James R. Woodyard

Wayne State University, Detroit, Michigan

* *

David B. Snyder, NASA Glenn Research Center

Cleveland, Ohio

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.

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)

where_{}is 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. _{}and_{}are 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 _{}and_{}are 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 the_{}and_{} 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.

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.

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
mass_{}is 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 the_{}of 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
is_{}and 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 the_{}wavelength 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 the_{}to_{}range 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 ^{o}C with a variation of less than 4 ^{o}C. 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 than_{}2 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, was_{}0.9 %. The AM0
short-circuit currents measured during three separate flights were reproducible
within _{}1 % even though the slopes of the Langley plots, and therefore
the atmospheric conditions, were different.

Hadley analyzed data from three single-junction silicon cells. Two were balloon calibrated primary standards and one was a secondary standard calibrated using mountaintop measurements with Equation 10. All three of the cells were characterized with the aircraft method. He found that the cell AM0 short-circuit currents measured by the aircraft method were consistently about 1.6 % lower [12]. Hadley pointed out that the Langley plots for different days had different slopes and some of the plots appeared to be concave up . While there was a need to make spectral corrections because the spectral responses of the cells were slightly different, it was not possible since the different slopes for different days “indicate that there cannot be a unique value of the spectral correction factor.” The effect of Hadley’s work was to suggest that while it was agreed that the use of the Langley plots in the mountaintop method was faulted, there was evidence that there were also problems in using Langley plots to analyze data from the aircraft method.

Subsequently,
the aircraft method was used to measure silicon single-junction solar cell
short-circuit currents versus altitude.
The measurements resulted in Langley plots that exhibited an anomalous
behavior. [13]. The plots had a curve
with two linear regions, each of which had a different slope. There was a “break” in the curve where the
linear segments met. It was determined
that the “break” occurred at an air mass that corresponded to the altitude of
the tropopause. The short-circuit
currents measured at altitudes above the tropopause produced a linear plot with
a larger slope than the slope of the currents measured at altitudes below the
tropopause. Extrapolation of each of
the linear segments produced different AM0 short-circuit currents. The Langley plots for data collected at
altitudes above the tropopause extrapolated to larger AM0 short-circuit
currents than the plots for data collected at altitudes below the
tropopause. The slopes of the Langley
plots for data collected above the tropopause were the same on a month-to-month
basis while the slopes for data collected below the tropopause were different
on a month-to-month basis. The observation that
the slope above the tropopause was constant on a month-to-month basis suggests the concentrations of the
optically absorbing atomic and molecular species are the same on month-to-month basis for species that absorb in the region
of the solar spectrum that contributes to cell current [13]. The atmospheric optical absorption
coefficient determined from one of the Langley plots for the data collected
above the tropopause was about 0.20 per air mass. On the other hand, the fact that the slopes below the tropopause changed on a month-to-month basis
suggests concentrations
of the absorbing atomic and molecular species are different below the
tropopause on a month-to-month basis.
The atmospheric optical absorption coefficient determined from one of
the Langley plots for the data collected below the tropopause was about 0.09
per air mass.

A comparison was made of AM0 short-circuit
currents of five
silicon single-junction solar cells measured with the balloon and aircraft
methods [13]. The accuracy of the
balloon measurements was estimated at_{}0.9 %. Only aircraft data
collected above the tropopause were used.
Differences in the AM0 short-circuit currents measured by the two methods ranged
from 0.3 to 1.2 % with an average of 0.7 %.
The AM0 short-circuit currents measured with the aircraft method were
always larger than those measured with the balloon method. It was concluded that the measurements “show
excellent agreement”, and the aircraft method must be used above the tropopause
in order to produce good results.

Brandhorst carried out a series of experiments with the aircraft method to determine the wavelength region of the anomalous effect [14]. Optical filters were placed over solar cells and data collected both above and below the tropopause. The Langley plots had straight lines for data collected with filters that transmitted red and green light; an anomalous plot with a “break” was produced with data collected with a filter that transmitted blue light. The measurements suggested the anomalous effect was due to an atomic or molecular species that absorbed in the blue wavelength region of the solar spectrum, and that the species existed primarily above the tropopause.

