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Testing of solar cells by means of spectral analysis
Solar Cells, 29 (1990) 103 - 109
103
TESTING OF SOLAR CELLS BY MEANS OF SPECTRAL ANALYSIS* H. K. G U M M E L and F. M. SMITS
Bell Telephone Laboratories, Incorporated, Murray Hill, NJ (U.S.A.)
1. Introduction The solar cell is a device which converts light energy into electrical energy. The response characteristic depends on the wavelength of the incident light. Therefore the a m o u n t of electricity it produces for a given a m o u n t of light energy depends very strongly on the spectrum of the light source. For space applications the response of solar cells to the light of the sun n o t filtered by the atmosphere is of great importance. In characterizing the performance of a solar cell under outer space illumination, the most important parameter is the short-circuit current. Once this current is known, all tests related to the o u t p u t characteristic can be made under a light source of arbitrary spectral response but of an intensity adjusted to produce the outer space short-circuit current. Generally, two basic methods of approach have been taken to determine the outer space short-circuit current. One m e t h o d relies on measurements under terrestrial sunlight while the other m e t h o d attempts to simulate artificially the spectrum of the sun. In this report it will be shown t h a t the same information can be obtained from measurements of the spectral response of solar cells. Of the former methods, the first one requires o u t d o o r measurements preferably at high mountain altitudes. Even there, the sunlight reaching the earth is reduced in total intensity and modified in spectral composition from t h a t of outer space. The short-circuit current measured under such light is of the order of 15% to 25% below the outer space short-circuit current, the exact percentage depending upon the spectral response of the solar cell and atmospheric conditions. As a result of these factors, the short-circuit current depends non-linearly on the light intensity, as measured by a pyrheliometer for example, thus making the results somewhat ambiguous. Direct solar simulation requires a light source which is constant in time and which has a spectral composition equivalent to t h a t of the sun. To ensure this requires absolute spectral measurements performed with great accuracy, since the accuracy of the result will be directly related to the accuracy of these measurements.
*Reprinted with permission from Proceedings of the Solar Working Group Conference, February 1962, NASA, Washington D.C.
104 In the method described here spectral response measurements are performed on the solar cells themselves. The spectral response at a given wavelength multiplied by the sun's intensity at the same wavelength gives the contribution to the short-circuit current at this particular wavelength. The total short-circuit current is obtained by integrating over these contributions at all wavelengths. Thus the spectrum of the sun is only introduced in calculations, avoiding the problem of building and maintaining a sun simulator. The accuracy of such measurements depends on the accuracy with which the spectral measurements can be performed, a limitation similar to the one encountered in solar simulation.
2. Theory In deriving the relation between the spectral response of solar cells and the short-circuit current it is convenient to represent the spectral response of the solar cell in terms of the q u a n t u m efficiency. This is defined as the wavelength-dependent ratio of the number of electrons delivered into a short circuit to the number of photons incident on the solar cell. It should be noted that the quantum efficiency is here defined in terms of the total photon flux incident on the solar cell and not, as has occasionally been done by others, in terms of the photon flux which enters the cell. Thus the quantum efficiency as defined here includes the finite reflectivity of the solar cell surface. If the quantum efficiency is known, the outer space short-circuit current Iscos can be calculated by mutiplying the incident outer space p h o t o n flux density ¢(~) by the quantum efficiency Q(~,) of the cell and integrating over all wavelengths:
~os = Aq f Q(~,)¢(~)d~
(1)
where A is the cell area and q the electronic charge. The quantum efficiency of a solar cell is a smoothly varying function of wavelength. For this reason it is adequate to sample the q u a n t u m efficiency at only a small number of discrete wavelength points. To determine the outer space short-circuit current from this information, the integral can be approximated /Sos = Aq ~
{Q(~.i)¢()ki)Ai }
(2)
