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A comparative study of the values of diffused layer resistance in a solar cell calculated using different models
Solar Cells, 4 (1981) 195 - 198
195
Short Communication
A comparative study o f the values of diffused layer resistance in a solar cell calculated using different models
N. R. SAHA, D. BISWAS and P. K. BASU
Institute o f Radio Physics and Electronics, 92 Acharya Prafulla Chandra Road, Calcutta 700009 (India) (Received January 15, 1981; accepted February 10, 1981)
The total series resistance Rs of a solar cell consists of contributions from different parts of the cell, as discussed by Handy [ 1]. The contribution from the diffused layer is in many cases significant. Different workers [1 - 5] have outlined different models for calculating this resistance. In the following we shall compare the values obtained for identical configurations using different expressions and we also investigate h o w a change in the value of the resistance affects the fill factor FF. The expressions for the diffused layer resistance Rd given by different workers and used in the present computation are obtained from the references cited [1 - 5]. The following parameter values and expressions are used for computation: (a) total cell area, 2 cm × 2 cm; (b) grid structure, parallel grid lines with bus-bar, 5, 10, 20 and 30 lines cm -1 with 10% shading loss; (c) sheet resistance p / t = 500 ~2/[7 ; (d) photocurrent [ L (mA cm-2) = 32 × concentration ratio; (e) saturation current I0 = 13.4 × 10 -12 A; (f) diode factor n = 1.2 at 300 K; (g) fill factor FF = V m I m / V o c I s c is c o m p u t e d using the iterative m e t h o d described elsewhere [6] at intensities of 1, 5, 10, 100 and 300 suns for definite values of Rs. The c o m p u t e d values of diffused layer resistance for different values of the grid line density are shown in Fig. 1. Choosing arbitrarily the values calculated by using Wyeth's model [2] as standard, we calculated the percentage deviation in values using models other than the standard; these values are given in Table 1. The deviation remains within 15% in most cases. The large deviation (about 70%) of the values in Wolf's model [3] arises because he did n o t consider the current collection by the bus-bars. In order to assess h o w the above deviations affect the FF value we first plotted in Fig. 2 the relative FF values against different values of the total series resistance which is directly related to the grid line densities at different levels of illumination. The relative FF is the ratio of the value calculated for 0379-6787/81/0000-0000/$02.50
© Elsevier SequoiafPrinted in The Netherlands
196 0.6(
Wo
0.5C
0.40
~E I o
~:~Lu ~~~u 0.30
LL~ 0.20
D
0.10
10 20 DENSITY OF GRiD LINES [LINES/Cm)
30
Fig. 1. The c o m p u t e d values of diffused layer resistance for different values of grid line densities using different models [1 - 5 ] ( p i t = 500 ~ / o ) : curve Wo, ref. 3;curve Ch, ref. 4; curve Ft, ref. 5; curve Hy, ref. 1 ;curve Wy, ref. 2.
a finite Rs to that for zero Rs. Assuming the resistance contribution of the diffused layer to be 50% of the total series resistance we find that, for 5 lines cm -1 and 1 sun, R d = 0.33 ~2 and Rs = 0.66 ~2. For a 10% change in R d the FF changes by 1%. For 30 lines cm -1 and 100 suns, Rd = 0.01 ~2 and Rs = 0.02 ~2. For a 10% change in Rd the FF changes by about 1%. We should point o u t that in all the models considered the grid lines were assumed to be at zero potential corresponding to the short-circuit operating condition o f the cell. For operation o f the solar cell near the maximum power point, the grid lines are at an elevated potential. The potential distributions between two grid lines for operation of the cell in the short-circuit condition and near the maximum power p o i n t are depicted in Fig. 3. The differences in the power losses in the two cases are evident. Hence the power loss in the diffused layer decreases and the contribution of the resistance decreases. The values given in Fig. 1, therefore, are somewhat larger than the actual values when the cell is operated near maximum power point.
R d (~)
0.3295 0.0834 0.0209 0.0093
5 10 20 30
Wyeth [2] (0% deviation)
(lines cm - 1 )
Grid structure
0.358 0.084 0.0205 0.009
Rd (~-~)
Handy [1 ]
8.64 0.71 --1.91 --3.22
(%)
Deviation 0.3749 0.0843 0.0210 0.0093
R d (~) 13.77 1.07 0.47 0.00
(%)
Deviation
Flat and Milnes [5]
0.3839 0.0965 0.0241 0.010
R d (~) 16.41 15.70 15.31 15.05
(%)
Deviation
Chambouleyron [4]
0.5625 0.1406 0.0351 0.0156
R d (~)
Wolf [3]
Percentage deviation in the values of the diffused layer resistance R d c o m p u t e d using different models (pit = 500 ~1[])
TABLE 1
70.71 68.58 67.94 67.74
(%)
Deviation
198 100.0~i ' - - - - - - - . ~ ~
~
IOO'/. AT F~s = O.O O H M ALL INTENSITIES
ooL
'i S U N
b
.
