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Measurement of solar radiation by silicon solar cell
A 1966 Conference Paper
Measurement of Solar Radiation by Silicon Solar Cell M. G. B o n n e r and C. M. S a p s f o r d School of Mechanical Engineering, University of New South Wales I n v e s t i g a t i o n s i n t o t h e u s e o f a s i l i c o n s o l a r cell to measure solar radiation intensity are described. T h e effect o f o p t i c a l p a t h l e n g t h r a t i o a n d a t m o s p h e r i c c o n s t i t u e n t s a r e d i s c u s s e d . A s u r v e y is m a d e o f o t h e r p h o t o v o l t a i e devices. I t is c o n e l u d e d t h a t , o n p r e s e n t l y a v a i l a b l e d a t a , t h e silic o n cell is t h e m o s t s u i t a b l e f o r t h e p u r p o s e . Comparisons are made between the signals obtained from a silicon-solar-cell radiometer and a K i p p t h e r m o p i l e t y p e s o l a r i m e t e r u s e d as a s t a n d a r d . O n e s e t o f c o m p a r i s o n s is m a d e f o r 3 0 - m i n u t e i n t e r v a l s o n c l e a r d a y s a n d is a n a l y s e d so t h a t k n o w n effects d u e t o a n g l e o f i n c i d e n c e a r e a l lowed for and variations in the signals caused by spectral quality of the radiation can be separated. This set of comparisons shows an extreme spread o f 4-13 p e r c e n t o n a r e f e r e n c e c o n s t a n t d e t e r mined for midday clear sky. This extreme spread i n c l u d e s v a r i a t i o n s o f + 6 . 5 t o --3 p e r c e n t a t m i d day together with variations during the course of any one day. A second set of comparisons made during whole d a y s or l o n g p e r i o d s , d u r i n g w h i c h c o n d i t i o n s w e r e s t a b l e , g a v e rise t o t w o c a l i b r a t i o n c o n s t a n t s , one for clear-sky and one for overcast-sky conditions. I f a n o v e r - a l l c a l i b r a t i o n c o n s t a n t is d e s i r e d f o r all c o n d i t i o n s , t h e n a v a l u e o f 15.79 m A c m - " m i n / L a n g l e y is o b t a i n e d w i t h a p r o b a b l e e r r o r o f --3½ t o +8½ p e r c e n t . T h e s k e w effect h e r e is b e c a u s e more readings were taken for clear-sky conditions, thus favoring the lower constant for these conditions.
N ANY program of solar-energy utilization, measuremerit of the radiation income at the locality is important. Unfortunately most comprehensive radiationmeasuring networks exist in countries where solar-energy utilization competes with abundant alternative cheap sources of power. At the same time, only limited solar radiation records exist in those countries
I
Presented at Solar Energy Conference, Boston, Massachusetts, March 21--23, 1966. Vol. 10, No..~, 1966
where solar energy could be effectively and economically utilized to improve the standard of living. To meet this situation, a number of original radiationmeasuring instruments have been proposed recently2, 2, 4, 8, 11, 25, 23. T h e equipment should operate independently of power supplies. A feature of some of these proposals has been the use of a silicon solar cell as a radiation-sensitive surface. The major objective here is to assess the suitability of the silicon cell as a radiation-sensitive element, to compare it with some alternative elements of a similar nature, and to investigate its linearity with existing instruments for solar-radiation measurements. The investigations described here form a part of studies carried out in Sydney over the period 1960-1963. During this time, certain other features of the application of the silicon cell to the measurement of solar radiation were studied and have been reported b y Bonner. 8 I n particular, theoretical calibration constants have been computed for various conditions, and the effect of changes in the angle of incidence of the direct collimated solar b e a m to the silicon-cell surface has been investigated. This additional work is not reported here as it has been included in a recent publication by other authors, s° A n A p p r a i s a l o f S o m e P h o t o v o h a i c Devices Is the silicon cell the most suitable photovoltaic device for the measurement of solar-radiation intensity? An examination and comparison of various semiconductor photovoltaic devices is given in answer to this question, based on research reports as well as the practical experience of workers in the field. However, in m a n y eases, information is not available, indicating lhat further developments of some of the devices can be expected. Over a dozen semiconductor materials have been developed for photovoltaic conversion of radiant energy, including indium phosphide, gallium arsenide, cadmium telluride, cadmium sulphide, cadmium selenide, aluminium antimonide and selenium. Of these, selenium and cadmium sulphide are selected for detailed comparison with silicon, the reason being t h a t there is more comprehensive d a t a available on these. Nevertheless, from the limited information relating to other photovoltaic materials (for example, spectral response curves), similar reasoning and deductions would apply. 195
Some important properties of silicon, selenium, and cadmium sulphide photocells are listed in Table 1. The metal-semiconductor type of junction is formed by the deposition of a suitable transparent metallic film by evaporation or sputtering on to the semiconductor. This forms the so-called "barrier layer" cell. The technique for making the p-n junction cell has been described fully by other workers} a, ~7.2t In the past, the primary application of the selenium photocell has been in photometric equipment and lightmeasuring devices such as spectral photometers and photographic light meters. However, it has many severe practical disadvantages for these applications as well as for solar-insolation measurements. The mounting of the selenium cell presents two major problems: moisture damage to the cell is possible if sealing is not effective, and means must be incorporated to correct for the cosine error. This correction is normally done by means of an opal perspex diffusing disc. Regarding the cosine error for the selenium cell, Pleijel and Longmore '4 comment that "for directional illumination at angles greater than 60 deg, the response may easily fall 30 percent below the theoretical value". Another important consideration is the life of the selenium cell. Manufacturers recommend that if a cell is to be used to measure high illumination levels, such as direct sunlight, neutral-density filters should be used to cut down the illumination level at the surface of the cell in order to prolong its life. Trickett and Moulsley 2~ conclude that "the chief objection to the selenium photocell is that it is possible for it to deteriorate slowly and this may occur unnoticed". Turifing to the silicon cell, various authors report confidently of its long-terln reliability. Browne, Francis, and Enslow 5 make these observations. " N o effect was found due to ageing for 233 days for cells aged as follows: (a) at room temperature, (b) at a constant temperature of 60 deg C, and (c) in a desiccant". Prince '5
12OC
I
f-~.
Moon(m:2)
IOOO 8
/
,,'x
S¢
u
~oo
A \
/>1
--St
k / - --7OOO K
400
02
/
i/
04
,
~
08 1"2 16 WAVELENGTH (Microns)
col_
2"0
2"2
FIG. l--Proposed standard curve (after Moon I~, to the vertical scale). Spectral distribution for 7000°K black body. Relative response of Cadmium sulphide (Cd) Selenium (Se) and Silicon (St) photocells. (after Sasuga TM and Prince~% not to vertie'd scale). 196
TABLE 1--COMPARISON OF PHOTO CELL TYPES Photocell Material
Crystal form Type of junction Forbidden energy gap Ea electron volts Wavelength corresponding to energy gap (Eo) microns
Silicon
Single crystal Diffused
Selenium
Cadmium Sulphide
1.1
Polycrystalline Metal-semiconductor 1.5
Single crystal Unknown (complex) 2.4
1.1
0.83
0.52
p-n
affirms "there is no known possibility of deterioration occurring in silicon solar cells at the earth's surface". Large temperature effects are reported with the selenium photocell. For example, makers' data sheets show as much as 10 percent deviation in output for temperature variations in the range 0 to 50 deg C. Although not nearly as much information is available on the cadmium-sulphide cell, Rappaport 1~ reports a rapid fall of the short-circuit current with increasing temperature for this device. In the idealized case, for a particular semiconductor, the number of electron-hole pairs collected by the p-n junction is equal to the number of photons in the spectrum of energy greater than the energy gap, Ea, of the solid. This, in effect, assumes the existence of a sharp absorption edge with complete absorption and zero losses on its high-energy side. Table 1 quotes values of the energy gap for silicon, selenium, and cadmium sulphide. Values of Ea for other semiconductors, previously cited as having been developed for photovoltaic energy conversion, are as follows: indium phosphide: 1.3 ev; gallium arsenide: 1.4 ev; cadmium telluride: 1.5 ev; aluminium antimonide: 1.6 ev; cadmium selenide: 1.7 ev. From the ideal viewpoint, the lower the value of the energy gap, E , , the more accurate will be the device to measure incident radiation of varying spectral quality, since a greater part of the spectrum will be utilized for the generation of electron-hole pairs. Ideally, silicon utilizes all photons of energy greater than 1.1 ev; selenium, those of energy greater than 1.5 ev, etc. Silicon, therefore, is the most suitable from this viewpoint. Perhaps .~ more important comparison is gained by examination of ,~ctual spectral response curves in relation 1o solar spectral distributions. The responses of the selenium and cadmium sulphide photocells (from Sasuga ~9) and the silicon cell (from Prince 16) in terms of short-circuit current, are shown in Fig. 1.3"he responses are not to scale. Also plotted is Moon's t2 proposed standard curve for the spectral distribution of the direct component of solar r'~diation for optical-path-length ratio m = 2, and the distribution of energy emitted from a black body at a temperature of 7000 deg K. The opticalpath-length ratio (m) is the optical path length of the Solar Energy
sun's direct rays through the atmosphere as a ratio of the depth of the atmosphere. Following Loferski, 9 it is assumed that the black body at 7000 deg K approximates the spectral distribution of radiation at the earth's surface with an overcast sky. Examining the three spectral-response curves, the broadness of the silicon curve compared with those of the cadmium-sulphide and selenium photocells is most striking. The sensitivity of the cadmium-sulphide cell is almost confined to the visible range; the selenium device is responsive through the ultraviolet range and the visible; and the silicon cell is sensitive over the visible and part of the infrared. This comparative broadness is, of course, highly desirable. The ideal converter for a radiometer would, of course, have a response independent of wavelength so that a constant fraction of the energy at each wavelength interval would be converted to electrical current. Some comments on the seemingly anomalous cadmium-sulphide response curve is necessary. The predicted cut-off of 0.52 microns is not in fact true. The cell is actually responsive to wavelengths up to approximately 0.8 microns. I t is noted in Table I that the mechanism of operation of the cadmium-sulphide cell is not understood and is apparently complex in nature. Cherry 6 notes that cadmium sulphide "is a material outside the theoretical optimum energy gap range that displays unusual photovoltaic properties". Intensive development is continuing into the characteristics of semiconductor materials and into methods of manufacture. The silicon cell may, in the future, have to give way to a cell made of another material with better characteristics, or one that can be made by significantly simpler or cheaper methods. However, at present, the silicon cell appears to be the most stable and the most suitable of the semiconductor materials for application to the measurement of solar radiation.