Now the p h o t o n flux entering the sum also has to be smoothed according to the intervals at which the q u a n t u m efficiency is sampled. The hi are the wavelengths at which the quantum efficiency is measured and the Ai are determined by the wavelength intervals between these points and the integration scheme used, e.g. trapezoidal approximation, Simpson's rule, gaussian quadrature, etc. To apply such a m e t h o d in practice, one has to measure the q u a n t u m efficiency with high precision. By measuring the short-circuit current of a
105 solar cell together with a monitor cell under monochromatic light as obtained through a narrow band interference filter, and determining the ratio of the short-circuit current response of the sample cell to the shortcircuit current of the monitor cell, one obtains the ratio of the quantum efficiency between sample cell and monitor cell. Such a ratio is independent of small changes in light intensity and it can be measured with high precision. In terms of such ratios Ri, the quantum efficiency of the sample cell can be expressed as Q ( k i ) = RiQref(~,i )
(3)
where Qref (ki) is the quantum efficiency of the monitor celt. The sum (2) can thus be written
Iscos
=
~_¢Ri{AqQref(ki)¢(ki)Ai}
(4)
i
Defining the quantities in the brackets as "weight factors" W i = AqQre,(~l)¢(~i)Ai
(5)
gives for the outer space short-circuit current
Iscos = ~ Ri Wi
(6)
i
The weight factors include the spectral composition of o u t e r space sunlight and the quantum efficiency of the monitor cell. In the derivation, outer space sunlight served as an example only. However, the m e t h o d is n o t restricted to outer space illumination, b u t can be applied with appropriate weight factors for any illumination of fixed spectral composition and intensity. 3. Experimental details The equipment for the measurement of the quantum efficiency is schematically indicated in Fig. 1. Light from a tungsten light source is passed through interference filters which are m o u n t e d on a turntable. Eight narrow bandpass filters transmitting at 0.4, 0.45, 0.5, 0.6, 0.7, 0.8, 0.9, and 0.95 #m are used. The sample cell and the monitor cell are m o u n t e d under the filter and the measurements are performed by generating the ratio of the sample cell response to the monitor cell response in digital form and recording the ratio on IBM cards. As a test of the feasibility of predicting short-circuit current from the spectral measurements, weight factors have been determined for calculation of short-circuit current of a set of solar cells measured under a particular sun condition at Table Mountain, California. The set of solar cells had a wide range in spectral response characteristics caused b y various levels of electron b o m b a r d m e n t such as shown in Fig. 2 .
106
Light source
1
I
Narrow band interference filter
1/
Monitor cell - - ~ - [ ~
~
Sample cell
Ratio formation
L Fig. I. Schematic diagram of the spectral test equipment.
I00 80 60
40 l'8 x I0 ~ 9-0 x 1013/ 5.4 x I014/ 5
20
2.7 x 1015/ 1.8
/
I016/
x
g 0-
8
Blue sensitiven/p
iI 0.4
I
l
I
I
I
0.5
0.6
0.7
0.8
0.9
I.O
Fig. 2. Spectral r e s p o n s e c h a r a c t e r i s t i c s o f e l e c t r o n - i r r a d i a t e d solar cells.
107
Ideally, the weight factors are found by first calibrating the spectral response for relative quantum efficiencies by the use of spectrally fiat detectors such as thermocouples. Combining this information with relative spectral intensities of the sun under which the observation was taken will give the short-circuit current to within a c o m m o n constant factor for all cells. This factor is readily determined from the actual measurements of the short-circuit currents. It is significant to note that only the current measurements determine the absolute scale, while all other measurements only need to be performed on a relative scale. However, if the universe of solar cells used in such measurements has a sufficiently wide spread in spectral response characteristics it could, in principle, be possible to find the weight factors even without any prior information on the quantum efficiency calibration and on the spectral composition of the sun. The appropriate weights are simply those which reproduce the current of all cells with the least error. If such a fit is possible for a spread in spectral characteristics, which is at least as wide as will ever be encountered, it becomes clear that this fit is fully adequate and that it must be the correct one. In the present work, the weight factors have been determined by a combination of both methods. Figure 3 shows the resulting comparison of the measured short-circuit current and the calculated current. In this figure the most heavily prebombarded cells appear at the lower left-hand corner.
j/"
-o
o 4-0 ~e-
%
y
._E
/-/
O
a 3o
3
°/
o 2C
IC ~)
./ I 20
I 30
[ 40
50
Measured short circuit current in M ~ l o
Fig. 3. C o m p a r i s o n b e t w e e n s h o r t - c i r c u i t c u r r e n t s m e a s u r e d o n Table California, a n d s h o r t - c i r c u i t currents calculated f r o m s p e c t r a l r e s p o n s e data.
