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HIGH-ALTITUDE AIR MASS ZERO CALIBRATION OF SOLAR CELLS[1]

James R. Woodyard

Wayne State University, Detroit, Michigan

David B. Snyder, NASA Glenn Research Center

Cleveland, Ohio

ABSTRACT

Air mass zero calibration of solar cells has been carried out for several years by NASA Glenn Research Center using a Lear-25 aircraft and Langley plots. The calibration flights are carried out during early fall and late winter when the tropopause is at the lowest altitude. Measurements are made starting at about 50,000 feet and continue down to the tropopause. A joint NASA/Wayne State University program called Suntracker is underway to explore the use of weather balloon and communication technologies to characterize solar cells at elevations up to about 100 kft. The balloon flights are low-cost and can be carried out any time of the year. AM0 solar cell characterization employing the mountaintop, aircraft and balloon methods are reviewed. Results of cell characterization with the Suntracker are reported and compared with the NASA Glenn Research Center aircraft method.

INTRODUCTION

It is important in characterizing solar cells for use in space-power applications that the spectral irradiance of the calibration-light source is within a percent of the spectral irradiance of air mass zero conditions (AM0). Spectral irradiance differences greater than a few percent can result in calibration errors; the magnitude of the errors depends on the structure of the solar cell. In the case of single-junction cells, the current-voltage characteristics are not very sensitive to small differences in the spectral irradiances of calibration-light sources because the spectral response is not sensitive to spectral irradiance. The current in a single-junction solar cell under AM0 normal incidence operating at a voltage is given by

(1)

whereis the absolute AM0 spectral irradiance of sunlight and is the spectral response of the cell at wavelength and voltage . In the ideal case, the spectral response is independent of the irradiance of the light source. The spectral response depends on the opto-electronic properties of the materials used in the fabrication of the cell that include, but are not limited to, the wavelength dependence of the optical absorption coefficient; optical band gap, material thickness, doping, temperature and quality; and carrier mobility and lifetime. andare the lower and upper cut-off wavelength values where the spectral response no longer contributes to cell current.

The spectral irradiance of laboratory-based solar simulators is different than the AM0 spectral irradiance. The simulator is set to “AM0” intensity by adjusting the intensity to produce the short-circuit current in a standard cell, i.e., a cell calibrated under AM0 conditions. This approach may be used because the spectral response of single-junction solar cells is somewhat insensitive to spectral irradiance. Adjusting the intensity of the simulator will compensate for spectral irradiance differences when compared to AM0 over the range of the spectral response of the cell. The adjustment produces a spectral irradiance that is larger than AM0 in some regions of the spectrum and smaller than AM0 in other regions of the spectrum. Following adjustment of the simulator intensity, cells may be characterized under “AM0” conditions. This method may be used as long as two conditions are met. First, it is necessary that the simulator is stable, meaning that spectral irradiance remains constant during the measurements on the standard cell and the cells to be characterized. Second, the voltage dependence of the spectral responses of the standard cell and cells to be characterized must be the same and not influenced by differences in the spectral irradiances of the solar simulator and AM0. The method requires stable standard cells for each of the types of single-junction cells to be characterized. Laboratory-based “AM0”characterization of single-junction solar cells has been carried out for many years with good results using this method.

The evolution of solar-cell technology for space applications has resulted in “state-of-the-art” cells with four and five junctions in series. Each junction is designed with a spectral response matched to one region of the spectral irradiance of AM0 in order to optimize the efficiency of solar cells. The current in a four-junction solar cell operating at a given voltage is given by:

and (2)

(3)

where the variables in Equation 2 are the same as in Equation 1 except andare the lower and upper cut-off wavelength values, above and below which the spectral response is negligible and no longer contributes to cell current. The spectral response in Equation 2 characterizes the overall operation of the four junctions in optical absorption and carrier transport. However, the spectral responses and voltages in Equation 3, and respectively, are subscripted to show that they are different for each of the four junctions. The voltage across the cell is equal to the sum of the voltages across each of the four junctions, namely, . The wavelength ranges on each of the integrals, in the most general case, will overlap since it is not possible to fabricate materials with sharp wavelength cut-offs. Equation 3 shows the series nature of the current in multi-junction solar cells, namely, the current is the same in each of the junctions.