The Relative Importance of Atmospheric Variables Differing quantities of the various components of the earth's atmosphere are responsible for changes in the spectral distribution of solar radiation incident at the surface of the earth. These components include ozone, carbon dioxide, water vapor, and dust particles. Another variable affecting radiation from the sun is the distance through which the rays travel to the particular location on the earth's surface. Because of the spectrally selective nature of the silicon cell, a variation in the spectral distribution of the incident solar radiation can affect the rate at which the device converts radiation energy to electrical energy. This conversion rate, expressed as the short-circuit current generated by unit intensity of radiation on the cell surface ( m A c m -2 min/ly) is the calibration ratio of the silicon-cell radiometer. Vol. 10, No. ,~, 1966
2000 r Energy Outside Atmosphere .($')
Sotor Energy At Sea-Lever
oI-Iooo
, 111 -, 2°
4000
1200 WAVELENGTH
20000 ( ANGSTROMS )
28000
Fio. 2--Spectral distribution of solar energy outside the atmosphere and at sea level (after Luckieshl°). Moon 1~ points out that, because dust particles are comparatively large (of the order of one micron diameter), "the effect of wavelength is less marked than with molecular scattering, and it is customary to assume that scattering by dust is independent of wavelength". Making this assumption, it follows that an increase in the concentration of dust particles in the atmosphere would reduce the intensity of the radiation over the whole spectrum in a uniform manner. Variation in dust content of the atmosphere should not therefore influence the calibration ratio for the silicon cell. Ozone, water vapor, and carbon dioxide are the atmospheric components remaining for consideration. If, as a result of a change in the value of one of these variables, a variation in the spectral distribution of solar radiation occurs in a wavelength band to which the silicon cell is not sensitive (wavelengths less than 0.35 microns or greater than 1.11 microns) then this variation in spectral distribution, and in solar radiation intensity, will not be registered by the cell. The cell will register a change in output current due to changes in the radiation intensity occurring within its sensitive range. However, as the spectral response is variable over this range, as shown on Fig. 1, wavelengthdependent changes in radiation intensity will not be reflected in a linear fashion by cell output current. Referring to Fig. 2, which is from Luckiesh, l° it is seen that water-vapor absorption accounts for a considerable percentage of the radiation attenuated; beyond 1.1 microns especially, there are large watervapor absorption bands. Changes in water-vapor content of the atmosphere can be expected to have all influence on the calibration ratio. In the peculiar case of ozone, we see from Fig. 2 that absorption occurs at the shorter wavelengths. Primarily, ozone causes a sharp cutoff in the spectrum below 0.29 microns, this occurring for all concentrations found in the atmosphere. Carbon dioxide has a similar effect on radiation of wavelengths longer than 2.3 microns (see Fig. 2). Moon 12 states that "radiation at wavelengths 197
beyond 2.3 microns is strongly absorbed by H20 and C O 2 . . . " . Variations in the concentrations of these two constituents will therefore cause little change in the spectral distribution. Moon 12 has made an excellent study of the spectral distribution of direct solar radiation on cloudless days. He has computed the effect on the distribution of changes in the optical-path-length ratio of the sun's direct rays through the earth's atmosphere. He assumes fixed values for barometric pressure and quantity of precipitable water, dust, and ozone in the atmosphere. His paper presents spectral distributions for each of five optical path lengths. Table 2 has been computed from these plots. In the table, the energy contained within a particular wavelength band is expressed as a percentage of the total energy available. Numerical methods of integration (trapezoidal-rule approximation ,tpplied to scaled ordinates) have been used to determine areas under the curves. The considerable changes that occur in the forms of the spectral distributions as changes in the optical path length are demonstrated in Table 2. For example, in the wavelength range, 0.4 to 0.5 micron, the percentage of the energy available is seen to range from 8.1 to 14.6 percent. Since, as shown in Fig. 1, the cell is almost insensitive to wavelengths below 0.35 microns, while significant variations in this wavelength band are shown in Table 2, these variations in the intensity of the incident energy will not be registered by the cell. Thus, it is expected that the optical-path-length ratio, which varies from a mininmm at solar noon to maximum at day-break and sunset,, should have some influence on the calibration ratio over any day. The above qualitative assessment has indicated that variations in dust content of the atmosphere should have little impression on the calibration ratio, but changes in the water vapor content could have some influence. Also, the hourly and daily variations in the optical path length of the sun's rays through the earth's atmosphere are important. Calibration Ratio of a Silicon-Cell Radiometer
The calibration ratio of the silicon cell, when used as a radiometer, was investigated experimentally by comparing the output from a cell with that from a Kipp solarimeter taken as the standard. The Kipp solarimeter uses a blackened thermopile as the radiation-sensitive receiver. The observations indicated that no one calibration ratio could be defined. However, a reference constant has been determined and correction factors for angle of incidence of the solar beam and for spectral quality have been isolated. For the purpose of qualitative comparison, in Fig. 3 a whole-day record from the horizontally exposed silicon 198
T A B L E 2 - - R A D I A N T E N E R G Y IN T H E D I R E C T SOLAR BEAM FOR DIFFERENT OPTICAL PATH LENGTH RATIOS T h e d a t a has been computed from spectral d i s t r i b u t i o n s published by Moon2~ Optical Path Length Ratio (m)
Wavelength Band (micron)
1.7
0.5 8.1
Up to 0.4 0.4-O.5 0.5-0.6
4.3 14.6 16.3
2.7 12.9 16.0
11.2 15.6
1.1 9.6 14.6
0.(;-0.7 0.7-0.9 0.9-1.1
14.5 20.6 12.7
15.5 22.4 13.7
15.9 23.3 14.8
16.2 24.5 15.8
9.2 6.4 1.4
9.0 6.6 1.2
9.1 7.2 1.2
9.2 7.8 1.2
9.5
lOO.o%
100.0%
1.1-1.4 1.4-1.8 greater t h a n 1.8
100.~o
lOO.O7o 100.0%
13.6 16.4
25.5 16.9 8.4 1.1
cell has been superimposed on the Kipp solarimeter record for the same period. The day selected, 7th October, 1962, was essentially cloudless. Bumps in the record were probably due to one or two wispy clouds or perhaps smoke. Comparison reveals corresponding rises and falls in each record, and an approximate proportionality of one output to the other. No irregular aspects can be discerned. In fact, for all comparisons made by the authors over the eleven-month period of recording the output from the fully exposed silicon cell, similar conclusions were reached. Description of test equipment--A silicon cell was mounted in a horizontal position adjacent to the Kipp solarimeter on the roof of the Project Laboratory of the School of Mechanical Engineering. Both solarimeter and cell were fully exposed to both direct and diffuse components of solar radiation. The location for the equipment was about 60 feet from ground level, free fi'om interference by neighboring buildings, hills, etc. The current output from the silicon cell was passed through a 0.270-
'5< ~-
Kipp Sola
imeter
t--W
-- ]8OO
1600 14OO 12OO I000 0800 0600 AU~TDALIAN EASTERN STANDARD TIME (Hours)
FIG. 3--Conlparison of records from silicon cell solar radiom e t e r and Kipp solarimeter m o u n t e d horizontally. Sydney 7 October, 1962.