Mountain,
108 The measurements at Table Mountain were done for an extrapolation to outer space sun, described in detail elsewhere [1]. To obtain the outer space response from the spectral information it is necessary to increase the weight factors at each wavelength by the ratio of outer space solar intensity to terrestrial solar intensity at this particular wavelength. Such information was readily available from solar spectral recordings performed by the Smithsonian Institution. For the set of solar cells shown in Fig. 3 an outer space extrapolation was performed by the procedure outlined above. Thus weight factors became available for the prediction of outer space short-circuit currents from the spectral measurements. The calibrated cells serve as standards for the weight factors. Thus it is not necessary that the monitor cell in the test equipment provides the longtime standard. It only serves as a short-time standard that can be compared readily against the calibrated cells. Through the cooperation of R. E. Fischell of APL it was possible to test a test panel of two solar cells, a duplicate of which has been flown on the TRAAC satellite. The short-circuit current predicted for this panel from the spectral measurements differs by approximately 4% from the short-circuit current one would predict from telemetry results on a flight panel closest in characteristics to the measured one as determined by preflight comparison. It is felt t h a t this agreement is better than one should expect, since a variety of uncertainties are present in this comparison. These involve on the one hand differences between the tested panel and the flight panel, errors in the telemetry, possible changes in the flight panel after launch, and on the other hand the calibration of the test equipment. The encapsulation of the calibrated solar cells was n o t designed for use of the cells as long-time standards and changes in the characteristics of the encapsulated cells are presently considered the cause of uncertainty in the measurements. For further characterizing solar cells additional measurements under tungsten light filtered through heat absorbing glasses are performed, namely the short-circuit current, the open-circuit voltage, the current delivered into a 10 ~ load, and the current delivered into 0.45 V. The reverse leakage and the forward voltage with 50 mA passing through the solar cell are measured in the dark. The outer space short-circuit current is calculated on a digital computer and the result is used in conjuction with the measurements under white light to calculate the overall o u t p u t characteristic for outer space illumination, in particular the m a x i m u m power point and the voltage at m a x i m u m power. In addition, the short-circuit current under the white light source is also calculated from the spectral response by using an appropriate set of weight factors. The percentage difference between the calculated and the measured short-circuit current is determined and recorded. Generally this difference is small indicating t h a t the outer space short-circuit current calculation can be trusted. Occasionally solar cells are observed where the calculated current deviates substantially from the measured current. This indicates t h a t the
109 particular solar cell shows a non-linear response, e.g. its q u a n t u m efficiency is light level dependent. The results obtained on such solar cells are disregarded.
4. Discussion
The testing of solar cells by means of a spectral analysis permits an evaluation of outer space performance with an error of a few percent at present. The major limitation in the accuracy is caused by the limited accuracy in the calibration for outer space response. Non-linearities in solar cell response appear to be the second most important source of error for a fraction of solar cells tested. The m e t h o d as presently developed applies primarily to silicon solar cells, since the choice of the wavelengths at which measurements are taken, and the integration scheme used, were tailored to the spectral characteristics of silicon cells. For this reason, tests on GaAs solar cells, for example, have a somewhat greater error (estimated at -+10%)with the equipment presently in use at Bell Telephone Laboratories. In principle, these limitations can be eliminated w i t h o u t excessive efforts. Additional interference filters would readily lead to an improved accuracy for GaAs solar cells. The accuracy of the calibration for outer space response could be significantly improved by terrestrial measurements on carefully encapsulated solar cell standards or by satellite experiments or a combination of both. The effect of non-linearities would be virtually eliminated if a shortcircuit measurement could be made under a convenient and stable artificial light source of k n o w n spectral composition. The spectral analysis could then be used to predict the short-circuit current corresponding to the difference spectrum between the artificial light source and outer space sunlight. This current added to the response under the artificial light source would give the outer space response. Since it will be relatively easy to keep the difference below 10% of the outer space response, any error in the difference will correspond to only a very small relative error in the outer space response.
Reference 1 H. K. Gummel, F. M. Smits and A. R. Froiland, W/ESCON, 1961, paper 73.