The sensitivity of a four-junction solar cell to spectral irradiance can be illustrated with an example. Consider a cell that has been optimally designed for AM0 is to be characterized with a solar simulator. Assume the solar simulator has a spectral irradiance that is less than AM0 in the and wavelength range and the same as AM0 in the other three wavelength ranges shown in Equation 3. The lower spectral irradiance will result in less current in the junction optimized for the and wavelength range which in turn will limit the current in the cell due to the series nature of the four junctions. Equation 3 shows that the current reduction in the four junctions must be accomplished through changes in spectral responses of the other three junctions; this is the case because the spectral irradiances in the other three wavelength ranges are assumed to be the same as AM0. The collective interaction of the four junctions will result in redistribution of the cell voltage across the four junctions, which in turn changes the spectral responses of the four junctions and the cell current.

The role of the interaction of four junctions in the operation of a multi-junction solar cell, as compared to a single-junction cell, can be illustrated with an example. Assume the average spectral irradiance and the average spectral response are the same in the four wavelength regions in Equation 3. A one percent decrease in the spectral irradiance relative to AM0 over theand wavelength range will result in about a one percent decrease in the cell short-circuit current. A single-junction junction solar cell that responds in a similar fashion over the to wavelength range will experience only a 0.25 % decrease in short-circuit current. The reason is a one percent decrease in the integrated spectral irradiance over the and wavelength range in the multi-junction cell corresponds to a 0.25 % decrease in the integrated spectral irradiance over the to wavelength range in the single-junction cell

A calibration procedure for multi-junction solar cells that uses a standard cell to set a solar simulator to “AM0” intensity may result in data that are not useful in optimizing the design of a test cell for space power generation. Assuming the voltage dependence of the spectral responses of each of the junctions in the standard and test cells are the same under the simulator “AM0” conditions, the junctions may be operating under conditions that are vastly different than AM0 conditions. It is possible that the test cell current-voltage characteristics measured under “AM0” conditions may not be useful in optimizing the cell design to improve efficiencies at the one percent level. Moreover, the complex nature of the interaction of the junctions does not lend itself to the use of an optical technique to compensate for the deficiencies in the “AM0” spectral irradiance.

The differences in the “AM0” and AM0 spectral irradiances are more problematic at the maximum power point than short-circuit conditions. The reason is the electrostatic potential barriers in each of the junctions are relatively small at the maximum power point as compared to short-circuit current conditions. Redistribution of voltages across the junctions can produce relatively large changes in the electrostatic potential barriers and produce major changes in the spectral responses of the junctions. Figure 1 shows the effect of forward bias on the quantum efficiency of a solar cell [1]. The solar cell is a triple-junction a-Si:H alloy-based thin-film solar cell that was illuminated with a solar simulator with an AM0 spectral irradiance. The spectral irradiance was within one percent of AM0 in the wavelength range where the spectral response contributed to cell current. The figure shows the maximum quantum efficiency is at a wavelength of about 450 nm, serving as evidence that the top junction in this particular cell was limiting the current of the cell under short-circuit conditions. The maximum in the quantum efficiency shifted from 450 to 600 nm as the forward bias approached the maximum-power point showing that the middle and bottom junctions limited the cell current. The quantum efficiency of the cell changed markedly when the spectral irradiance of the simulator was altered [1]. A history of particle irradiation can also have a large effect on the dependence of the quantum efficiency of multi-junction cells on forward bias thereby further complicating the optimization of design of cells for space power generation in radiation environments.

It is clear that the voltage dependence of the spectral responses of multi-junction solar cells complicates optimization of cell design. While there are characterization methods that make it possible to use solar simulators in advancing the multi-junction solar cell technology, the series nature of the cells places more demands on the need for standard cells characterized under AM0 conditions. AM0 conditions are available only in space; near AM0 conditions can be achieved at altitudes in excess of 100,000 ft. The demand for greater access to AM0, and the costs associated with AM0 calibration, has generated interest in exploring lost-cost methods for AM0 solar cell calibration. The NASA supported Suntracker program is an attempt to meet this challenge.