Solar Energy
TABLE 3--VALUES OF f (a), CORRECTION FACTOR. FOR ANGLE OF INCIDENCE FROM BONNER 3 a, Degrees
f(a)
a, Degrees
f(a)
0 5 10
1.000 1.000 0.995
45 50 55
0.988 0.981 0.963
15 20 25
0.997 0.998 1.000
60 65 70
0.947 0.911 0.866
30 35 40
0.995 0.998 0.992
75 80 85
0.805 0. 692 0.566
Let = f(a)f(Q)KIr
Formula L~ = A I cos a f(~) where L~ = deflection of meter attached to silicon cell radiometer when reading direct radiation only A = calibration constant I = direct radiation incident on cell = angle of incidence between direct radiation beam and the normal to the cell surface. ohm standard resistance and the voltage generated across this resistance recorded. T h e value of the resistance was calculated to give a m a x i m u m deflection of the galvanometer on the millivolt recorder within full scale, and at the same time to approximate short-circuit operation of the cell. The voltage generated across this resistance was recorded on a K i p p clockwork operated recording millivoltmeter. The recording of the output from the totally exposed silicon solar cell was commenced on 8th December, 1961, and continued through to 14th November, 1962. Periodic maintenance of the equipment as a whole consisted simply of dusting the surface of the silicon cell with a soft brush and at the same time, cleaning the glass dome of the X i p p solarimeter. This was done each week-day morning. T e m p e r a t u r e compensation was not provided on the silicon cell tested, as the cell was fixed to a rather massive metallic m o u n t t h a t would have had the effect of stabilizing the cell t e m p e r a t u r e near to ambient, while the daytime ambient variation experienced was approxim a t e l y from 55 to 90 deg F. A m a x i m u m variation of -4-1.5 percent on a mean calibration constant was expected for this t e m p e r a t u r e variation and confirmed b y the readings published b y Selcuk and Yellott? ° The shunting resistance of Manganin wire was subject to a variation of =t=0.025 percent over the same t e m p e r a t u r e range and this effect was considered insignificant. A s s u m p t i o n s involved in the c o m p a r i s o n - - I n a t t e m p t ing to use the silicon solar cell as a solar radiometer, and in determining a cell calibration constant b y comparison with a K i p p solarimeter, two i m p o r t a n t assumptions are made. First, it must be assumed t h a t the measured deflection on the K i p p recorder is directly proportional to the incident solar radiation as represented b y the equation: LKr = C d r Vol. 10, No. 4, 1966
where L~r = deflection on recorder attached to totally exposed Kipp solarimeter C1 = constant = 5.04 c m / l y min. -1 I r = total solar radiation. Second, it must be assumed that the deflection of the recorder connected across the standard resistance is a measure of the short-circuit current of lhe silicon solar ceil, and t h a t this deflection is in turn related to the incident solar radiation b y the equation:
(1)
(2)
where L c r = deflection on recorder attached to totally exposed silicon cell radiometer f(a) = correction factor to allow for the effect of the angle of incidence of the direct solar beam to the surface f(Q) = correction factor to allow for the variation of the spectral quality of the radiation K = reference constant for the cell. Values for f(a) were determined separately and are listed in Table 3. To allow for the fact t h a t the Kipp total solarimeter and the silicon cell are exposed to the full hemispherical radiation, while a correction factor for angle of incidence effects, f(a), applies strictly to the direct b e a m of solar radiation only, the deflection L c r c'm be subdivided into components Lc due to direct radiation, and LeD due to diffuse radiation, where the proportions of diffuse and direct radiation in the total can be determined from simultaneous readings of the totally exposed K i p p solarimeter and an adj:~cent shaped Kipp solarimeter. T h e shaded K i p p solarimeter is equipped with a shading ring similar to the t y p e developed by D r u m mond, 7 but of slightly greater width, and the correction factor for obscuration of part of the sky b y the shading ring has been determined b y Robertson Is on this particular installation. Thus the equation relating deflection to diffuse radiation is: LD =
C2CdD
(3)
where LD = deflection of recorder attached to the shaded K i p p solarimeter C2 = constant = 4.35 c m / l y min. -1 Ca = correction factor for shading ring ID = diffuse solar radiation. For the types of records studied, mostly clear skies with limited amounts of cloud, the percentage of the total radiation t h a t was diffuse varied from approximately 5 percent at solar noon to approximately 15 percent at five hours from solar noon. Subdivision of the total radiation into direct a n d diffuse components does involve some quite troublesome errors due to the relatively small deflection on the shaded solarimeter record and the poor accuracy of the shading ring correction C.~, estimated at -I-5 199
percent. An analysis of these errors showed that the uncertainty ill the final result would be greater if calculations to separate the radiation into components were carried out, than if the correction factor for the angle of incidence effects f(a) were applied incorrectly to both diffuse and direct components of the radiation. For this reason, comparisons between the Kipp and cell records were carried out to the total radiation records b y applying Eqs. (1) and (2) as follows:
LKr/Lcr = (CiIr)/(f(o~)f(Q)KIT)
rF
u
8oc
.J
5~
Z X.z
B ~4o(
(4)
The reference constant K was determined at midday for a particularly clear day, 2nd September, 1962, when the angle of incidence was small enough to allow f(a) to be unity, and f(Q) was assigned the value unity for these clear conditions. All the remaining records were dealt with by the use of Eq. (4) b y applying the angle of incidence correction, f(a), to the deflections of the two recorders, Lcr and LKr • This process allowed separation of the effect of the changing spectral quality of the radiation. Comparisons for short periods over complete clear days--A number of records for clear-sky conditions have been extracted from the Observations made during 1962, and integrated radiation income over short periods of 30 minutes over the day have been compared from the millivolt meter traces from the silicon cell and Kipp solarimeter. Note here that the mean deflection for the 30-minute period has been determined so that in this case, values of LCT and LKT represent integrated values over the interval. Allowance has been made for the angle of incidence effect by the use of f(a) at the mean angle a over the 30-minute period. These results are given in Table 4. Mean calibration ratios for complete days--From the data obtained over the period of continuous records, it was possible to select a number of complete-day records for comparison and also some part days. The selection used here was essentially to eliminate periods of intermittent cloud when the records were subject to very sudden changes of radiation intensity. Insolation during selected periods was found by measuring the area under the recorded output trace from the Kipp solarimeter by planimeter. The area traced out by the recorded output of the silicon cell was also measured for the same time period. Records, or parts of records were selected for measurement providing they were continuous. Records were divided into two categories, those for clear-sky conditions and those for overcast-sky conditions. It was relatively easy to determine, from the records, the day or part of the day that had been overcast. During such a period the radiation received was
..J ¢
•' J" . 60C
U
C3 W I--
f(Q) = (LcrC1)/(LKrKf(~))
/
lOOC
UJ~ U
Thus
200
~z l.u
I"-
_z
J
20(
J
i00 2o0 INTEGRATED DIRECT
I
I
I
I
I
3o0 4oo 5o0 6o0 2oo PLUS DIFFUSE RADIATION (Langley)
:FIG. 4--Comparison between silicon cell solar radiometer output and total solar radiation income. Sydney 1962, 64 observations, overcast sky. clear sky. almost completely diffuse in nature, and the record of total radiation followed closely the record of diffuse radiation. This criterion was used to group the overcastsky records. Clear-sky periods were readily discernible b y examination of the total radiation record, and here the familiar "near-sine" shape of the distribution of energy over the day was the criterion. As a check, during periods of cloudless sky, diffuse radiation forms a small percentage of the total radiation, providing the time is not too close to sunrise or sunset. A total of 64 separate comparisons were made between the insolation as recorded from the output of the Kipp solarimeter, and the integrated record of the output from the silicon cell over the same time period. Of the total, 47 were for clear sky conditions (18 complete days of clear sky and 29 for long periods of clear sky), and 17 were for overcast-sky conditions. The ratio of the integrated record from the horizontally exposed silicon cell for the same time period, was calculated for each of the above. This area ratio was used directly in the statistical analysis of the results. Very briefly, the analysis was carried out b y approximating the statistical properties of the observations by the normal or gaussian distribution. An unbiased estimator for the variance was determined and a 99 percent confidence interval for the mean area ratio then calculated. The results of this comparison are summarized on Fig. 4 in which the integrated output of the siliconcell radiometer, in units of milliamps per cm ~ surface area X time interval in minutes is compared to the corresponding integrated radiation income in langleys. The observations fall into two definite categories representing clear-sky and overcast-sky conditions, while the analysis of these results leads to two calibration constants: 15.5 4- 2 percent mA cm -2 m i n / l y for clear sky, and 16.6 -4- 3 percent m A c m -2 min/ly for overcast sky
Solar Energy
TABLE 4--AVERAGE VALUES OF f(Q) OVER 30-MINUTE PERIODS ON CLEAR DAYS 30-min Interval from Solar Noon
31/5/62
i
23/6/62 i 29/6/62
I4/7/62
28/7/62 2/8/62
7/8/62
--10 --9 --8
23/8/t2
28/8/62 29/8/62
1.022
0. 962 0.870 0.978 0.929 0.971 1.128 1.020 0.948 0.921 1.005 0.951 0.976
2/9/62
8/9/62