The anomalous Langley plot can be understood by modifying
Equations 7, 8 and 9 to include the effect of two atmospheric optical
absorption coefficients. The
atmospheric optical absorption coefficient for an optically absorbing species
that exists primarily above the tropopause is taken as _{} for a range of
wavelengths from _{} to _{}, the wavelength range where the spectral response
contributes to the cell current. The
optical absorption coefficient in the same wavelength range is _{}for a different species that exists primarily below
the tropopause in the same range of wavelengths. Equations 7, 8 and 9 above the tropopause become:

_{} and

(12)

_{}.

The slope of the Langley plot above the tropopause is _{} and the extrapolated AM0 short-circuit
current is_{}. Below the
tropopause:

_{} and

(13)

_{}

where _{}is the solar spectral irradiance just below the tropopause;
it is corrected for absorption due to the optically absorbing species above the
tropopause. _{} is the short-circuit
current due to the convolution of _{} with_{}. The slope of the Langley plot below the tropopause is
_{} and the extrapolated AM0 short-circuit
current is_{}. The “break” in the straight line segments on the
Langley plot defines two regions of air mass where the data have linear
characteristics, namely, a straight line segment with a larger slope at lower
air masses and a straight line segment with a smaller slope at larger air
masses. It follows that _{} in the region of
lower air is greater than_{}in the region of larger air masses. Hence, the anomalous plots may be explained by assuming the
atmospheric optical absorption coefficients are different above and below the
tropopause.

The aircraft method has been developed over the
years by investigators at NASA Glenn Research Center [15,16]. A large body of calibration data has been
collected and AM0 standards provided to the PV community. The aircraft has been replaced twice and the
method improved. The current aircraft
is a Lear 25 that houses the instrumentation and collimator in a pressurized
and temperature controlled compartment.
Photographs of the Lear 25 aircraft, collimation tube and test cell may
be viewed on the NASA Glenn Research Center Web site [17]. The ratio of the collimation has been
increased to 1:4.5. The method was
upgraded to carry out measurements every nine seconds during a 6E-4 air mass
per second rate of descent from 50 kft down to the tropopause. Sources of random error were estimated to be
about 0.04 % and agrees with measurements.
The difference in the average of measurements on a single-junction cell
carried out over a twenty-year period and a recent measurement was at the 0.05
% level. Systematic errors were
estimated to be at the one percent level.
Space shuttle AM0 short-circuit current measurements on two cells were
compared with the aircraft method. The
aircraft measurements were less than the shuttle measurements by 1.0 and 0.8 %
for the two cells; the errors were consistent with the estimated systematic
errors.

The role of ozone on the solar cell AM0
short-circuit current measured with the aircraft method has been investigated
by Snyder and collaborators [18]. The
extrapolated AM0 short-circuit current was corrected using an ozone correction
factor. The correction factor was
determined using a calculated AM0 short-circuit current and a calculated
short-circuit current that included the effects of ozone absorption. The WMO solar spectral irradiance [19] and solar cell spectral
response were convoluted using Equation 1 to calculate the AMO short-circuit
current _{} where x corresponds
to Si, GaAs and InGaP single-junction solar cells. The short-circuit current_{} was calculated using Equation 7 and the WMO solar spectral
irradiance, solar cell spectral response, ozone absorption coefficients [20]
and total column ozone value_{}. The ozone correction factor _{} for each of the types
of solar cells was found using:

_{} (14)

where the units of_{}are Dobson units, d.u.
The correction factors were found to be insensitive, at the 5 % level,
to the value of the total column ozone, different sets of spectral response
data, and the resolution of the spectral response data used in the
calculations. The ozone correction
factor was reported to increase with an increase in the optical band gap of the
materials used in the solar cells.

The ozone correction method consisted of
employing a Langley plot to first determine the extrapolated AM0 short-circuit
current _{}. Then the current
was corrected for optical absorption in the ozone column on the day of the
flight. The sun zenith angle, total
column ozone on the day of the flight and the ozone correction factor were used
in the following equation to determine the AM0 short-circuit current for the
various types of cells:

_{}. (15)

The 0.83 factor results from assuming that 83 %
of the total column ozone was above the aircraft during the measurements. The correction method was used to analyze Si
solar cell data collected during 20 flights.
The correction resulted in an increase of 0.52 % in the Si AM0
short-circuit current as compared to the earlier one percent correction method
introduced by Brandhorst [9]. Applying
Equation 15 to the earlier aircraft measurements also reduced the differences
noted by Hadley in currents determined with the aircraft and balloon methods
[12]. The percentage standard
deviation of the ozone corrected currents decreased from 0.49 % with the
earlier correction method to 0.28 %, thereby suggesting the importance of using
Equation 15 to correct for the effect of ozone.

