resistances

Pj on top of the junction and pg on the bottom. The corresponding

bulk resistivities are S2T and iig, respectively. An edge view of the

model is shown in figure Bl. The effect of light is to place a current

source of total magnitude I L across the diodes illuminated. A top view

of the electrode configuration is shown in figure B2. The electrodes are

of length W. Figure B3 shows an element of the distributed network of

figure Bl and indicates the notation used in the analysis; 6(x - xj) is a delta function centered at x = xj. The notation used here is con- sistent with that used in reference [ B— 1 J

B.2. Basic Equations

The dark current per unit area JD depends exponentially on the

voltage across the junction:

J n

= J (e

BV - 1) . ( B 1

)

D O

The pre-exponential coefficient J Q is the reverse saturation current

per unit area and B = q/akT with a the diode quality factor.

By neglecting lateral diffusion currents, the lateral sheet current

densities are

J

T

= " VV

T

/“

T

0*-2a)

and

J

s = - Ws /«

s (B-2b)

where the subscripts refer to top and substrate (i.e., base) of the junction, respectively. Conservation of charge requires that

12
Figure Bl . One-dimensional cross-section through the equivalent circuit

of a solar cell portion illuminated by a modulated light beam at x = xj_

Output is ac-shorted by a large capacitive load.

X

Figure B2 . Top view of the solar cell showing finger electrodes spaced

by distance s and an illuminated spot at (x]_, 0).

9T/dx

I0 dx|e8v-1|t itM*

Ps/i*

Figure B3 . Element of the distributed network shown in figure Bl indicating the notation used in this report.

13
- ftr /pT

V.J

T + JL - JD

= 3QT

/3t (B-3a)

and

VPS

7>J

S + JL

- J

D

= - 3Q

S

/3t (B-3b)

where Q<p and Qg are the net charges per unit area above and below the

metallurgical junction. Charge neutrality in any vertical section of the

panel requires that 3Q^/ 3t = - 3Qg/ 3t = 3Q/3t. When eqs (B-2a) and

(B-2b) are substituted into eqs (B-3a) and (B-3b), respectively,

V

2V

t

= - pT UL

- J

D - 3Q/3tJ (B-4a)

and

V

2

V

g = pg

[J

L

- J

D - 3Q/3t] , (B-4b)

so that

V

2

V S V

2 (V

t - Vg

) = - (pT + p

s

) • [J

L

- J

D - 3Q/3t] . (B-5)

Now 3Q/3t = 3Q/3V • 3V/3t = C3V/3t, so that

V

2

V = - p[JL

- J

D - C3V/3t] (B-6)

with p = pT + pg the sum of the sheet resistances and C = 3Q/3V the

incremental diode capacitance per unit area.

B.3. Low Intensity, Modulated Illumination

Next, consider the case of a generation current comprising dc and ac components

:

J

L

= J

L + J

L

. (B-7)

There will then be both dc and ac voltage components:

V = V + V , (B-8)

and eq (B-6) separates for small ac signals (BV « 1) into the relations

V

2

V = - p[J

L

- J

D

] (B-9)

and

V

2V = - p[JT - YVj (B-10)

where

14
Y = G

D + jwC ( B— 1 1

)

is the diode admittance per unit area and Gp = B(Jp + JQ

) is the

incremental diode conductance per unit area.

In the unilluminated region,

V

2

V = VYp . (B-12)

Since Z = Z(V), there will be in general a positional dependence of p/Z.

Equation (B-12) defines a position-dependent complex characteristic

length. For scanning in the X-direction with a line of light oriented

parallel with the electrodes, V will vary only along the X-direction, and

the characteristic length may be designated xQ

. It is convenient to

work with the inverse of xQ

. The inverse has both a real and imaginary

component; these may be designated x0

' and x0

", respectively,

x

"X - (V)"

1 + j(x -r1 = (Yp) 1/2

. (B-13)

o o o The real part of this length provides an attenuation of V(x), while

the imaginary part provides an oscillatory component. The characteristic

decay length is

x

q

' = \/l /p M / cos(<j)/2) (B-14

)

and

x

o

" = \/l/p M / sin( <j)/2 ) . ( B— 1 5

)

The wavelength of the oscillating component is

X = 2ttxo

" = 2tt^/1 / p M /sin(<j>/2) , (B-16)

where

<f> = tg

_1

(wCK^) ( B— 1 7 )

and

M = (Rp"2

+ (0 2 C

2

) 172

. (B-18)

B.4. Fault-Free Cells; Uniform xQ

Now apply these considerations to the special case of a fault-free

cell operated under conditions that xQ defined in eq (B-13) is

independent of position. This can be realized by using a cell without

external bias and without background illumination and by modulating the

scanning light beam at a sufficiently high frequency that Xq has the

desired value of about the finger electrode spacing s.