9,/9/62 14/9/62 7/10/62
--7 -6 -5
1.038 1.083 1.087
0.917 0.969 1.017 0.892 0.978 1.079 1.052 1.035 0.992 0.951 0.995 0.993 0.998 0.934 0.990 1.007 1.030 0.935 1.021 1.067 1.051 1.016 1.000 0.965 0.998 1.005 1.000 0.978 1.018 1.019 1.026 0.990 1.032 1.036 1.047 1.019 0.994 0.966 0.998 1.008 0.998
--4 --3 -2
1.085 1.082 1.070
1.001 1.024 1.021 1.023 0.991 1.031 1.030 1.040 1.023 0.996 0.966 1.003 1.013 0.996 1.010 1.033 1.022 1.010 0.991 1.039 1.029 1.037 1.030 0.999 0.968 1.003 1.015 0.989 0.998 1.033 1.014 1.012 1.009 1.036 1.017 1.040 1.029 0.997 0.972 1.010 1.011 0.987
-- 1 +1 +2
1.065 1.067 1.071
1.000 1.032 1.010 1.022 1.019 1.038 1.017 1.031 1.021 1.000 0.972 1.010 1.010 0.982 1.008 1.030 1.013 1.021 1.011 1.040 1.001 1.019 1.027 0.995 0.972 0.986 1.010 0.980 1.011 1.025 1.017 1.020 1.011 1.035 1.011 1.019 1.022 0.995 0.975 0.!)85 1. 004 0.990
+3 +4 +5
1.072 1.075 1.075
1.014 1.020 1.015 1.022 1.006 1.036 1.013 1.003 1.021 0.990 1.013 1.020 1.011 1.026 1.021 1.030 1.010 1.025 1.025 0.990 1.015 1.021 1.005 1.029 1.029 1.039 1.008 1.031 1.032 0.990
+6 +7 +8
1.067 1.062 1.083
1.008
1.002 1.011 1.025 1.060 1.007 1.032 1.039 0.982 1.000 1.008 1.018 1.025 1.019 1.005 1.010 0.995 0.996 1.039 1.055 1.011 1.033 1.043 0.975 0.995 1.004 1.031 1.040 1.002 1.084 1.051 1.051 1.054 1.070 0.971 1.011 1.011 1.106 1.053 1. 018 ]
+9
+10
f t
CONCLUSIONS The theoretical study of the way in which a silicon cell responds to solar radiation has indicated that certain changes in calibration constant should be expected, due to the changes of spectral quality of the radiation caused by the normal variations of atmospheric constituents and of optical path length. The values summarized in Table 2 indicate that when account is taken only of variations of optical-path-length ratio, with constant atmospheric constituents at the standard values proposed by Moon, 12 then the calibration constant of a silicon-cell radiometer should increase significantly with increase of opticM-path-length ratio. Considering the observations of angle of incidence response of the silicon cell, the values in Table 3 show that there was a marked drop in signal from the cell as the angle of incidence increased past 30 deg. When corrections were made for these angle-of-incidence effects on the comparative signals from the silicon cell and the Kipp solarimeters over 30-minute intervals, it was possible to isolate the variations in signal due to changes of spectral quality, as summarized in Table 4. These variations appeared to be rather random, with midday variations about the mean of approximately +6½ to --3 percent. Superimposed upon this variation from day to day, there was a variation during the course of any one day. The trend of the variation during the course of a day, which would be predicted by the consideration of changes of optical-path-length ratio only, was only confirmed by the observations made on 28th August, 1962. The other observations show different patterns of variations, with a general trend toward low values of f(Q) Vol. 10, No. 4, 1966
0.985 1.000 1.000 0.995 0.991 1.009 1. 004 1. 005 0.996 1.010 1.004 1.012
1.117 1.133 0.968 1.018 1.021 1.074 I 1.068 i 1.059 (corresponding to low values of the calibration constant) in the early morning, and higher values during the afternoon. At this stage, in the absence of more comprehensive data, it can only be concluded that the variations due to changes of atmospheric constituents overshadowed the variations due to changes of optical-pathlength ratio. Considering the comparisons made during whole days and portions of days when steady conditions prevailed, a significant increase in calibration constant for overcast sky is noticed. I t is likely that the amount of water vapor in the atmosphere will be higher for the overcast sky, and this should cause a greater percentage of the total radiation to be in the wavelength bands to which the cell responds, thus causing the higher calibration constant observed. I n most situations where the silicon cell is used for whole-day records, it will be necessary for the two calibration constants specified for whole-day observations to be combined to provide a mean over-all constant for all conditions. To meet this requirement, the accuracies determined from the statistical analysis for the clear-sky and overcast-sky observations, -4-2 percent and -+-3 percent respectively, when combined with the values of the two constants, lead to a value of the mean over-all constant of 15.79 mA cm -2 m i n / l y with a probable error of +8½ percent and --3½ percent. The mean over-M1 constant is in fact centrally placed with respect to the distribution, but the particular set of observations discussed here included far more for clear sky than for overcast sky, so that a skew distribution was obtained. The main concern here is to study the variations that 201
m u s t be considered when utilizing t h e silicon cell as a solar r a d i o m e t e r , for t h e a c t u a l v a l u e of t h e c a l i b r a t i o n c o n s t a n t will h a v e to b e d e t e r m i n e d for each i n d i v i d u a l cell. On t h i s basis t h e results p r e s e n t e d h e r e i n could be said to i n d i c a t e a p r o b a b l e error of -4-6 p e r c e n t on a mean calibration constant. T h e s e n s i t i v i t y of t h e silicon-cell r a d i o m e t e r to changes in a t m o s p h e r i c c o n s t i t u e n t s a n d o p t i c a l p a t h length, i n d i c a t e t h a t t h e p r o b a b l e s p r e a d of c a l i b r a t i o n c o n s t a n t o b s e r v e d a t a n y p a r t i c u l a r l o c a l i t y is a f u n c t i o n of t h e w e a t h e r changes f o u n d in t h a t locality. T h i s m a y p a r t l y explain t h e difference b e t w e e n t h e s p r e a d of 4-6 p e r c e n t o b s e r v e d in S y d n e y a n d t h e s p r e a d of 4-4 percent found for m o s t of t h e o b s e r v a t i o n s p u b l i s h e d b y W h i l l i e r a n d T o u t 24 for B a r b a d o s . T h e r e are of course m a n y s i t u a t i o n s where t h e accuracies discussed a b o v e are p e r f e c t l y s a t i s f a c t o r y , so t h a t this t y p e of c h e a p solar r a d i o m e t e r is p o t e n t i a l l y useful. I f g r e a t e r a c c u r a c y is desired front silicon-cell solar r a d i o m e t e r s , t h e n it a p p e a r s t h a t t w o p r e l i m i n a r y steps m u s t be t a k e n . F i r s t l y , m o r e extensive research is n e e d e d into t h e effect of changes of a t m o s p h e r i c c o n s t i t u e n t s a n d optical p a t h l e n g t h on t h e silicon-cell response, a n d secondly, o b s e r v a t i o n s of t h e a t m o s p h e r i c c o n d i t i o n s will h a v e to be m a d e s i m u l t a n e o u s l y w i t h t h e silicon-cell o b s e r v a t i o n s , in o r d e r t o a p p l y t h e corrections factors d e t e r m i n e d in t h e first phase.
ACKNOWLEDGMENT The support of Mr. M. G. Bonner by a Commonwealth of Anstralia Post graduate award, during the progress of this work, is gratefully acknowledged.
BIBLIOGRAPHY 1. Anderson, J. C. V. "Solar Energy--A Fuel for the Future". Thesis for Diploma of University of New South Wales. 1960. 2. Ash, R. S. "Greenhouse Climate Control". Refrigeration Engineering, Feb. 1958. p. 41. 3. Bonner, M. G. "The Investigation of the Silicon Solar Cell for Use as a Solar Radiometer at Normal Levels of Radiation". Thesis for M.E University of New South Wales. 1964. 4. Brodie, H. W. "The Wig-Wag"; Solar Energy, 9, No. 1, 1965. p. 27. 5. Browne, M. E,, Francis, A. B. and Enslow, G. M. "Study and Evaluation of Silicon Solar Cells". Lockheed Missile
202
systems division, solid state electronics dept. Contract No. AFO4(647)-97. 1958. 6. Cherry, W. R. "Military Considerations for a Photovoltaic Solar Energy Converter". Trails. Conf. on Use of Solar Energy, The Scientific Basis, V, Oct.-Nov. 1955. p. 127. 7. Drummond, A. J. "The Measurement of Sky Radiation". Archly fur Met, Geophys, Biokl. 1956. p. 413. 8. Heywood, H. "Simple Instruments for the Assessment of Daily Radiation Intensity". U.N. Conf. on New Sources of Energy--Solar Energy, Wind Power and Gocthermal Energy. Aug. 1961. E/Conf. 35/S/9. 9. Loferski, J. J. "Theoretical Considerations Governing the Choice of the Optimuin Semiconductor for Photovoltaic Solar Energy Conversion". Trails. Conf. on Use of Solar Energy, The scientific basis. V. Oct.-Nov. 1955. p. 65. 10. Luckiesh, M. "Applications of Germicidal, Erythermal and Infrared Energy". D. V'm Nostrand, Co. Inc., New York 1946. 1st Edition. Chap. 2. 11. Majumdar, N. C. and Kaushik, S. R. "Simple Instruments for the Measurement of Direct Solar Radiation"; Solar Ertergy, 8, No. 3, 1964. p. 91. 12. Moon, P. "Proposed Standard Solar Radiation Curves for Engineering Use". J. Franklin Inst. 230, Nov. 1940. p. 583. 13. Pearson, G. L. "Electricity from the Sun". Proc. World Symposium on Applied Solar Energy. Pheonex, Arizona. Nov. 1955. 14. Pleijel, G. and Longmore, J. "A Method of Correcting the Cosine Error of Selenium Rectifier Photocells". J. Sci. Instrum., 26, No. 5, May, 1955. p. 534. 15. Prince. Private communication. 1961. 16. Prince, J. B. "Latest Developments in the Field of Photovoltaic Conversion of Solar Energy". U. N. Conf. on New Sources of Energy--Solar Energy, Wind Power and Geothermal Energy. Aug. 1961. E/Conf. 35/S/65. 17. Rappaport, P. "The Photovoltaic Effect and Its Utilization". Solar Energy, 3, No. 4, Dec. 1959. p. 8. 18. Robertson, R. G. "Measurements of Diffuse Solar Radiation and Its Distribution Over the Sky Hemisphere". Thesis for M. E. University of New South Wales. 1963. 19. Sasuga, J. "International Rectifier Solar Cell and Photocell Handbook". International Rectifier Corp., E1 Segundo, Calif. 1960.1st Edition. Chap. 1. 20. Selcuk, K. and Yellott, J. 2. "Measurement of Direct, Diffuse and Total Solar Radiation with Silicon Photovoltaic Cells". Solar Energy, 6, No. 4. Oct.-Dec. 1962. 21. Shockley, W. "Electrons and Holes in Semiconductors-With Applications to Transistor Electronics". D. Van Nostrand Co. Inc. New York, 1950. 1st Edition, Chap. 1. 22. Trickett, E. S. and Moulsley, L. J. "Integrating Photometer". J. Agric. Engng. Res. 1, No. 1, 1956. p. 1. 23. Whillier, A. "Integrating Instrmnent for Measuring Solar Radiation"; Solar Energy, 8, No. 4, 1964. p. 134.