103
TESTING OF SOLAR CELLS BY MEANS OF SPECTRAL ANALYSIS* H. K. G U M M E L and F. M. SMITS
Bell Telephone Laboratories, Incorporated, Murray Hill, NJ (U.S.A.)
1. Introduction The solar cell is a device which converts light energy into electrical energy. The response characteristic depends on the wavelength of the incident light. Therefore the a m o u n t of electricity it produces for a given a m o u n t of light energy depends very strongly on the spectrum of the light source. For space applications the response of solar cells to the light of the sun n o t filtered by the atmosphere is of great importance. In characterizing the performance of a solar cell under outer space illumination, the most important parameter is the short-circuit current. Once this current is known, all tests related to the o u t p u t characteristic can be made under a light source of arbitrary spectral response but of an intensity adjusted to produce the outer space short-circuit current. Generally, two basic methods of approach have been taken to determine the outer space short-circuit current. One m e t h o d relies on measurements under terrestrial sunlight while the other m e t h o d attempts to simulate artificially the spectrum of the sun. In this report it will be shown t h a t the same information can be obtained from measurements of the spectral response of solar cells. Of the former methods, the first one requires o u t d o o r measurements preferably at high mountain altitudes. Even there, the sunlight reaching the earth is reduced in total intensity and modified in spectral composition from t h a t of outer space. The short-circuit current measured under such light is of the order of 15% to 25% below the outer space short-circuit current, the exact percentage depending upon the spectral response of the solar cell and atmospheric conditions. As a result of these factors, the short-circuit current depends non-linearly on the light intensity, as measured by a pyrheliometer for example, thus making the results somewhat ambiguous. Direct solar simulation requires a light source which is constant in time and which has a spectral composition equivalent to t h a t of the sun. To ensure this requires absolute spectral measurements performed with great accuracy, since the accuracy of the result will be directly related to the accuracy of these measurements.
*Reprinted with permission from Proceedings of the Solar Working Group Conference, February 1962, NASA, Washington D.C.
104 In the method described here spectral response measurements are performed on the solar cells themselves. The spectral response at a given wavelength multiplied by the sun's intensity at the same wavelength gives the contribution to the short-circuit current at this particular wavelength. The total short-circuit current is obtained by integrating over these contributions at all wavelengths. Thus the spectrum of the sun is only introduced in calculations, avoiding the problem of building and maintaining a sun simulator. The accuracy of such measurements depends on the accuracy with which the spectral measurements can be performed, a limitation similar to the one encountered in solar simulation.
2. Theory In deriving the relation between the spectral response of solar cells and the short-circuit current it is convenient to represent the spectral response of the solar cell in terms of the q u a n t u m efficiency. This is defined as the wavelength-dependent ratio of the number of electrons delivered into a short circuit to the number of photons incident on the solar cell. It should be noted that the quantum efficiency is here defined in terms of the total photon flux incident on the solar cell and not, as has occasionally been done by others, in terms of the photon flux which enters the cell. Thus the quantum efficiency as defined here includes the finite reflectivity of the solar cell surface. If the quantum efficiency is known, the outer space short-circuit current Iscos can be calculated by mutiplying the incident outer space p h o t o n flux density ¢(~) by the quantum efficiency Q(~,) of the cell and integrating over all wavelengths:
~os = Aq f Q(~,)¢(~)d~
(1)
where A is the cell area and q the electronic charge. The quantum efficiency of a solar cell is a smoothly varying function of wavelength. For this reason it is adequate to sample the q u a n t u m efficiency at only a small number of discrete wavelength points. To determine the outer space short-circuit current from this information, the integral can be approximated /Sos = Aq ~
{Q(~.i)¢()ki)Ai }
(2)
Now the p h o t o n flux entering the sum also has to be smoothed according to the intervals at which the q u a n t u m efficiency is sampled. The hi are the wavelengths at which the quantum efficiency is measured and the Ai are determined by the wavelength intervals between these points and the integration scheme used, e.g. trapezoidal approximation, Simpson's rule, gaussian quadrature, etc. To apply such a m e t h o d in practice, one has to measure the q u a n t u m efficiency with high precision. By measuring the short-circuit current of a