Applying the correction method to a GaAs solar cell, which has a larger
band gap than Si, resulted in AM0 short-circuits that were different from
flight-to-flight. The corrected
currents increased with increases in total column ozone suggesting that the
method was sensitive to the band gap of the cell. The correction method was revised in an effort to eliminate the
dependence of currents on total column ozone [21]. The revised method called for first correcting the short-circuit
current measured at each altitude for ozone absorption, then plotting the data
and extrapolating to air mass zero. The
approach requires the column ozone at each of the
altitudes at which the cell current is measured. The TOMS standard ozone profiles were used to calculate column
ozone as function of altitude [22].
Figure 2 shows the TOM ozone profiles used in calculating the column
ozone. The average ozone density in the
figure is plotted at the midpoint of each Umkehr layer [23], starting at layer
zero corresponding to an altitude of 9 kft, through layer 9 at 143 kft. The density shown in the figure at 156 kft
includes the ozone above 156 kft. The
profiles in the figure are for mid latitudes and total column ozone values
ranging from 175 to 475 d.u. Mid
latitudes are around 45 degrees north, the latitude of the NASA Glenn Research
Center flights. The maximum altitude
for the flights is about 50 kft. Figure
2 shows the fraction of the total column ozone above 55 kft decreases with
increasing total column ozone. The
fraction at 55 kft is about 0.87 of the total column ozone when the total
column ozone is 175 d.u.; the fraction decreases to about 0.77 at 475 d.u. The fraction is about 0.92 and fairly
independent of total column ozone at 40 kft.

The revised AM0 short-circuit current correction
method included converting the aircraft altitudes to atmospheric pressure,_{}. The total column
ozone on the day of the flight was obtained and used to select the appropriate
TOMS ozone profile in Figure 2. The
fraction of the total ozone column _{}above the aircraft during each of the measurements was calculated. The ozone corrected short-circuit current_{}was calculated for each measurement_{}using:

_{} (16)

The ozone corrected short-circuit currents were plotted as a function of
pressure on a Langley plot, instead of a function of air mass. The linear plot was extrapolated to zero
pressure to determine the AM0 short-circuit current. Results with the revised method were compared to the one percent
method using data for a Si single-junction solar cell. Data collected over two time intervals,
namely a short term and long term, were compared. The short-term data were collected on one cell during twenty
flights in one year. The long-term data
were collected on the same cell during thirteen flights over a period of eight
years. Table 1 shows differences in the
average AM0 short-circuit currents using the one percent, Av. Isco 1%, and
revised ozone correction methods, Av. Isco Revised. The percentage difference in the averages of the currents are 0.52
and 0.54 % for the short and long terms, respectively, showing the percentage
differences are essentially the same for the two periods. The percent standard deviation decreases
from 0.49 to 0.26 % and 0.72 and 0.48 % for the short and long terms, respectively,
showing the importance of the revised ozone correction method in reducing the
systematic error in the aircraft method. The percentage differences between the
highest and lowest AM0 short-circuit currents decreases from 3.2 to 1.2 % and
2.5 to 1.0 % for the short and long terms, respectively, again showing the
improvement of the results with the revised ozone correction method. The relatively larger percentage differences
in the highest and lowest AM0 short-circuit currents is due to the fact that
the zenith angle ranged between about 48 and 68 degrees during the various
flights. Both methods show a decrease
in the ozone corrected AM0 short-circuit currents as the zenith angle
increases. However, the revised ozone
correction method is considerably more effective in correcting for the effect
of the zenith angle. Not shown in
Table 1 is the percentage difference in the average AM0 short-circuit currents
using the revised method for the short and long terms; the difference is 0.26 %
which is within the standard deviation for the measurements.