Solar Energy
Measurement of Solar Radiation by Silicon Solar Cell M. G. B o n n e r and C. M. S a p s f o r d School of Mechanical Engineering, University of New South Wales I n v e s t i g a t i o n s i n t o t h e u s e o f a s i l i c o n s o l a r cell to measure solar radiation intensity are described. T h e effect o f o p t i c a l p a t h l e n g t h r a t i o a n d a t m o s p h e r i c c o n s t i t u e n t s a r e d i s c u s s e d . A s u r v e y is m a d e o f o t h e r p h o t o v o l t a i e devices. I t is c o n e l u d e d t h a t , o n p r e s e n t l y a v a i l a b l e d a t a , t h e silic o n cell is t h e m o s t s u i t a b l e f o r t h e p u r p o s e . Comparisons are made between the signals obtained from a silicon-solar-cell radiometer and a K i p p t h e r m o p i l e t y p e s o l a r i m e t e r u s e d as a s t a n d a r d . O n e s e t o f c o m p a r i s o n s is m a d e f o r 3 0 - m i n u t e i n t e r v a l s o n c l e a r d a y s a n d is a n a l y s e d so t h a t k n o w n effects d u e t o a n g l e o f i n c i d e n c e a r e a l lowed for and variations in the signals caused by spectral quality of the radiation can be separated. This set of comparisons shows an extreme spread o f 4-13 p e r c e n t o n a r e f e r e n c e c o n s t a n t d e t e r mined for midday clear sky. This extreme spread i n c l u d e s v a r i a t i o n s o f + 6 . 5 t o --3 p e r c e n t a t m i d day together with variations during the course of any one day. A second set of comparisons made during whole d a y s or l o n g p e r i o d s , d u r i n g w h i c h c o n d i t i o n s w e r e s t a b l e , g a v e rise t o t w o c a l i b r a t i o n c o n s t a n t s , one for clear-sky and one for overcast-sky conditions. I f a n o v e r - a l l c a l i b r a t i o n c o n s t a n t is d e s i r e d f o r all c o n d i t i o n s , t h e n a v a l u e o f 15.79 m A c m - " m i n / L a n g l e y is o b t a i n e d w i t h a p r o b a b l e e r r o r o f --3½ t o +8½ p e r c e n t . T h e s k e w effect h e r e is b e c a u s e more readings were taken for clear-sky conditions, thus favoring the lower constant for these conditions.
N ANY program of solar-energy utilization, measuremerit of the radiation income at the locality is important. Unfortunately most comprehensive radiationmeasuring networks exist in countries where solar-energy utilization competes with abundant alternative cheap sources of power. At the same time, only limited solar radiation records exist in those countries
I
Presented at Solar Energy Conference, Boston, Massachusetts, March 21--23, 1966. Vol. 10, No..~, 1966
where solar energy could be effectively and economically utilized to improve the standard of living. To meet this situation, a number of original radiationmeasuring instruments have been proposed recently2, 2, 4, 8, 11, 25, 23. T h e equipment should operate independently of power supplies. A feature of some of these proposals has been the use of a silicon solar cell as a radiation-sensitive surface. The major objective here is to assess the suitability of the silicon cell as a radiation-sensitive element, to compare it with some alternative elements of a similar nature, and to investigate its linearity with existing instruments for solar-radiation measurements. The investigations described here form a part of studies carried out in Sydney over the period 1960-1963. During this time, certain other features of the application of the silicon cell to the measurement of solar radiation were studied and have been reported b y Bonner. 8 I n particular, theoretical calibration constants have been computed for various conditions, and the effect of changes in the angle of incidence of the direct collimated solar b e a m to the silicon-cell surface has been investigated. This additional work is not reported here as it has been included in a recent publication by other authors, s° A n A p p r a i s a l o f S o m e P h o t o v o h a i c Devices Is the silicon cell the most suitable photovoltaic device for the measurement of solar-radiation intensity? An examination and comparison of various semiconductor photovoltaic devices is given in answer to this question, based on research reports as well as the practical experience of workers in the field. However, in m a n y eases, information is not available, indicating lhat further developments of some of the devices can be expected. Over a dozen semiconductor materials have been developed for photovoltaic conversion of radiant energy, including indium phosphide, gallium arsenide, cadmium telluride, cadmium sulphide, cadmium selenide, aluminium antimonide and selenium. Of these, selenium and cadmium sulphide are selected for detailed comparison with silicon, the reason being t h a t there is more comprehensive d a t a available on these. Nevertheless, from the limited information relating to other photovoltaic materials (for example, spectral response curves), similar reasoning and deductions would apply. 195
Some important properties of silicon, selenium, and cadmium sulphide photocells are listed in Table 1. The metal-semiconductor type of junction is formed by the deposition of a suitable transparent metallic film by evaporation or sputtering on to the semiconductor. This forms the so-called "barrier layer" cell. The technique for making the p-n junction cell has been described fully by other workers} a, ~7.2t In the past, the primary application of the selenium photocell has been in photometric equipment and lightmeasuring devices such as spectral photometers and photographic light meters. However, it has many severe practical disadvantages for these applications as well as for solar-insolation measurements. The mounting of the selenium cell presents two major problems: moisture damage to the cell is possible if sealing is not effective, and means must be incorporated to correct for the cosine error. This correction is normally done by means of an opal perspex diffusing disc. Regarding the cosine error for the selenium cell, Pleijel and Longmore '4 comment that "for directional illumination at angles greater than 60 deg, the response may easily fall 30 percent below the theoretical value". Another important consideration is the life of the selenium cell. Manufacturers recommend that if a cell is to be used to measure high illumination levels, such as direct sunlight, neutral-density filters should be used to cut down the illumination level at the surface of the cell in order to prolong its life. Trickett and Moulsley 2~ conclude that "the chief objection to the selenium photocell is that it is possible for it to deteriorate slowly and this may occur unnoticed". Turifing to the silicon cell, various authors report confidently of its long-terln reliability. Browne, Francis, and Enslow 5 make these observations. " N o effect was found due to ageing for 233 days for cells aged as follows: (a) at room temperature, (b) at a constant temperature of 60 deg C, and (c) in a desiccant". Prince '5
12OC
I
f-~.
Moon(m:2)
IOOO 8
/
,,'x
S¢
u
~oo
A \
/>1
--St
k / - --7OOO K
400
02
/
i/
04
,
~
08 1"2 16 WAVELENGTH (Microns)
col_
2"0
2"2
FIG. l--Proposed standard curve (after Moon I~, to the vertical scale). Spectral distribution for 7000°K black body. Relative response of Cadmium sulphide (Cd) Selenium (Se) and Silicon (St) photocells. (after Sasuga TM and Prince~% not to vertie'd scale). 196
TABLE 1--COMPARISON OF PHOTO CELL TYPES Photocell Material
Crystal form Type of junction Forbidden energy gap Ea electron volts Wavelength corresponding to energy gap (Eo) microns
Silicon
Single crystal Diffused
Selenium
Cadmium Sulphide
1.1
Polycrystalline Metal-semiconductor 1.5
Single crystal Unknown (complex) 2.4
1.1
0.83
0.52
p-n
affirms "there is no known possibility of deterioration occurring in silicon solar cells at the earth's surface". Large temperature effects are reported with the selenium photocell. For example, makers' data sheets show as much as 10 percent deviation in output for temperature variations in the range 0 to 50 deg C. Although not nearly as much information is available on the cadmium-sulphide cell, Rappaport 1~ reports a rapid fall of the short-circuit current with increasing temperature for this device. In the idealized case, for a particular semiconductor, the number of electron-hole pairs collected by the p-n junction is equal to the number of photons in the spectrum of energy greater than the energy gap, Ea, of the solid. This, in effect, assumes the existence of a sharp absorption edge with complete absorption and zero losses on its high-energy side. Table 1 quotes values of the energy gap for silicon, selenium, and cadmium sulphide. Values of Ea for other semiconductors, previously cited as having been developed for photovoltaic energy conversion, are as follows: indium phosphide: 1.3 ev; gallium arsenide: 1.4 ev; cadmium telluride: 1.5 ev; aluminium antimonide: 1.6 ev; cadmium selenide: 1.7 ev. From the ideal viewpoint, the lower the value of the energy gap, E , , the more accurate will be the device to measure incident radiation of varying spectral quality, since a greater part of the spectrum will be utilized for the generation of electron-hole pairs. Ideally, silicon utilizes all photons of energy greater than 1.1 ev; selenium, those of energy greater than 1.5 ev, etc. Silicon, therefore, is the most suitable from this viewpoint. Perhaps .~ more important comparison is gained by examination of ,~ctual spectral response curves in relation 1o solar spectral distributions. The responses of the selenium and cadmium sulphide photocells (from Sasuga ~9) and the silicon cell (from Prince 16) in terms of short-circuit current, are shown in Fig. 1.3"he responses are not to scale. Also plotted is Moon's t2 proposed standard curve for the spectral distribution of the direct component of solar r'~diation for optical-path-length ratio m = 2, and the distribution of energy emitted from a black body at a temperature of 7000 deg K. The opticalpath-length ratio (m) is the optical path length of the Solar Energy
sun's direct rays through the atmosphere as a ratio of the depth of the atmosphere. Following Loferski, 9 it is assumed that the black body at 7000 deg K approximates the spectral distribution of radiation at the earth's surface with an overcast sky. Examining the three spectral-response curves, the broadness of the silicon curve compared with those of the cadmium-sulphide and selenium photocells is most striking. The sensitivity of the cadmium-sulphide cell is almost confined to the visible range; the selenium device is responsive through the ultraviolet range and the visible; and the silicon cell is sensitive over the visible and part of the infrared. This comparative broadness is, of course, highly desirable. The ideal converter for a radiometer would, of course, have a response independent of wavelength so that a constant fraction of the energy at each wavelength interval would be converted to electrical current. Some comments on the seemingly anomalous cadmium-sulphide response curve is necessary. The predicted cut-off of 0.52 microns is not in fact true. The cell is actually responsive to wavelengths up to approximately 0.8 microns. I t is noted in Table I that the mechanism of operation of the cadmium-sulphide cell is not understood and is apparently complex in nature. Cherry 6 notes that cadmium sulphide "is a material outside the theoretical optimum energy gap range that displays unusual photovoltaic properties". Intensive development is continuing into the characteristics of semiconductor materials and into methods of manufacture. The silicon cell may, in the future, have to give way to a cell made of another material with better characteristics, or one that can be made by significantly simpler or cheaper methods. However, at present, the silicon cell appears to be the most stable and the most suitable of the semiconductor materials for application to the measurement of solar radiation.