AM0 SOLAR CELL CALIBRATION MEHTODS

Efforts to develop new methods for AM0 calibration of solar cells should be founded in an awareness of current calibration methods, a knowledge of fundamental principles, and possible shortcomings of existing methods. Reviewing analyses of data collected by various methods is also an instructive way to gain a better understanding of the methods. Mountaintop, aircraft and balloon-based methods for AM0 calibration of solar cells are reported in the literature. While there have been a number of satellite-based measurements, no space calibration method has emerged that is available to the photovoltaic community for producing solar cell standards. A photovoltaic engineering test bed facility for use on the International Space Station has been designed but not implemented [2]. This section will review the mountaintop, aircraft and balloon-based methods used in AM0 calibration of solar cells.

Mountaintop method

Laboratory-based solar simulators have been used since solar cells became attractive for space-power applications. However, it was recognized by Zoutendyk that sunlight should be used “ to diminish uncertainty in the design of space solar cell power systems” [3]. He was one of the first investigators to attempt to correct for the effects of the atmosphere on the spectral irradiance of sunlight. A review of his work with silicon single-junction solar cells serves as a basis for understanding some of the challenges associated with AM0 calibration methods.

Zoutendyk assumed the spectral irradiance at a given air massis given by:

(4)

where is the monochromatic atmospheric absorption coefficient per unit air mass and is the geometric air mass. He defined the geometric air mass as the ratio of the path length of the sunlight through the atmosphere at a zenith angle to the path length for the sunlight when the sun is overhead and the zenith angle is zero. The geometric air mass was taken as the secant of the zenith angle, namely, . The sea-level irradiance at a given air mass is:

. (5)

The monochromatic short-circuit current at a given air mass was assumed to be given by:

where (6)

where is the monochromatic short-circuit current under AM0 conditions. The short-circuit current of a single-junction cell over to wavelength range where the spectral response contributes to the current is:

. (7)

Equation 7 serves as the basis for the use of Langley plots to characterize solar cells. The exponential term may be factored out of the integral if is assumed to be constant over the and wavelength range. The short-circuit current for a given air mass can then be written as:

(8)

where is the AM0 cell short-circuit current. Taking theof both sides of Equation 8 gives:

(9)

which is the theoretical equation used to determine the short-circuit current of solar cells under AM0 conditions. The logarithm of the short-circuit current is plotted on the ordinate of a semi-log graph and the air mass on the abscissa. The graph is referred to as a Langley plot. The data are fitted to a straight line using a least-squared method and the line extrapolated to . The intercept of the straight line with the ordinate is taken as the short-circuit current under AM0 conditions. The slope of the graph isand may be used to determine the atmospheric optical absorption coefficient. It is important to emphasize the constancy of the atmospheric optical absorption coefficient and the use of the “air mass” concept implies the following:

1. The optical absorption coefficient must be constant with respect to wavelength over the range of wavelengths where the solar cell spectral response contributes to cell current. If it is not constant, using Equation 9 to analyze data will produce errors in the extrapolated AM0 short-circuit current.

2. The concentration of optically absorbing atomic and molecular species in the atmosphere and their altitude dependence must not change for the duration of the short-circuit current as a function of air mass measurements. If the concentrations are changing during the measurements as a result of weather fronts, turbulence in the atmospheric, solar heating of the atmosphere etc., Equation 9 may not be linear and linear extrapolation of the short-circuit current to zero air mass may be in error.

3. The optical absorption coefficient must not be large enough to totally absorb the AM0 spectral irradiance at any air mass over the range of wavelengths where the solar cell spectral response contributes to cell current. If there are regions of the spectral irradiance where the sunlight is totally absorbed as it travels through the air mass, then the use of the Langley method to determine the AM0 short circuit will produce erroneous results.

4. Only normally incident sunlight must contribute to the short-circuit current. Scattered sunlight, referred to as “sky radiation” by Zoutendyk, must not contribute to the short-circuit current. Additionally, the presence of reflected light, or light produced by any other mechanisms, may introduce errors in the determination of the AM0 short-circuit current.

Zoutendyk set up a tracking system with silicon single-junction solar cells at an elevation of 7.4 kft on a mountaintop and carried out diurnal measurements of cell short-circuit current and temperature as a function of the zenith angle as the sun moved across the sky. The cell short-circuit current was defined at the current through a 1.000 precision resistor in series with the cell. The sea level geometric air mass was calculated using . The data were analyzed using a Langley plot to arrive at cell AM0 short-circuit currents. The short-circuit current was corrected for cell temperature, precision resistor temperature and the earth-sun distance. The cells were then flown on the Ranger III spacecraft and cell data downlinked. The agreement between the AM0 short-circuit current measurements on the mountaintop and space was reported to be [3].