Table 1 also shows the differences in the
average AM0 short-circuit currents for GaAs
and InGaP single-junction solar cells using the 1%, and revised ozone
correction methods. The GaAs data were
measured in 31 flights over a nine-year period. The InGaP data were collected during seven flights over a few
years. The band gap of GaAs is 1.43
eV. The band gap of the InGaP cell is
not known because the alloy concentrations were not reported for this
particular cell; however, it is expected that it is greater than the band gap
of GaAs. The percentage difference in
the averages of the currents corrected by the 1% and revised methods are 1.0
and 2.3 % for the GaAs and InGaP cells, respectively, showing the revised
method gives larger currents as the band gap increases. The percent standard deviations are reduced
for both the cells as was observed for the Si cell, again confirming the
importance of the ozone correction. The
differences in the high and low current values are reduced for both cells when
the revised method is used. A larger
zenith angle results in a larger correction in the AM0 short-circuit currents
for both cells. The revised method is
more effective in correcting for larger zenith angles as is illustrated by the
smaller high-low percentage differences in the AM0 short-circuit currents. However, there is a trend for corrected
currents to exhibit a decreasing trend with increasing zenith angle.

**Balloon Method**

The first balloon method measurements to
determine the AM0 short-circuit current of single-junction silicon solar cells
was reported by Zoutendyk [24]. A sun
tracker weighing about 70 lbs was flown mounted on the top of a balloon, as
opposed to in a gondola suspended below the balloon. Mounting the sun tracker on top of the balloon also reduced the
effect of sunlight reflections from the balloon on the cell measurement. The top mounting also eliminated anticipated
complicating effects of pendulum and torsional motion of the gondola on tracking
of the sun. The downlinked data
included three solar cell temperatures, fourteen cell short-circuit currents
and seven precision standard voltages. The cell short-circuit current was defined at the
current through a 1.000 _{} precision resistor
that was placed in series with the cell.
The
weight of the balloon, parachute, sun tracker, batteries, transmitter, data
acquisition system and other incidental items was 425 lb; the batteries and
transmitter were mounted in a gondola attached to the parachute which is turned
was attached to the bottom of the balloon.
The maximum volume of the balloon was 175,000 cubic feet and required
7,150 cubic feet of helium to provide an ascent rate of about 1000 feet per
minute. It took about two hours for the
balloon to reach the 80,000 ft float altitude.
The float time for flights was about four hours with two hours of
floating time before solar noon and two hours after solar noon. Two vehicles were used in support of
flights. One was a bus with
communications equipment that
maintained a distance of less than 200 miles from the balloon and received the
downlinked data. The other vehicle was
a chase truck that retrieved the equipment and solar cells. An aircraft was also available to assist if
necessary with tracking the balloon.

The solar irradiance at a zero zenith angle and
the 80 kft float altitude was estimated to be 95 % of AM0, corresponding to an
air mass of 0.05. A reduction of 0.3 %
was estimated in the air mass 0.05 cell short-circuit current, as compared to
AM0, considering the spectral response of the solar cells. The sun tracker was able to track the sun to
within_{} 4 degrees. An error
analysis of the measurement system showed a maximum error of about _{} 0.6 %. Three flights were carried out over a period
of three months and the results of the calibration of two silicon solar cells
were reported. The cell temperatures were 19 _{}1 ^{o}C during the first flight and 32 _{}1 ^{o}C during the last two flights. The data were corrected for
temperature. AM0 short-circuit currents
were reported for the mean earth-sun distance and 28 ^{o}C cell
temperature. No corrections were made
for ozone absorption. The repeatability
in AM0 short-circuit currents for three flights was better than _{} 0.5 % and the
accuracy estimated at _{} 0.6 %.

The balloon method has been further developed
over the years by Anspaugh and collaborators [25]. It has been used by the NASA Jet Propulsion Laboratory to provide
primary standards to the space photovoltaic community. The standards are calibrated at about 120,000
ft, the float altitude of the balloon.
Balloon flights are carried out at least once a year during the summer
months. The combined weight of the
balloon and top and bottom payloads is about 1,400 lb. The main balloon has a volume of about 3.6
E6 cubic feet and requires about 24,000 cubic feet of helium. Launching requires the use of a tow balloon,
spool vehicle, launch vehicle and helium tanker. The top payload weighs about 140 lb and consists of the sun
tracker, solar panel, transmitters, command receivers, data acquisition
electronics, video camera, batteries and miscellaneous items. The bottom payload is tethered in a gondola
and includes of batteries, ballast module, flight terminate equipment, pressure
transducer, transmitters, GPS receivers, and a variety of supporting electronic
systems. The top and bottom payloads
have separate parachute and release mechanisms. In excess of 75 cells and modules can be calibrated during a
flight. An on-board
microprocessor-based system is used for data acquisition and storage during
flights. Current-voltage measurements
are made over a voltage range from about 100 mV to the cell open-circuit
voltage. Cell temperatures are measured
both during ascent and at float altitude.
Cell temperatures are between 30 and 40 ^{o}C during ascent and
about 75 ^{o}C at float altitude. The balloon ascent rate was about 900 ft/min
and the time from launch to a 120 kft float altitude was about two hours; float
times ranged between 1.5 to 3.0 hours.
Data are downlinked to a base station at the launch site. An aircraft with a two-person crew direct
both the termination of the flight and recovery activities. The aircraft crew in retrieving the two
payloads directs a chase truck equipped with communications equipment.