15
While the solution for line illumination of the perfect cell has

previously been derived by D. Sawyer [B-2], its derivation here is still

of interest as a starting point of calculations for faulty cells, com- pleted subsequent to the present reporting period.

B.4.1. Illumination of a fault-free cell by a line-shaped light beam at x = X}

This line shape is of interest since it leads to simple analytical

solutions. In case of only one pair of electrodes (at x = 0) of length

W, one electrode contacting the top semiconductor sheet and the other

contacting the bottom semiconductor sheet, the small-signal photovoltage

for a short-circuit load is

V(x) = I T x p/W

L o

-x

l/

X

o e sinh(x/x ) for x < x. o — 1 -x/x

sinh(x, /x ) for x > x. lo — 1

(B-iy)

The photocurrent crossing unit length of a line parallel to the finger

electrode and located at 0 _< x j< x^ is

J exp(- x, /x ) cosh x/x

1 o < (B-20)

The short-circuit output current is

*SC

* exp( ‘ W• (B'21)

The quantities x0

’ and x0

" can be obtained from the magnitude

Pscl = PJ exp( ” X

l /xo'

) (B-22)

and phase

= " W (B’23)

of the short-circuit output current. The limit for I^q for x^ - 0

is I L. From these data, Rq/p and CRp can be derived. Since the

dc diode conductance per unit area is I/Rq, C and p can be determined.

/V The potential V(x} in eq ( B— 1 9 ) has been composed of two exponential

terms to satisfy the boundary conditions V(x) = 0 at the electrode x = 0.

If there^is a second finger electrode at x = s > Xj , the boundary con- ditions V(x) = 0 at x = 0 and x = s may be satisfied by adding an infinite series of potentials from line source images with respect to these

electrodes. This is a well-known procedure in electrostatic and optical

problems. The result is

16
sinh(x/x )sinh[ (s-x_ )/x J o 1 o (B-24

)

V (x) =

J t px^ L O

sinh(s/x ) o

for 0 x _< x^

sinh[(s-x)/x ] sinh(x. /x ) for x. < x < s o 1 o 1— —

and

I sc = IL {[sinh[(s-x

1 )/x

q

] + sinh^/x^] }/sinh(s/x

Q

) (B-25)

where the first term in brackets results from the current collected by

the finger electrode at x = s, and the second term results from the

current collected by the finger electrode at x = 0.

B.4.2. Point illumination of a fault-free cell

The illumination of the point xj_, 0 induces the current source

IL

at xx

, 0 in the equivalent circuit of figure Bl. The resulting

potential in the case of the presence of only one set of finger electrodes located at x = 0, i.e., assuming that s - xj. » xQ> is

V(x,y) = (I

L

p/2TT)[K

o (r*( Xl )) - KQ

(r*(- x^)] (B-26)

where

r*(x.) = [(x - x.) 2

+ y

2

] 1/2 /x (B-27)

1 1 o and KQ is a modified Bessel function of the second kind. The second

term in the bracket of eq (B-26) results from the mirror image of the

current source with respect to the finger electrode. The short-circuit

current collected by the finger electrode is

(av/3x) x=0

dy = (I LX

K (\/x

2

1 J f 2

“

J -°° Vx, +

(v/x, 2 + y

2 /x ) dy ( B-28)

assuming infinite finger electrode length. The integral is a simple case

of the general Sonine-Gegenbauer Type [ B—3 ]

d SCILeXp(_ X

l /Xo

) • <B'29)

Note that the current for the point illumination is identical to the

current, eq (B-21), for the line illumination. This result illustrates

the equivalence theorem (to be proven generally in the next report) of

currents generated by point and line illumination. This equivalence

theorem also applies to the case of two finger electrodes so that eq

(B-24) derived for line illumination applies also to point illumination.

17
B.5. Output of Faulty Cells Having a Noncontacting Electrode Section

The general solution to the potential problem of a point current source located at r^ = (xj, y^) surrounded by an arbitrarily shaped ac- grounded electrode contour T is

V(r) = G(r

x

, r) - J

J(r‘ )G( £

- r'| )dr' (B-30)

where G(rj, "r) = G( £

- rjJ ) is the potential at r due to the point source located at 1:^ , and JC?') is the current density entering the

electrodes. This current density satisfies the integral equation

J(r')G( £

- r*| )dr

(B-31)

thus assuring that V(r') = 0. The effect of a poor electrode contact is

taken into account by excluding the noncontacting electrode section from

the contour. The poor contact problem is mathematically related to a diffraction optical aperture problem.

References

B-l. Lehovec, K., and Fedotowsky, A., Degradation of Solar Cell

Efficiency by Sheet Resistance, Solar Energy 21_, 81-86 (1978).