It is noteworthy to evaluate the constancy of the atmospheric optical absorption coefficient in mountaintop work to understand the utility of Langley plots. Equations 8 and 9 show that the exponential term is assumed to be constant over the and wavelength range in order to permit factoring it out of the integral. The cut off wavelength of Zoutendyk’s solar cell at low wavelengths was because of the optical properties of the cover glass on the cells. The high wavelength cut off was about due to the band gap of the silicon material used in the solar cells. Analyses were carried out using values of the atmospheric optical absorption coefficients in thewavelength range that were reported by Moon [4]. The coefficients ranged between 0.05 and 0.96 per air mass. The spectral response of the solar cells peaked at about where the atmospheric optical absorption was about 0.1 per air mass. The geometrical air masses used by Zoutendyk must be multiplied by 0.7 to correct for the 7.4 kft altitude [5]. For per air mass and , the exponential term in Equation 8, has a value of about 0.93. At the largest and smallest values of the optical absorption coefficient, 0.96 and 0.05 per air mass, the values of the exponential term will be 0.51 and 0.96, respectively. Clearly the exponential term varies with wavelength when Moon’s atmospheric optical absorption coefficients are used in Equation 8. However, as shown in Equation 7, the exponential term is convoluted with the cell spectral response. The spectral response is always less than one; it decreases from a maximum value at to approximately zero at the cut off wavelengths. The effect of convolution of the spectral response with the exponential term in Equation 7 is to decrease the weighting of the exponential term in the integral. A non-constant exponential term in Equation 7 will produce a concave up feature in Langley plots [4]. There is no evidence of a concave up feature in the Langley plots in Zoutendyk’s work. This suggests variations in the atmospheric optical absorption coefficients were small enough so as to not invalidate the use of Langley plots to determine solar cell AM0 short-circuit currents.

It is surprising the extrapolated AM0 short-circuit currents agree with the space measurements to within 2 %. It may be the case that the optical absorption coefficients used by Zoutendyk are not appropriate for the conditions under which the mountaintop measurements were carried out. There are three reasons for this conjecture.

1. The ratios of Zoutendyk’s measured and calculated short-circuit currents as a function of air mass differ considerably. He used Equation 7 to calculate short-circuit currents along with a standard AM0 spectral irradiance [5], the spectral response of the cells and atmospheric optical absorption coefficients [6]. In every case, the calculated short-circuit currents are smaller than the ones measured, suggesting the atmospheric optical absorption coefficients used are larger than the effective optical absorption coefficients at 7,400 ft.

2. The irradiances measured as a function of air mass are also considerably larger than the irradiances calculated using Equation 5. Zoutendyk plotted measured irradiance as a function of air mass on semi-log plots. The curves are clearly concave up providing convincing evidence of the effect of non-constant atmospheric optical absorption coefficients. In the case of the irradiance curves, Equation 5 shows the integral extends over a larger wavelength range and is not convoluted with the cell spectral response. The larger wavelength range and absence of the convolution both lead to the full effect of the atmospheric optical absorption coefficients on the transmitted sunlight and a concave up feature in irradiance plots.

3. An analysis of Zoutendyk’s data in six Langley plots yields atmospheric optical absorption coefficients ranging between 0.079 and 0.101 per unit air mass; the average is 0.087 per unit air mass. The average value of Moon’s optical absorption coefficients is about 0.15 per unit air mass in thetorange where the solar cell spectral response is the largest. The fact that the average slope is about 60 % of Moon’s optical absorption coefficients suggests either Moon’s coefficients are too large to be used in predicting AM0 short- circuit currents or the atmospheric conditions that prevailed during Zoutendyk’s measurements are different than the conditions under which Moon’s coefficients were determined. Additionally, the variation in the slopes of the Langley plots measured from day-to-day suggests changing atmospheric conditions may have played a role in the mountaintop measurements.