Laboratory characterization of solar cells and
modules is carried out both before and after balloon flights to insure the
cells are not damaged. Cells with a
variety of structures have been flown including single and multi-junction cells
fabricated from crystalline and amorphous materials. Both thick crystalline and thin-film cells have been calibrated. Only data collected with the tracker pointed
to within _{}2 % of the sun are used in characterizing cells. “Wild” data points have been observed in
recent years with modifications in the equipment, e.g., adding a video camera
and placing some of the transmitters in the top package [26]. The data acquisition system has been
programmed to exclude “wild” data points from the data files that were used in
determining the cell AM0 characteristics.
The cause of the “wild” points was not know but it was suggested that
they may be due to water condensation or radio
interference.

A module was flown for 41 flights to evaluate
both measurement repeatability and the role of position on the solar
panel. It was felt that changing the
position of the module on solar panel could be used to evaluate the geometric
quality of the solar irradiance “with regard to uniformity, shadowing, or
reflections” [27]. The standard
deviation for 41 flights was 0.46 % and it was concluded that there are no
geometric problems. The cell used in
the 41 flights was damaged and replaced.
It was replaced with a set of nine standard cells and modules to
continue checking the repeatability of the balloon method. The nine standard cells and modules were not
flown on every flight. Cells and
modules were flown between 6 and 26 times.
The standard deviations of the AM0 short-circuit currents for the
flights range between 0.23 and 1.0 %.
The percent differences between the maximum and minimum AM0
short-circuit currents range between 1.3 and 4.4 % for all the standard cells
[28]. Two of the silicon
single-junction standard cells were flown on the Discovery Shuttle and the AM0
short-circuit current measured in a manner similar to the balloon method. The differences between one measurement on
the shuttle flight for each of the two cells, and the average of the AM0
short-circuit currents measured on multiple balloon flights, were 0.21 and 0.11
%, respectively. The agreement is seen
as “verifying the accuracy of the calibration procedures used on the balloon
flights” [29].

The agreement between shuttle and balloon
calibrations for two Si solar cells was
0.21 and 0.11 %, yet the set of standard cells have standard deviations
for multiple balloon flights that range between 0.23 and 1.0 %. Moreover, the percentage differences between
the maximum and minimum AM0 short-circuit currents range between 1.3 and 4.4 %
for the set of nine standard cells [28]. If the agreement between the shuttle
and balloon methods is taken as representative of the accuracy of the balloon
method for silicon single-junction cells, then the differences in the balloon
measurements may be due to either the spectral responses or instabilities in
the standard cells. The cell structure
and materials are not given for the nine standard cells [28], and for this
reason, it is not possible to correlate the differences with cell spectral
response. The standard cell with a 1.0
% standard deviation and a 4.4 % difference between the maximum and minimum AM0
short-circuit current was flown on 13 balloon flights. The data may be used to evaluate the role of
cell instability on measurements. The
first current measurement was 166.83 mA; the current measured on the thirteenth
flight was 611.11 mA. Inspection of the
measurements for the 13 balloon flights shows the trend is for the cell current
to decrease with each successive flight.
The data show that the reason for the relatively large cell statistics
is a gradual decrease in the cell’s current.
The behavior suggests the existence of a cell degradation
mechanism. It in noteworthy that the
cell operates at 75 ^{o}C at the float altitude. The cell will operated at 75 ^{o}C
in excess of twenty hours during the 13 flights. It is probable that thermal degradation resulted in the
relatively large change in cell current.
However, opto-electronic degradation and other sources of instability
should also be considered.