B-2. Sawyer, D. E., Kessler, H. K. , and Schafft, H. A., Measurement

Techniques for Solar Cells, Quarterly Report, January 1 to March

31, 1978, NBSIR 78-1513 (September 1978).

B-3. Petian, G. , La Theorie dee Functions due Beeeel, p. 210 (Centre

National de la Recherche Scientif ique, Paris, 1955).

18
APPENDIX C

8:30

9:15

9:45

1:00

2:00

STABILITY OF (THIN-FILM) SOLAR CELLS AND MATERIALS

WORKSHOP PROGRAM

Monday, May 1, 1978

.m. REGISTRATION

.m. WELCOME, PERSPECTIVE, AND WORKSHOP OVERVIEW

.m. SESSION I: Status of Present Reliability Testing, Failure Modes, Failure

Mechanisms, and Data for Advanced-Cell Materials

Chairman: A. Barnett (Institute for Energy Conversion, U. of Delaware,

Newark, DE)

[ CdZn\S/CuzS

J. D. Meakin and J. E. Phillips (Institute for Energy Conversion, U. of

Delaware, Newark, DE)

CdS/Cu-Temaries

L. Kazmerski (Solar Energy Research Institute, Golden, CO)

Polycrystalline Si

T. L. Chu (Southern Methodist U., Dallas, TX)

COFFEE

MIS and Conducting Oxide/Si

W. Anderson (Rutgers U. , Piscataway, NJ)

Conducting Oxide/Si Heterojunctions

R. L. Anderson (Syracuse U., Syracuse, NY)

MIS

S. J. Fonash (Pennsylvania State U. , University Park, PA)

.m. LUNCH

.m. SESSION I (Continued)

AMOS GaAs

R. Stirn (Jet Propulsion Laboratory, Pasadena, CA)

Polycrystalline GaAs

S. Chu (Southern Methodist U., Dallas, TX)

Amorphous Si

D. Carlson (RCA Corp., Princeton, NJ)

COFFEE

19
5:00

6:30

7:30

9:15

1:00

2:00

SESSION II: Measurements and Tests used to Define Stability in Related

Technologies

Chairman: R. I. Scace (National Bureau of Standards, Washington, DC)

Silicon Cell Space Program Experience

P. lies (Optical Coating Laboratory, Inc., City of Industry, CA)

Concentrator Solar Cells

W. McLevige (Sandia Laboratories, Albuquerque, NM)

p.m. ADJOURN

p.m. CASH BAR (Ramada Inn)

p.m. WORKSHOP DINNER (Ramada Inn)

Tuesday, May 2, 1978

a.m. SESSION II (Continued)

DoD Experience

J. Adolphson (NASA Goddard Space Flight Center, Greenbelt, MD)

Methods and Tests for Devices at the Bell Telephone Laboratory

C. W. Green (Bell Telephone Laboratories, Allentown, PA)

Power and CMOS Devices

S. Kukumaris (RCA Corp., Somerville, NJ)

COFFEE

Interdiffusion Phenomena

L. Kazmerski (Solar Energy Research Institute, Golden, CO)

Corrosion

R. Frankenthal (Bell Telephone Laboratories, Murray Hill, NJ)

Terrestrial Silicon Array Field and Test Experience

R. Ross (Jet Propulsion Laboratory, Pasadena, CA)

p.m. LUNCH

p.m. SESSION II (Continued)

Designing Accelerated Aging Tests for Predicting Array Life

D. Carmichael (Battelle Columbus Laboratories, Columbus, OH)

20
2:30 p.m.

5:00 p.m.

9:15 a.m.

10:50 a.m.

11:20 a.m.

1 :00 p.m.

SESSION III: Working Group Sessions - To identify tests and measurement

procedures that can be used to enhance the prediction of

material and device stability for each of the three solar

cell groups.

GROUP 1: [CdZn]S/Cu 2 S, CdS/Cu-Ternaries, CdS/InP, and Amorphous Si

Chairman: L. Kazmerski (Solar Energy Research Institute, Golden, CO)

Location: Green Auditorium

GROUP 2: Polycrystalline Si, MIS, and Conducting Oxide Si

Chairman: J. Shewchum (McMaster U., Hamilton, Ontario)

Location: • Lecture Room A

GROUP 3: Polycrystall ine and AMOS GaAs

Chairman: R. Stirn (Jet Propulsion Laboratory, Pasadena, CA)

Location: Lecture Room D (n.b.: Wednesday, Group meets in Employee's Lounge)

ADJOURN

Wednesday, May 3, 1978

SESSION III (Continued)

GROUP 1: [CdZn]S/Cu 2 S, CdS/Cu-Ternaries , CdS/InP, and Amorphous Si

Chairman: L. Kazmerski (Solar Energy Research Institute, Golden, CO)

Location: Green Auditorium

GROUP 2: Polycrystall ine Si, MIS, and Conducting Oxide Si

Chairman: J. Shewchum (McMaster U., Hamilton, Ontario)

Location: Lecture Room A

GROUP 3: Polycrystall ine and AMOS GaAs

Chairman: R. Stirn (Jet Propulsion Laboratory, Pasadena, CA)

Location: Employee's Lounge

COFFEE

TOUR (Selected Energy-Related Projects of NBS)

Tour is for all participants not involved in the preparation of working

group summaries for presentation in Session TV.