105 solar cell together with a monitor cell under monochromatic light as obtained through a narrow band interference filter, and determining the ratio of the short-circuit current response of the sample cell to the shortcircuit current of the monitor cell, one obtains the ratio of the quantum efficiency between sample cell and monitor cell. Such a ratio is independent of small changes in light intensity and it can be measured with high precision. In terms of such ratios Ri, the quantum efficiency of the sample cell can be expressed as Q ( k i ) = RiQref(~,i )
(3)
where Qref (ki) is the quantum efficiency of the monitor celt. The sum (2) can thus be written
Iscos
=
~_¢Ri{AqQref(ki)¢(ki)Ai}
(4)
i
Defining the quantities in the brackets as "weight factors" W i = AqQre,(~l)¢(~i)Ai
(5)
gives for the outer space short-circuit current
Iscos = ~ Ri Wi
(6)
i
The weight factors include the spectral composition of o u t e r space sunlight and the quantum efficiency of the monitor cell. In the derivation, outer space sunlight served as an example only. However, the m e t h o d is n o t restricted to outer space illumination, b u t can be applied with appropriate weight factors for any illumination of fixed spectral composition and intensity. 3. Experimental details The equipment for the measurement of the quantum efficiency is schematically indicated in Fig. 1. Light from a tungsten light source is passed through interference filters which are m o u n t e d on a turntable. Eight narrow bandpass filters transmitting at 0.4, 0.45, 0.5, 0.6, 0.7, 0.8, 0.9, and 0.95 #m are used. The sample cell and the monitor cell are m o u n t e d under the filter and the measurements are performed by generating the ratio of the sample cell response to the monitor cell response in digital form and recording the ratio on IBM cards. As a test of the feasibility of predicting short-circuit current from the spectral measurements, weight factors have been determined for calculation of short-circuit current of a set of solar cells measured under a particular sun condition at Table Mountain, California. The set of solar cells had a wide range in spectral response characteristics caused b y various levels of electron b o m b a r d m e n t such as shown in Fig. 2 .
106
Light source
1
I
Narrow band interference filter
1/
Monitor cell - - ~ - [ ~
~
Sample cell
Ratio formation
L Fig. I. Schematic diagram of the spectral test equipment.
I00 80 60
40 l'8 x I0 ~ 9-0 x 1013/ 5.4 x I014/ 5
20
2.7 x 1015/ 1.8
/
I016/
x
g 0-
8
Blue sensitiven/p
iI 0.4
I
l
I
I
I
0.5
0.6
0.7
0.8
0.9
I.O
Fig. 2. Spectral r e s p o n s e c h a r a c t e r i s t i c s o f e l e c t r o n - i r r a d i a t e d solar cells.
107
Ideally, the weight factors are found by first calibrating the spectral response for relative quantum efficiencies by the use of spectrally fiat detectors such as thermocouples. Combining this information with relative spectral intensities of the sun under which the observation was taken will give the short-circuit current to within a c o m m o n constant factor for all cells. This factor is readily determined from the actual measurements of the short-circuit currents. It is significant to note that only the current measurements determine the absolute scale, while all other measurements only need to be performed on a relative scale. However, if the universe of solar cells used in such measurements has a sufficiently wide spread in spectral response characteristics it could, in principle, be possible to find the weight factors even without any prior information on the quantum efficiency calibration and on the spectral composition of the sun. The appropriate weights are simply those which reproduce the current of all cells with the least error. If such a fit is possible for a spread in spectral characteristics, which is at least as wide as will ever be encountered, it becomes clear that this fit is fully adequate and that it must be the correct one. In the present work, the weight factors have been determined by a combination of both methods. Figure 3 shows the resulting comparison of the measured short-circuit current and the calculated current. In this figure the most heavily prebombarded cells appear at the lower left-hand corner.
j/"
-o
o 4-0 ~e-
%
y
._E
/-/
O
a 3o
3
°/
o 2C
IC ~)
./ I 20
I 30
[ 40
50
Measured short circuit current in M ~ l o
Fig. 3. C o m p a r i s o n b e t w e e n s h o r t - c i r c u i t c u r r e n t s m e a s u r e d o n Table California, a n d s h o r t - c i r c u i t currents calculated f r o m s p e c t r a l r e s p o n s e data.