A joint NASA Glenn Research Center/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 120,000 feet [30-32]. The balloon flights are low-cost and can be carried out any time of the year.

The Suntracker scientific package includes a collimator with a cell to be calibrated, two GPS receivers, two transmitters, two separate battery packs, control electronics and a video camera. Figure 3 shows the scientific package. The main body of the package is cylindrical and fabricated from urethane foam; it measures 11” in diameter and 11” high. The package is about one inch thick and provides thermal insulation for the electronics. Two battery packs are supported 22” from the main body by light carbon composite tubes that are arranged in a “z” configuration. The battery packs are mounted in this fashion to increase the rotational inertia of the package; the 22” length is limited by the interior width of the mobile unit. The two battery packs are enclosed in separate carbon tubes and wrapped in foam insulation to provide thermal insulation. The dimensions of the collimator are 1.25"x1.25"x4.00"; the front aperture is 1.00"X1.00" and the cell area 0.79"x0.79" [x]. The dimensions of the collimator were selected to provide a 1:4 collimation ratio and a one degree pointing accuracy. The collimator prevents light scattered from the balloon, earth, moon or clouds from contributing to solar cell current . Two motors and supporting electronics control the altitude and bearing angles of the collimator during a flight. A video camera is mounted on top of the package and used to observe the operation of the Suntracker as it ascends though low temperatures to the stratosphere. The weight of the payload is about six pounds. Photographs showing the system components inside the scientific package may be viewed on the Suntracker Web site [33].

The scientific package is
attached to a parachute that is affixed to a latex balloon. The balloon weighs about three pounds and is
inflated with about 250 cubic feet of helium and launched by a three-person
team. The Suntracker scientific package
is tethered below the balloon and the electronics is programmed to point the
collimator at the sun during ascent.
The balloon ascends at a rate of about 800 ft/min to a burst altitude
ranging between about 87 and 100 kft in about two hours and then parachutes to
a landing site. Data are downlinked
continuously during the flight on 2 m and 70 cm bands to a mobile unit that is
equipped with receivers, computers and tracking software. The three-person team in the mobile unit
chases the balloon, records the data and retrieves the scientific package. The data includes cell voltage, cell
temperature, electronics module temperature, video, reference voltage, and
atmospheric pressure. The short-circuit
current is determined from the cell voltage across a 1.000 _{} precision resistor
that is in series with the cell.

**RESULTS**

Seven flights have been attempted with five
successful launches. Table 2 shows the
launch dates and locations, burst altitudes, landing sites and balloon
trajectory ranges. The scientific
package was retrieved on the same day for the Suntracker I, III and IV
flights. Hardware problems developed
during the Suntracker VI and VII flights that resulted in the loss of GPS
signals; the package was found within a few days of the launch by individuals
and subsequently retrieved. A
single-junction silicon solar cell was mounted in the collimator during the
flights. The cell voltage data
downlinked during the Suntracker IV and VI flights have been analyzed using
Langley plots to determine the AM0 short-circuit current. The Suntracker IV uncorrected short-circuit
current versus altitude is shown in Figure 4.
Only the maximum currents were selected for use in the Langley
plot. The cell current data illustrate
the tracking characteristics during the ascent. For the most part the Suntracker was not locked on the sun during
the flight. The video data showed the
motors slowed down during the ascent as a result of the low atmospheric
temperatures. Motor assemblies using
lubricant with lower temperature specifications will be evaluated in future
flights. Additionally, the stability of
the scientific package and the collimator control algorithm will be
investigated in order to improve the performance of the Suntracker system.

The cell temperature versus altitude during the Suntracker VI flight is
shown in Figure 5. Also shown are the
radiosonde data reported by the National Weather Service (NWS) on the day of
the flight. The effect of solar heating
on the cell current is apparent . While
the solar cell temperature increased from –10 to about 0 ^{o}C as the balloon ascended from
80 to 96 kft, the

atmospheric temperature remained at about –45 ^{o}C. The dependence of the cell and NWS temperatures in this altitude range suggests that the cell
temperature may be higher at higher altitudes.
If this is the case, it will be possible to operate cells closer to 25 ^{o}C
at higher altitudes, and to determine the temperature coefficient of the
short-circuit current as the package ascends.