LUNCH

21
2:00 p.m. SESSION IV: Working Group Presentations of Summaries and Recommendations

Chairman: H. A. Schafft (National Bureau of Standards, Washington, DC)

3:30 p.m. SESSION V: Closing Remarks

Chairman: D. E. Sawyer (National Bureau of Standards, Washington, DC)

4:00 p.m. ADJOURN

CREDITS:

Workshop Sponsor:

Advanced Materials R&D Branch

Division of Solar Technology

Department of Energy

Steering Committee:

Allen Barnett Joseph M. Morabito

University of Delaware Bell Telephone Laboratories

Gordon Gross

Solar Energy Research Institute

Gary Jones

Sandia Laboratories

J. W. Lathrop

Clemson University

Ronald Ross

Jet Propulsion Laboratory

R. J. Stirn

Jet Propulsion Laboratory

Brown Williams

David Sarnoff Laboratories

L. M. Magid

Department of Energy

Organizing Committee:

Donald L. Feucht

Department of Energy

David E. Sawyer

National Bureau of Standards

Harry A. Schafft

National Bureau of Standards

NBS Workshop Committee:

Chairman - David E. Sawyer

Coordination - Harry A. Schafft

Registration - Elaine C. Cohen

Arrangements - Sara R. Torrance, JoAnn Lorden, Elaine C. Cohen

22
NBS-114A (REV. 9-7 B )

U.S. DEPT. OF COMM. 1. PUBLICATION OR REPORT NO. BIBLIOGRAPHIC DATA

SHEET -——

NBSIR 79-1909

» N©.| 5. Accession No. 5

Measurement Techniques for Solar Cells: Quarterly Report

for the Period April 1 to June 30, 1978

5. Publication Date October 1979

*. Perforating Organization Code

7. AUTHOR(S)

D. E. Sawyer, H. K. Kessler, and H. A. Schafft

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

11. Contract/Grant No. Task Order A05*i-SE

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, state, ZIP)

Advanced Materials R 6 D Branch

Division of Distributed Solar Technology

Department of Energy

20 Massachusetts Avenue, N.W., Washington, DC 205^*5

13. Type of Report & Period Covered Interim

Apr 1 to June 30, 1978

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

I | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

IS. ABSTRACT (A 200-word or leas factual summary of moat aighificant information. If document includes a significant bibliography or

literature survey, mention it here.) This is the quarterly report of the work in a program on solar cell measurement technique development and other services which was performed in the period April 1 to

June 30, 1978. The objectives of the program are to assist the DOE thin-film photovoltaic effort by developing solar cell device and material measurement techniques

using the NBS-developed laser flying-spot scanner, by assisting DOE in organizing and

hosting appropriate workshops and symposia, and by providing general consultation and

liaison services,,

The technique proposed last quarter employing cell forward-biasing during scanning to

reveal cell defects was implemented. Using an electrical current source, cell cracks

and metallization regions disconnected from the cell output electrode have been readily

revealed. The mathematical analysis work supporting the experimental scanning of cells

has been extended to more realistic cell geometries than the one-dimensional one previously treated. Developments in scanner equipment and ancillary techniques include

the completion of the h i gh- i ntens i ty insolation source for forward-biasing cells with

light during scanning, an improvement in coupling biased and scanned cells to the

display-screen electronics, and an increase in the cell scanning area.

The workshop on Stability of (Thin Film) Solar Cells and Materials was held May 1-3,

1978 at the National Bureau of Standards, Gaithersburg, Maryland.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons) m Device measurements; laser scanning; light-biasing; metallization; ohmic contacts;

reliability; semiconductor measurements; sheet resistance; solar cell stability;

solar cel Is.

18. AVAILABILITY |xl Unlimited

I I For Official Distribution. Do Not Release to NTIS

I I Order From Sup. of Doc., U.S. Government Printing Office, Washington, DC

20402, SD Stock No. SN003-003- [3 Order From National Technical Information Service (NTIS), Springfield, VA. 22161

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

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21. NO. OF

PRINTED PAGES

27

22. Price

$4.00

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