Ritchie recognized the problems associated with using Moon’s atmospheric optical absorption coefficients to correct solar cell short-circuit currents. He employed measurements on a mountaintop to produce secondary standards [7] that did not employ Langley plots. The secondary standards were based on the use of primary standards calibrated with the balloon method and the following equation:

(10)

where and are the calculated secondary and measured primary standard AM0 short-circuit currents, respectively; and are the secondary and primary standard short-circuit currents, respectively, measured at the same time on a mountaintop. The balloon method was used to measure. Following the mountaintop measurements, the secondary standards were flown on a balloon flight and the AM0 short-circuit currents measured; the currents agreed to within 0.5% with the currents predicted using the mountaintop measurements based on Equation 10. It is important to note that the spectral responses of the primary and secondary standards must be the same when using a primary balloon standard, Equation 10 and mountaintop measurements to produce secondary standards.

Aircraft method

The use of an aircraft to carry out high-altitude solar cell measurements at altitudes between 47 kft and 6 kft and air masses in the 0.180 – 0.862 range was first reported by Brandhorst [8]. It was suggested that the aircraft method is attractive when compared to the mountaintop method for three reasons. First, measurements are made at lower values of air mass than the mountaintop method resulting in shorter extrapolations of the short-circuit current on Langley plots. It is expected that the more accurate values of the AM0 short-circuit currents will be obtained if the extrapolation is over a smaller range of air masses. Second, the atmosphere should be less prone to compositional changes during the relatively short time of the aircraft measurements as compared to diurnal mountaintop measurements, i.e., minutes versus hours. Third, the measurements are made at altitudes that are above ground haze and low-altitude atmospheric disturbances.

The aircraft method employed a 4.5” diameter windowless collimator with a collimation ratio of 4:1 that was mounted inside the aircraft and extended through a hole in the side of the tail section [9]. The collimator was designed to over-fill the cell holder so that the cells were uniformly illuminated even when the orientation of the aircraft resulted in a 2-degree error in the pointing of the collimator. The collimator angle was set before each flight to the zenith angle of the sun during the measurements. The tail section was not pressurized and the cells were exposed to the low pressure and temperature environment that is characteristic of the altitudes at which the measurements were carried out. Single-junction silicon solar cells were mounted on a heated stage and the cell temperature maintained between 15 and 30 ^oC with a variation of less than 4 ^oC. The cell short-circuit current was taken as the current through a 1.000 precision resistor that was placed in series with the cell, as was done by Zoutendyk. The aircraft altimeter was used to measure pressure to an accuracy of 75 ft. The pilot used a sight tube mounted next to the controls in the cockpit to orient the aircraft and control the pitch, roll and yaw so as to point the collimator at the sun with a pointing accuracy of better than2 degrees. Altitude, cell short-circuit current and cell holder temperature were measured at altitude intervals of 5 kft during descent from 47 to 6 kft.

A standard atmospheric model was used to convert the altitude measurements to pressure [5]. The air mass was calculated using:

(11)

where is the pressure at which the cell short-circuit current was measured and is the sea-level pressure. Langley plots were produced and extrapolations carried out to determine the AM0 short-circuit current of the single-junction silicon solar cells. The AM0 short-circuit currents were corrected for cell temperature, precision resistor temperature, ozone absorption and the earth-sun distance. The extrapolated AM0 short-circuit current was corrected for ozone absorption using the cell spectral response; ozone absorption coefficients in the wavelength range [10]; ozone altitude profile [11]; and the percent of the total column ozone above the aircraft during measurements. The effect of ozone absorption on the short-circuit current of single-junction Si and GaAr solar cells was estimated to be 1.04 and 1.23 %, respectively. Brandhorst reported that all the Langley plots were straight lines [8,9]. However, there were differences in the slopes of the Langley plots from flight-to-flight suggesting atmospheric conditions, while perhaps constant during a flight, changed from flight-to-flight. The atmospheric optical absorption coefficients, as determined from the slopes of the Langley plots in the publications, ranged between 0.09 and 0.30 per air mass. The change in the slopes suggests there were variations in the concentration of optically absorbing atomic and molecular species in the atmosphere from flight-to-flight. The agreement in the AM0 short-circuit currents, measured by the aircraft method and the mountaintop method that used Equation 10, was0.9 %. The AM0 short-circuit currents measured during three separate flights were reproducible within