Figure 6 is a Langley plot of the data for a
single-junction silicon solar cell from the Suntracker IV and VI flights. The optical air masses were calculated using
Equation 11. The data have been
corrected for the earth-sun distance and cell temperature, and fit with
straight lines. The extrapolated AM0
short-circuit currents are 144.32 and 144.38 mA for the Suntracker IV and VI
measurements, respectively. The average
AM0 short-circuit current is 144.35 mA _{}0.02 %. The
resolution of the eight-bit ADC in the Suntracker data acquisition system is _{}0.2 %, showing that the agreement between the two flights is
better than the uncertainty in the measurements and probably reflects the
statistics of the curve fitting etc.
The AM0 short-circuit current of the single-junction silicon solar cell flown on the Suntracker flights
was determined using the aircraft method at NASA Glenn Research Center
[21]. The AM0 short-circuit current was
144.88 mA and within _{}0.36 % of the Suntracker average value. The results agree to within the statistics
of the two methods, namely about _{}0.2 % for the Suntracker measurements and _{}0.6 % for the aircraft method.

It is instructive to determine the atmospheric optical absorption
coefficients for the two methods using Equation 9. The slopes of the two straight lines in Figure 6 were analyzed to
determine the absorption coefficients; the coefficients are 0.265 and 0.293 per
air mass for the Suntracker IV and VI data, respectively. The average value of the atmospheric optical
absorption coefficient is 0.280 per air mass_{}5 %. An analysis of
the Langley plot produced with aircraft data gives absorption coefficients of
0.125 per air mass. The Suntracker
value is somewhat larger than the 0.20 per air mass determined from the earlier
aircraft measurements [13] while the absorption coefficients determined with
the current aircraft data is considerably less. The reasons for these differences are not understood and will be
the subject of future investigations.

**CONCLUSIONS**

The
voltage dependence of the spectral responses of multi-junction solar cells
complicates optimization of cell design.
The series nature of multi-junction solar cells places more demands on
the need for standard cells characterized under AM0 conditions. Cells selected for use as standards should have
a history of thermal cycling and light soaking that provides evidence of the level of cell stability. The AM0 short-circuit current of a single-junction silicon solar cell was determined
using data collected during two Suntracker flights. The agreement in the two measurements was _{}0.02 %. The agreement
in the AM0 short-circuit current of the cell measured with the Suntracker
balloon method and NASA Glenn Research Center aircraft method was _{}0.36 %, which is
within the uncertainty of the two methods.
There is a need to understand the role of ozone and atmospheric optical
absorption on the calibration of solar cells in the stratosphere.

**REFERENCE**

- James R. Woodyard, “Laboratory Instrumentation and Techniques for Characterizing Multi-Junction Solar Cells,”Proceedings of the Twenty-Fifth Photovoltaic Specialists Conference, page 203, 1996.

- Geoffrey A. Landis and Shelia G. Bailey, “Photovoltaic Engineering Testbed on International Space Station,” Proceedings of the Second World Conference on Photovoltaic Solar Energy Conversion, page 3564, 1998.

- John A. Zoutendyk, “A Method for Predicting the Efficiency of Solar Cell Power Systems Outside the Earth’s Atmosphere,” NASA Technical Report No. 32-259 (1962).

- Moon, P., “Proposed Standard Solar Radiation Curves for Engineering Use,” 1940, J. Franklin inst., 230, 583-617, 1940.

- National Technical
Information Office, ”Standard Atmosphere Model,” Springfield,
Virginia (Product Number: ADA-035-6000).

- Johnson, F. S., “The solar constant,” 1954, Journal of Meteorology, 11, 431-439.

- D. W. Ritchie, “Development of Photovoltaic Standards for NASA,” Proceedings of the Fourth Photovoltaic Specialists Conference, page C-5-1, 1964.

- Henry W. Brandhorst, Jr., “Airplane Testing of Solar Cells,” Proceedings of the Fourth Photovoltaic Specialists Conference, page C-2-1, 1964.

- Henry W. Brandhorst, Jr., and Earle O. Boyer, “Calibration of Solar Cells Using High-Altitude Aircraft,” NASA Technical Note, NASA TN D-2508, February 1665.