The Relative Importance of Atmospheric Variables Differing quantities of the various components of the earth's atmosphere are responsible for changes in the spectral distribution of solar radiation incident at the surface of the earth. These components include ozone, carbon dioxide, water vapor, and dust particles. Another variable affecting radiation from the sun is the distance through which the rays travel to the particular location on the earth's surface. Because of the spectrally selective nature of the silicon cell, a variation in the spectral distribution of the incident solar radiation can affect the rate at which the device converts radiation energy to electrical energy. This conversion rate, expressed as the short-circuit current generated by unit intensity of radiation on the cell surface ( m A c m -2 min/ly) is the calibration ratio of the silicon-cell radiometer. Vol. 10, No. ,~, 1966
2000 r Energy Outside Atmosphere .($')
Sotor Energy At Sea-Lever
oI-Iooo
, 111 -, 2°
4000
1200 WAVELENGTH
20000 ( ANGSTROMS )
28000
Fio. 2--Spectral distribution of solar energy outside the atmosphere and at sea level (after Luckieshl°). Moon 1~ points out that, because dust particles are comparatively large (of the order of one micron diameter), "the effect of wavelength is less marked than with molecular scattering, and it is customary to assume that scattering by dust is independent of wavelength". Making this assumption, it follows that an increase in the concentration of dust particles in the atmosphere would reduce the intensity of the radiation over the whole spectrum in a uniform manner. Variation in dust content of the atmosphere should not therefore influence the calibration ratio for the silicon cell. Ozone, water vapor, and carbon dioxide are the atmospheric components remaining for consideration. If, as a result of a change in the value of one of these variables, a variation in the spectral distribution of solar radiation occurs in a wavelength band to which the silicon cell is not sensitive (wavelengths less than 0.35 microns or greater than 1.11 microns) then this variation in spectral distribution, and in solar radiation intensity, will not be registered by the cell. The cell will register a change in output current due to changes in the radiation intensity occurring within its sensitive range. However, as the spectral response is variable over this range, as shown on Fig. 1, wavelengthdependent changes in radiation intensity will not be reflected in a linear fashion by cell output current. Referring to Fig. 2, which is from Luckiesh, l° it is seen that water-vapor absorption accounts for a considerable percentage of the radiation attenuated; beyond 1.1 microns especially, there are large watervapor absorption bands. Changes in water-vapor content of the atmosphere can be expected to have all influence on the calibration ratio. In the peculiar case of ozone, we see from Fig. 2 that absorption occurs at the shorter wavelengths. Primarily, ozone causes a sharp cutoff in the spectrum below 0.29 microns, this occurring for all concentrations found in the atmosphere. Carbon dioxide has a similar effect on radiation of wavelengths longer than 2.3 microns (see Fig. 2). Moon 12 states that "radiation at wavelengths 197
beyond 2.3 microns is strongly absorbed by H20 and C O 2 . . . " . Variations in the concentrations of these two constituents will therefore cause little change in the spectral distribution. Moon 12 has made an excellent study of the spectral distribution of direct solar radiation on cloudless days. He has computed the effect on the distribution of changes in the optical-path-length ratio of the sun's direct rays through the earth's atmosphere. He assumes fixed values for barometric pressure and quantity of precipitable water, dust, and ozone in the atmosphere. His paper presents spectral distributions for each of five optical path lengths. Table 2 has been computed from these plots. In the table, the energy contained within a particular wavelength band is expressed as a percentage of the total energy available. Numerical methods of integration (trapezoidal-rule approximation ,tpplied to scaled ordinates) have been used to determine areas under the curves. The considerable changes that occur in the forms of the spectral distributions as changes in the optical path length are demonstrated in Table 2. For example, in the wavelength range, 0.4 to 0.5 micron, the percentage of the energy available is seen to range from 8.1 to 14.6 percent. Since, as shown in Fig. 1, the cell is almost insensitive to wavelengths below 0.35 microns, while significant variations in this wavelength band are shown in Table 2, these variations in the intensity of the incident energy will not be registered by the cell. Thus, it is expected that the optical-path-length ratio, which varies from a mininmm at solar noon to maximum at day-break and sunset,, should have some influence on the calibration ratio over any day. The above qualitative assessment has indicated that variations in dust content of the atmosphere should have little impression on the calibration ratio, but changes in the water vapor content could have some influence. Also, the hourly and daily variations in the optical path length of the sun's rays through the earth's atmosphere are important. Calibration Ratio of a Silicon-Cell Radiometer
The calibration ratio of the silicon cell, when used as a radiometer, was investigated experimentally by comparing the output from a cell with that from a Kipp solarimeter taken as the standard. The Kipp solarimeter uses a blackened thermopile as the radiation-sensitive receiver. The observations indicated that no one calibration ratio could be defined. However, a reference constant has been determined and correction factors for angle of incidence of the solar beam and for spectral quality have been isolated. For the purpose of qualitative comparison, in Fig. 3 a whole-day record from the horizontally exposed silicon 198
T A B L E 2 - - R A D I A N T E N E R G Y IN T H E D I R E C T SOLAR BEAM FOR DIFFERENT OPTICAL PATH LENGTH RATIOS T h e d a t a has been computed from spectral d i s t r i b u t i o n s published by Moon2~ Optical Path Length Ratio (m)
Wavelength Band (micron)
1.7
0.5 8.1
Up to 0.4 0.4-O.5 0.5-0.6
4.3 14.6 16.3
2.7 12.9 16.0
11.2 15.6
1.1 9.6 14.6
0.(;-0.7 0.7-0.9 0.9-1.1
14.5 20.6 12.7
15.5 22.4 13.7
15.9 23.3 14.8
16.2 24.5 15.8
9.2 6.4 1.4
9.0 6.6 1.2
9.1 7.2 1.2
9.2 7.8 1.2
9.5
lOO.o%
100.0%
1.1-1.4 1.4-1.8 greater t h a n 1.8
100.~o
lOO.O7o 100.0%
13.6 16.4
25.5 16.9 8.4 1.1
cell has been superimposed on the Kipp solarimeter record for the same period. The day selected, 7th October, 1962, was essentially cloudless. Bumps in the record were probably due to one or two wispy clouds or perhaps smoke. Comparison reveals corresponding rises and falls in each record, and an approximate proportionality of one output to the other. No irregular aspects can be discerned. In fact, for all comparisons made by the authors over the eleven-month period of recording the output from the fully exposed silicon cell, similar conclusions were reached. Description of test equipment--A silicon cell was mounted in a horizontal position adjacent to the Kipp solarimeter on the roof of the Project Laboratory of the School of Mechanical Engineering. Both solarimeter and cell were fully exposed to both direct and diffuse components of solar radiation. The location for the equipment was about 60 feet from ground level, free fi'om interference by neighboring buildings, hills, etc. The current output from the silicon cell was passed through a 0.270-
'5< ~-
Kipp Sola
imeter
t--W
-- ]8OO
1600 14OO 12OO I000 0800 0600 AU~TDALIAN EASTERN STANDARD TIME (Hours)
FIG. 3--Conlparison of records from silicon cell solar radiom e t e r and Kipp solarimeter m o u n t e d horizontally. Sydney 7 October, 1962.