Mountain,
108 The measurements at Table Mountain were done for an extrapolation to outer space sun, described in detail elsewhere [1]. To obtain the outer space response from the spectral information it is necessary to increase the weight factors at each wavelength by the ratio of outer space solar intensity to terrestrial solar intensity at this particular wavelength. Such information was readily available from solar spectral recordings performed by the Smithsonian Institution. For the set of solar cells shown in Fig. 3 an outer space extrapolation was performed by the procedure outlined above. Thus weight factors became available for the prediction of outer space short-circuit currents from the spectral measurements. The calibrated cells serve as standards for the weight factors. Thus it is not necessary that the monitor cell in the test equipment provides the longtime standard. It only serves as a short-time standard that can be compared readily against the calibrated cells. Through the cooperation of R. E. Fischell of APL it was possible to test a test panel of two solar cells, a duplicate of which has been flown on the TRAAC satellite. The short-circuit current predicted for this panel from the spectral measurements differs by approximately 4% from the short-circuit current one would predict from telemetry results on a flight panel closest in characteristics to the measured one as determined by preflight comparison. It is felt t h a t this agreement is better than one should expect, since a variety of uncertainties are present in this comparison. These involve on the one hand differences between the tested panel and the flight panel, errors in the telemetry, possible changes in the flight panel after launch, and on the other hand the calibration of the test equipment. The encapsulation of the calibrated solar cells was n o t designed for use of the cells as long-time standards and changes in the characteristics of the encapsulated cells are presently considered the cause of uncertainty in the measurements. For further characterizing solar cells additional measurements under tungsten light filtered through heat absorbing glasses are performed, namely the short-circuit current, the open-circuit voltage, the current delivered into a 10 ~ load, and the current delivered into 0.45 V. The reverse leakage and the forward voltage with 50 mA passing through the solar cell are measured in the dark. The outer space short-circuit current is calculated on a digital computer and the result is used in conjuction with the measurements under white light to calculate the overall o u t p u t characteristic for outer space illumination, in particular the m a x i m u m power point and the voltage at m a x i m u m power. In addition, the short-circuit current under the white light source is also calculated from the spectral response by using an appropriate set of weight factors. The percentage difference between the calculated and the measured short-circuit current is determined and recorded. Generally this difference is small indicating t h a t the outer space short-circuit current calculation can be trusted. Occasionally solar cells are observed where the calculated current deviates substantially from the measured current. This indicates t h a t the
109 particular solar cell shows a non-linear response, e.g. its q u a n t u m efficiency is light level dependent. The results obtained on such solar cells are disregarded.
4. Discussion
The testing of solar cells by means of a spectral analysis permits an evaluation of outer space performance with an error of a few percent at present. The major limitation in the accuracy is caused by the limited accuracy in the calibration for outer space response. Non-linearities in solar cell response appear to be the second most important source of error for a fraction of solar cells tested. The m e t h o d as presently developed applies primarily to silicon solar cells, since the choice of the wavelengths at which measurements are taken, and the integration scheme used, were tailored to the spectral characteristics of silicon cells. For this reason, tests on GaAs solar cells, for example, have a somewhat greater error (estimated at -+10%)with the equipment presently in use at Bell Telephone Laboratories. In principle, these limitations can be eliminated w i t h o u t excessive efforts. Additional interference filters would readily lead to an improved accuracy for GaAs solar cells. The accuracy of the calibration for outer space response could be significantly improved by terrestrial measurements on carefully encapsulated solar cell standards or by satellite experiments or a combination of both. The effect of non-linearities would be virtually eliminated if a shortcircuit measurement could be made under a convenient and stable artificial light source of k n o w n spectral composition. The spectral analysis could then be used to predict the short-circuit current corresponding to the difference spectrum between the artificial light source and outer space sunlight. This current added to the response under the artificial light source would give the outer space response. Since it will be relatively easy to keep the difference below 10% of the outer space response, any error in the difference will correspond to only a very small relative error in the outer space response.
Reference 1 H. K. Gummel, F. M. Smits and A. R. Froiland, W/ESCON, 1961, paper 73.