- E. Vigroux, “Contribution to the Experimental Study of the Absorption of Ozone,” Annales de Phys., vol. 8, page 709, 1953.

- L. A. Biryukova, “Distribution of Energy in the Spectrum of Solar Rays a Various Altitudes,” JPRS 7488, Joint Pub. Res. Service, 1959. C. P. Hadley, Proceedings of the Fourth Photovoltaic Specialists Conference, page C-3-1, 1964.

- C. P. Hadley, “Comparison of Flight and Terrestrial Solar Measurements on Silicon Cells,” Proceedings of the Fourth Photovoltaic Specialists Conference, page C-3-1, 1964.

- Henry W. Brandhorst, Jr.,” Calibration of Solar Cells Using High-Altitude Aircraft,” Proceedings of the Fifth Photovoltaic Specialists Conference, page E-1-1, 1965.

- Henry
W. Brandhorst, Jr., “Anomalies in Solar Cell Langley Plots Associated with
the Tropopause,” Applied Optics, vol. 7, page 716, 1968.

- Philip Jenkins, David Brinker, and David
Scheiman, “Uncertainty Analysis of High Altitude Aircraft Air Mass Zero
Solar Cell Calibration,” Proceedings of the 26th Photovoltaic
Specialists Conference, page 857, 1997.

- David
J. Brinker, David A. Scheiman, and Phillip Jenkins, “Calibration of Space
Solar Cells Using High Altitude Aircraft,” Proceedings of the 2nd World
Conference on Photovoltaic Solar Energy Conversion, page 3654, 1998.

- David B. Snyder, David A. Scheiman, Philip P. Jenkins, William J. Rieke and Kurt S. Blankenship, “Ozone Correction for AM0 Calibrated Solar Cells for the Aircraft Method,” Proceedings of the 29th Photovoltaic Specialists Conference, page 832, 2002.

- http://rredc.nrel.gov/solar/spectra/am0/NewAM0.xls

- B. Leckner, “The Spectral Distribution
of Solar Radiation at the Earth’s Surface – Elements of a Model,” Solar
Energy, volume 20, page 143, 1978.

- David B. Snyder, Philip P. Jenkins and David A. Scheiman, “Historical Precision of an Ozone Correction Procedure for AM0 Solar Cell Calibration,” Proceedings of the Space Photovoltaic Research and Technology Conference, 2003, In Press.

- Richard D. McPeters, P. K. Bahartia, Arlin J. Krueger, Jay R. Herman, Charles G. Wellemeyer, Colin J. Seftor, Glen Jaross, William Byerly, Steven L. Taylor, Tom Swissler and Richard P. Cebula, “Earth Probe Total Ozone Mapping Spectrometer (TOMS) Data Products User’s Guide,” NASA Technical Publication 1998-206895, page 53, 1998.

- IBID, page 53.

- John A. Zoutendyk, “The Space Calibration of Standard Solar Cells Using High Altitude Balloon Flights,” Proceedings of the Fourth Photovoltaic Specialists Conference, page C-4-1, 1964.

- B. E. Anspaugh and R. L. Mueller, ”Results of the 2002 JPL Balloon Flight Solar Cell Calibration Program,” JPL Publication 02-03, 2002.

- IBID, page 20.

- IBID, page 22.

- IBID, page 26.

- IBID, page 1.

- Glenroy
A. Bowe, Qianghua Wang, James R. Woodyard, Richard R. Johnston and William
J. Brown, “Investigations to Characterize Multi-Junction Solar Cells in
the Stratosphere Using Low-Cost Balloon and Communication Technologies,”
Proceedings of 16
^{th}NASA Space Photovoltaic Research and Technology Conference, August 31-Septermber 2, 1999, page 189.

- Glenroy A. Bowe, Qianghua Wang and James R. Woodyard, ”Investigations to Characterize Multi-junction Solar Cells in the Stratosphere Using Low-Cost Balloon and Communication Technologies,” Twenty-Eight IEEE Photovoltaic Specialists Conference Proceedings, 2000, page 1328.

- Ali Mirza, David Sant, James R. Woodyard, Richard R. Johnston and William J. Brown, “Report on Project to Characterize Multi-junction Solar Cells in the Stratosphere Using Low-Cost Balloon and Communication Technologies,” Seventeen Space Photovoltaic Research and Technology Conference, 2001, page 137.

Go
Back_{}