Solar Energy
TABLE 3--VALUES OF f (a), CORRECTION FACTOR. FOR ANGLE OF INCIDENCE FROM BONNER 3 a, Degrees
f(a)
a, Degrees
f(a)
0 5 10
1.000 1.000 0.995
45 50 55
0.988 0.981 0.963
15 20 25
0.997 0.998 1.000
60 65 70
0.947 0.911 0.866
30 35 40
0.995 0.998 0.992
75 80 85
0.805 0. 692 0.566
Let = f(a)f(Q)KIr
Formula L~ = A I cos a f(~) where L~ = deflection of meter attached to silicon cell radiometer when reading direct radiation only A = calibration constant I = direct radiation incident on cell = angle of incidence between direct radiation beam and the normal to the cell surface. ohm standard resistance and the voltage generated across this resistance recorded. T h e value of the resistance was calculated to give a m a x i m u m deflection of the galvanometer on the millivolt recorder within full scale, and at the same time to approximate short-circuit operation of the cell. The voltage generated across this resistance was recorded on a K i p p clockwork operated recording millivoltmeter. The recording of the output from the totally exposed silicon solar cell was commenced on 8th December, 1961, and continued through to 14th November, 1962. Periodic maintenance of the equipment as a whole consisted simply of dusting the surface of the silicon cell with a soft brush and at the same time, cleaning the glass dome of the X i p p solarimeter. This was done each week-day morning. T e m p e r a t u r e compensation was not provided on the silicon cell tested, as the cell was fixed to a rather massive metallic m o u n t t h a t would have had the effect of stabilizing the cell t e m p e r a t u r e near to ambient, while the daytime ambient variation experienced was approxim a t e l y from 55 to 90 deg F. A m a x i m u m variation of -4-1.5 percent on a mean calibration constant was expected for this t e m p e r a t u r e variation and confirmed b y the readings published b y Selcuk and Yellott? ° The shunting resistance of Manganin wire was subject to a variation of =t=0.025 percent over the same t e m p e r a t u r e range and this effect was considered insignificant. A s s u m p t i o n s involved in the c o m p a r i s o n - - I n a t t e m p t ing to use the silicon solar cell as a solar radiometer, and in determining a cell calibration constant b y comparison with a K i p p solarimeter, two i m p o r t a n t assumptions are made. First, it must be assumed t h a t the measured deflection on the K i p p recorder is directly proportional to the incident solar radiation as represented b y the equation: LKr = C d r Vol. 10, No. 4, 1966
where L~r = deflection on recorder attached to totally exposed Kipp solarimeter C1 = constant = 5.04 c m / l y min. -1 I r = total solar radiation. Second, it must be assumed that the deflection of the recorder connected across the standard resistance is a measure of the short-circuit current of lhe silicon solar ceil, and t h a t this deflection is in turn related to the incident solar radiation b y the equation:
(1)
(2)
where L c r = deflection on recorder attached to totally exposed silicon cell radiometer f(a) = correction factor to allow for the effect of the angle of incidence of the direct solar beam to the surface f(Q) = correction factor to allow for the variation of the spectral quality of the radiation K = reference constant for the cell. Values for f(a) were determined separately and are listed in Table 3. To allow for the fact t h a t the Kipp total solarimeter and the silicon cell are exposed to the full hemispherical radiation, while a correction factor for angle of incidence effects, f(a), applies strictly to the direct b e a m of solar radiation only, the deflection L c r c'm be subdivided into components Lc due to direct radiation, and LeD due to diffuse radiation, where the proportions of diffuse and direct radiation in the total can be determined from simultaneous readings of the totally exposed K i p p solarimeter and an adj:~cent shaped Kipp solarimeter. T h e shaded K i p p solarimeter is equipped with a shading ring similar to the t y p e developed by D r u m mond, 7 but of slightly greater width, and the correction factor for obscuration of part of the sky b y the shading ring has been determined b y Robertson Is on this particular installation. Thus the equation relating deflection to diffuse radiation is: LD =
C2CdD
(3)
where LD = deflection of recorder attached to the shaded K i p p solarimeter C2 = constant = 4.35 c m / l y min. -1 Ca = correction factor for shading ring ID = diffuse solar radiation. For the types of records studied, mostly clear skies with limited amounts of cloud, the percentage of the total radiation t h a t was diffuse varied from approximately 5 percent at solar noon to approximately 15 percent at five hours from solar noon. Subdivision of the total radiation into direct a n d diffuse components does involve some quite troublesome errors due to the relatively small deflection on the shaded solarimeter record and the poor accuracy of the shading ring correction C.~, estimated at -I-5 199
percent. An analysis of these errors showed that the uncertainty ill the final result would be greater if calculations to separate the radiation into components were carried out, than if the correction factor for the angle of incidence effects f(a) were applied incorrectly to both diffuse and direct components of the radiation. For this reason, comparisons between the Kipp and cell records were carried out to the total radiation records b y applying Eqs. (1) and (2) as follows:
LKr/Lcr = (CiIr)/(f(o~)f(Q)KIT)
rF
u
8oc
.J
5~
Z X.z
B ~4o(
(4)
The reference constant K was determined at midday for a particularly clear day, 2nd September, 1962, when the angle of incidence was small enough to allow f(a) to be unity, and f(Q) was assigned the value unity for these clear conditions. All the remaining records were dealt with by the use of Eq. (4) b y applying the angle of incidence correction, f(a), to the deflections of the two recorders, Lcr and LKr • This process allowed separation of the effect of the changing spectral quality of the radiation. Comparisons for short periods over complete clear days--A number of records for clear-sky conditions have been extracted from the Observations made during 1962, and integrated radiation income over short periods of 30 minutes over the day have been compared from the millivolt meter traces from the silicon cell and Kipp solarimeter. Note here that the mean deflection for the 30-minute period has been determined so that in this case, values of LCT and LKT represent integrated values over the interval. Allowance has been made for the angle of incidence effect by the use of f(a) at the mean angle a over the 30-minute period. These results are given in Table 4. Mean calibration ratios for complete days--From the data obtained over the period of continuous records, it was possible to select a number of complete-day records for comparison and also some part days. The selection used here was essentially to eliminate periods of intermittent cloud when the records were subject to very sudden changes of radiation intensity. Insolation during selected periods was found by measuring the area under the recorded output trace from the Kipp solarimeter by planimeter. The area traced out by the recorded output of the silicon cell was also measured for the same time period. Records, or parts of records were selected for measurement providing they were continuous. Records were divided into two categories, those for clear-sky conditions and those for overcast-sky conditions. It was relatively easy to determine, from the records, the day or part of the day that had been overcast. During such a period the radiation received was
..J ¢
•' J" . 60C
U
C3 W I--
f(Q) = (LcrC1)/(LKrKf(~))
/
lOOC
UJ~ U
Thus
200
~z l.u
I"-
_z
J
20(
J
i00 2o0 INTEGRATED DIRECT
I
I
I
I
I
3o0 4oo 5o0 6o0 2oo PLUS DIFFUSE RADIATION (Langley)
:FIG. 4--Comparison between silicon cell solar radiometer output and total solar radiation income. Sydney 1962, 64 observations, overcast sky. clear sky. almost completely diffuse in nature, and the record of total radiation followed closely the record of diffuse radiation. This criterion was used to group the overcastsky records. Clear-sky periods were readily discernible b y examination of the total radiation record, and here the familiar "near-sine" shape of the distribution of energy over the day was the criterion. As a check, during periods of cloudless sky, diffuse radiation forms a small percentage of the total radiation, providing the time is not too close to sunrise or sunset. A total of 64 separate comparisons were made between the insolation as recorded from the output of the Kipp solarimeter, and the integrated record of the output from the silicon cell over the same time period. Of the total, 47 were for clear sky conditions (18 complete days of clear sky and 29 for long periods of clear sky), and 17 were for overcast-sky conditions. The ratio of the integrated record from the horizontally exposed silicon cell for the same time period, was calculated for each of the above. This area ratio was used directly in the statistical analysis of the results. Very briefly, the analysis was carried out b y approximating the statistical properties of the observations by the normal or gaussian distribution. An unbiased estimator for the variance was determined and a 99 percent confidence interval for the mean area ratio then calculated. The results of this comparison are summarized on Fig. 4 in which the integrated output of the siliconcell radiometer, in units of milliamps per cm ~ surface area X time interval in minutes is compared to the corresponding integrated radiation income in langleys. The observations fall into two definite categories representing clear-sky and overcast-sky conditions, while the analysis of these results leads to two calibration constants: 15.5 4- 2 percent mA cm -2 m i n / l y for clear sky, and 16.6 -4- 3 percent m A c m -2 min/ly for overcast sky
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TABLE 4--AVERAGE VALUES OF f(Q) OVER 30-MINUTE PERIODS ON CLEAR DAYS 30-min Interval from Solar Noon
31/5/62
i
23/6/62 i 29/6/62
I4/7/62
28/7/62 2/8/62
7/8/62
--10 --9 --8
23/8/t2
28/8/62 29/8/62
1.022
0. 962 0.870 0.978 0.929 0.971 1.128 1.020 0.948 0.921 1.005 0.951 0.976
2/9/62
8/9/62
9,/9/62 14/9/62 7/10/62
--7 -6 -5
1.038 1.083 1.087
0.917 0.969 1.017 0.892 0.978 1.079 1.052 1.035 0.992 0.951 0.995 0.993 0.998 0.934 0.990 1.007 1.030 0.935 1.021 1.067 1.051 1.016 1.000 0.965 0.998 1.005 1.000 0.978 1.018 1.019 1.026 0.990 1.032 1.036 1.047 1.019 0.994 0.966 0.998 1.008 0.998
--4 --3 -2
1.085 1.082 1.070
1.001 1.024 1.021 1.023 0.991 1.031 1.030 1.040 1.023 0.996 0.966 1.003 1.013 0.996 1.010 1.033 1.022 1.010 0.991 1.039 1.029 1.037 1.030 0.999 0.968 1.003 1.015 0.989 0.998 1.033 1.014 1.012 1.009 1.036 1.017 1.040 1.029 0.997 0.972 1.010 1.011 0.987
-- 1 +1 +2
1.065 1.067 1.071
1.000 1.032 1.010 1.022 1.019 1.038 1.017 1.031 1.021 1.000 0.972 1.010 1.010 0.982 1.008 1.030 1.013 1.021 1.011 1.040 1.001 1.019 1.027 0.995 0.972 0.986 1.010 0.980 1.011 1.025 1.017 1.020 1.011 1.035 1.011 1.019 1.022 0.995 0.975 0.!)85 1. 004 0.990
+3 +4 +5
1.072 1.075 1.075
1.014 1.020 1.015 1.022 1.006 1.036 1.013 1.003 1.021 0.990 1.013 1.020 1.011 1.026 1.021 1.030 1.010 1.025 1.025 0.990 1.015 1.021 1.005 1.029 1.029 1.039 1.008 1.031 1.032 0.990
+6 +7 +8
1.067 1.062 1.083
1.008
1.002 1.011 1.025 1.060 1.007 1.032 1.039 0.982 1.000 1.008 1.018 1.025 1.019 1.005 1.010 0.995 0.996 1.039 1.055 1.011 1.033 1.043 0.975 0.995 1.004 1.031 1.040 1.002 1.084 1.051 1.051 1.054 1.070 0.971 1.011 1.011 1.106 1.053 1. 018 ]
+9
+10
f t
CONCLUSIONS The theoretical study of the way in which a silicon cell responds to solar radiation has indicated that certain changes in calibration constant should be expected, due to the changes of spectral quality of the radiation caused by the normal variations of atmospheric constituents and of optical path length. The values summarized in Table 2 indicate that when account is taken only of variations of optical-path-length ratio, with constant atmospheric constituents at the standard values proposed by Moon, 12 then the calibration constant of a silicon-cell radiometer should increase significantly with increase of opticM-path-length ratio. Considering the observations of angle of incidence response of the silicon cell, the values in Table 3 show that there was a marked drop in signal from the cell as the angle of incidence increased past 30 deg. When corrections were made for these angle-of-incidence effects on the comparative signals from the silicon cell and the Kipp solarimeters over 30-minute intervals, it was possible to isolate the variations in signal due to changes of spectral quality, as summarized in Table 4. These variations appeared to be rather random, with midday variations about the mean of approximately +6½ to --3 percent. Superimposed upon this variation from day to day, there was a variation during the course of any one day. The trend of the variation during the course of a day, which would be predicted by the consideration of changes of optical-path-length ratio only, was only confirmed by the observations made on 28th August, 1962. The other observations show different patterns of variations, with a general trend toward low values of f(Q) Vol. 10, No. 4, 1966
0.985 1.000 1.000 0.995 0.991 1.009 1. 004 1. 005 0.996 1.010 1.004 1.012
1.117 1.133 0.968 1.018 1.021 1.074 I 1.068 i 1.059 (corresponding to low values of the calibration constant) in the early morning, and higher values during the afternoon. At this stage, in the absence of more comprehensive data, it can only be concluded that the variations due to changes of atmospheric constituents overshadowed the variations due to changes of optical-pathlength ratio. Considering the comparisons made during whole days and portions of days when steady conditions prevailed, a significant increase in calibration constant for overcast sky is noticed. I t is likely that the amount of water vapor in the atmosphere will be higher for the overcast sky, and this should cause a greater percentage of the total radiation to be in the wavelength bands to which the cell responds, thus causing the higher calibration constant observed. I n most situations where the silicon cell is used for whole-day records, it will be necessary for the two calibration constants specified for whole-day observations to be combined to provide a mean over-all constant for all conditions. To meet this requirement, the accuracies determined from the statistical analysis for the clear-sky and overcast-sky observations, -4-2 percent and -+-3 percent respectively, when combined with the values of the two constants, lead to a value of the mean over-all constant of 15.79 mA cm -2 m i n / l y with a probable error of +8½ percent and --3½ percent. The mean over-M1 constant is in fact centrally placed with respect to the distribution, but the particular set of observations discussed here included far more for clear sky than for overcast sky, so that a skew distribution was obtained. The main concern here is to study the variations that 201
m u s t be considered when utilizing t h e silicon cell as a solar r a d i o m e t e r , for t h e a c t u a l v a l u e of t h e c a l i b r a t i o n c o n s t a n t will h a v e to b e d e t e r m i n e d for each i n d i v i d u a l cell. On t h i s basis t h e results p r e s e n t e d h e r e i n could be said to i n d i c a t e a p r o b a b l e error of -4-6 p e r c e n t on a mean calibration constant. T h e s e n s i t i v i t y of t h e silicon-cell r a d i o m e t e r to changes in a t m o s p h e r i c c o n s t i t u e n t s a n d o p t i c a l p a t h length, i n d i c a t e t h a t t h e p r o b a b l e s p r e a d of c a l i b r a t i o n c o n s t a n t o b s e r v e d a t a n y p a r t i c u l a r l o c a l i t y is a f u n c t i o n of t h e w e a t h e r changes f o u n d in t h a t locality. T h i s m a y p a r t l y explain t h e difference b e t w e e n t h e s p r e a d of 4-6 p e r c e n t o b s e r v e d in S y d n e y a n d t h e s p r e a d of 4-4 percent found for m o s t of t h e o b s e r v a t i o n s p u b l i s h e d b y W h i l l i e r a n d T o u t 24 for B a r b a d o s . T h e r e are of course m a n y s i t u a t i o n s where t h e accuracies discussed a b o v e are p e r f e c t l y s a t i s f a c t o r y , so t h a t this t y p e of c h e a p solar r a d i o m e t e r is p o t e n t i a l l y useful. I f g r e a t e r a c c u r a c y is desired front silicon-cell solar r a d i o m e t e r s , t h e n it a p p e a r s t h a t t w o p r e l i m i n a r y steps m u s t be t a k e n . F i r s t l y , m o r e extensive research is n e e d e d into t h e effect of changes of a t m o s p h e r i c c o n s t i t u e n t s a n d optical p a t h l e n g t h on t h e silicon-cell response, a n d secondly, o b s e r v a t i o n s of t h e a t m o s p h e r i c c o n d i t i o n s will h a v e to be m a d e s i m u l t a n e o u s l y w i t h t h e silicon-cell o b s e r v a t i o n s , in o r d e r t o a p p l y t h e corrections factors d e t e r m i n e d in t h e first phase.
ACKNOWLEDGMENT The support of Mr. M. G. Bonner by a Commonwealth of Anstralia Post graduate award, during the progress of this work, is gratefully acknowledged.
BIBLIOGRAPHY 1. Anderson, J. C. V. "Solar Energy--A Fuel for the Future". Thesis for Diploma of University of New South Wales. 1960. 2. Ash, R. S. "Greenhouse Climate Control". Refrigeration Engineering, Feb. 1958. p. 41. 3. Bonner, M. G. "The Investigation of the Silicon Solar Cell for Use as a Solar Radiometer at Normal Levels of Radiation". Thesis for M.E University of New South Wales. 1964. 4. Brodie, H. W. "The Wig-Wag"; Solar Energy, 9, No. 1, 1965. p. 27. 5. Browne, M. E,, Francis, A. B. and Enslow, G. M. "Study and Evaluation of Silicon Solar Cells". Lockheed Missile
202
systems division, solid state electronics dept. Contract No. AFO4(647)-97. 1958. 6. Cherry, W. R. "Military Considerations for a Photovoltaic Solar Energy Converter". Trails. Conf. on Use of Solar Energy, The Scientific Basis, V, Oct.-Nov. 1955. p. 127. 7. Drummond, A. J. "The Measurement of Sky Radiation". Archly fur Met, Geophys, Biokl. 1956. p. 413. 8. Heywood, H. "Simple Instruments for the Assessment of Daily Radiation Intensity". U.N. Conf. on New Sources of Energy--Solar Energy, Wind Power and Gocthermal Energy. Aug. 1961. E/Conf. 35/S/9. 9. Loferski, J. J. "Theoretical Considerations Governing the Choice of the Optimuin Semiconductor for Photovoltaic Solar Energy Conversion". Trails. Conf. on Use of Solar Energy, The scientific basis. V. Oct.-Nov. 1955. p. 65. 10. Luckiesh, M. "Applications of Germicidal, Erythermal and Infrared Energy". D. V'm Nostrand, Co. Inc., New York 1946. 1st Edition. Chap. 2. 11. Majumdar, N. C. and Kaushik, S. R. "Simple Instruments for the Measurement of Direct Solar Radiation"; Solar Ertergy, 8, No. 3, 1964. p. 91. 12. Moon, P. "Proposed Standard Solar Radiation Curves for Engineering Use". J. Franklin Inst. 230, Nov. 1940. p. 583. 13. Pearson, G. L. "Electricity from the Sun". Proc. World Symposium on Applied Solar Energy. Pheonex, Arizona. Nov. 1955. 14. Pleijel, G. and Longmore, J. "A Method of Correcting the Cosine Error of Selenium Rectifier Photocells". J. Sci. Instrum., 26, No. 5, May, 1955. p. 534. 15. Prince. Private communication. 1961. 16. Prince, J. B. "Latest Developments in the Field of Photovoltaic Conversion of Solar Energy". U. N. Conf. on New Sources of Energy--Solar Energy, Wind Power and Geothermal Energy. Aug. 1961. E/Conf. 35/S/65. 17. Rappaport, P. "The Photovoltaic Effect and Its Utilization". Solar Energy, 3, No. 4, Dec. 1959. p. 8. 18. Robertson, R. G. "Measurements of Diffuse Solar Radiation and Its Distribution Over the Sky Hemisphere". Thesis for M. E. University of New South Wales. 1963. 19. Sasuga, J. "International Rectifier Solar Cell and Photocell Handbook". International Rectifier Corp., E1 Segundo, Calif. 1960.1st Edition. Chap. 1. 20. Selcuk, K. and Yellott, J. 2. "Measurement of Direct, Diffuse and Total Solar Radiation with Silicon Photovoltaic Cells". Solar Energy, 6, No. 4. Oct.-Dec. 1962. 21. Shockley, W. "Electrons and Holes in Semiconductors-With Applications to Transistor Electronics". D. Van Nostrand Co. Inc. New York, 1950. 1st Edition, Chap. 1. 22. Trickett, E. S. and Moulsley, L. J. "Integrating Photometer". J. Agric. Engng. Res. 1, No. 1, 1956. p. 1. 23. Whillier, A. "Integrating Instrmnent for Measuring Solar Radiation"; Solar Energy, 8, No. 4, 1964. p. 134.
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