Y
/
%
_J
/ I ///
"~\
EL
30"0 1 25.0 O.01
I
___
0.02 TOTAL
[ 0.05 SERIES
I .......... ~.___ 0.1 0.2 RESISTANCE
I O.5
I
1 1.0
(OHMS)
YzX
T~
O SPACE
O BETWEEN
TWO
GRID
LINES
Fig. 2. Relative fill factor vs. total series resistance at different levels of illumination. Fig. 3. Potential distribution between two grid lines: - - , d i t i o n ; - - , near the maximum power point.
under the short-circuit con-
It can be stated that the different models of diffused layer resistance c o m p u t a t i o n e x c e p t t h a t in r e f . 3 p r o d u c e n e g l i g i b l e d e v i a t i o n in t h e c o m p u t a t i o n o f t h e m a x i m u m d e r i v a b l e p o w e r f r o m t h e cell. T h e a u t h o r s a r e g r a t e f u l t o P r o f e s s o r B. R. N a g f o r his i n t e r e s t in t h i s work.
References
1 2 3 4
R . J . Handy, S o l i d - S t a t e Electron., 10 (1967) 765. N. C. Wyeth, S o l i d - S t a t e Electron., 2 0 (1977) 629. M. Wolf, Proc. I R E , 48 (1960) 1246. I. Chambouleyron, Proc. Int. Conf. o n P h o t o v o l t a i c Solar Energy, L u x e m b o u r g , S e p t e m b e r 2 7 - 30, 1977, Reidel, Dordrecht, 1977, p. 987. 5 A. Flat and A. G. Milnes, Sol. Energy, 2 3 (1979) 289. 6 M. A. Green, S o l i d - S t a t e Electron., 2 0 (1977) 265.
. X
195
Short Communication
A comparative study o f the values of diffused layer resistance in a solar cell calculated using different models
N. R. SAHA, D. BISWAS and P. K. BASU
Institute o f Radio Physics and Electronics, 92 Acharya Prafulla Chandra Road, Calcutta 700009 (India) (Received January 15, 1981; accepted February 10, 1981)
The total series resistance Rs of a solar cell consists of contributions from different parts of the cell, as discussed by Handy [ 1]. The contribution from the diffused layer is in many cases significant. Different workers [1 - 5] have outlined different models for calculating this resistance. In the following we shall compare the values obtained for identical configurations using different expressions and we also investigate h o w a change in the value of the resistance affects the fill factor FF. The expressions for the diffused layer resistance Rd given by different workers and used in the present computation are obtained from the references cited [1 - 5]. The following parameter values and expressions are used for computation: (a) total cell area, 2 cm × 2 cm; (b) grid structure, parallel grid lines with bus-bar, 5, 10, 20 and 30 lines cm -1 with 10% shading loss; (c) sheet resistance p / t = 500 ~2/[7 ; (d) photocurrent [ L (mA cm-2) = 32 × concentration ratio; (e) saturation current I0 = 13.4 × 10 -12 A; (f) diode factor n = 1.2 at 300 K; (g) fill factor FF = V m I m / V o c I s c is c o m p u t e d using the iterative m e t h o d described elsewhere [6] at intensities of 1, 5, 10, 100 and 300 suns for definite values of Rs. The c o m p u t e d values of diffused layer resistance for different values of the grid line density are shown in Fig. 1. Choosing arbitrarily the values calculated by using Wyeth's model [2] as standard, we calculated the percentage deviation in values using models other than the standard; these values are given in Table 1. The deviation remains within 15% in most cases. The large deviation (about 70%) of the values in Wolf's model [3] arises because he did n o t consider the current collection by the bus-bars. In order to assess h o w the above deviations affect the FF value we first plotted in Fig. 2 the relative FF values against different values of the total series resistance which is directly related to the grid line densities at different levels of illumination. The relative FF is the ratio of the value calculated for 0379-6787/81/0000-0000/$02.50
© Elsevier SequoiafPrinted in The Netherlands
196 0.6(
Wo
0.5C
0.40
~E I o
~:~Lu ~~~u 0.30
LL~ 0.20
D
0.10
10 20 DENSITY OF GRiD LINES [LINES/Cm)
30
Fig. 1. The c o m p u t e d values of diffused layer resistance for different values of grid line densities using different models [1 - 5 ] ( p i t = 500 ~ / o ) : curve Wo, ref. 3;curve Ch, ref. 4; curve Ft, ref. 5; curve Hy, ref. 1 ;curve Wy, ref. 2.
a finite Rs to that for zero Rs. Assuming the resistance contribution of the diffused layer to be 50% of the total series resistance we find that, for 5 lines cm -1 and 1 sun, R d = 0.33 ~2 and Rs = 0.66 ~2. For a 10% change in R d the FF changes by 1%. For 30 lines cm -1 and 100 suns, Rd = 0.01 ~2 and Rs = 0.02 ~2. For a 10% change in Rd the FF changes by about 1%. We should point o u t that in all the models considered the grid lines were assumed to be at zero potential corresponding to the short-circuit operating condition o f the cell. For operation o f the solar cell near the maximum power point, the grid lines are at an elevated potential. The potential distributions between two grid lines for operation of the cell in the short-circuit condition and near the maximum power p o i n t are depicted in Fig. 3. The differences in the power losses in the two cases are evident. Hence the power loss in the diffused layer decreases and the contribution of the resistance decreases. The values given in Fig. 1, therefore, are somewhat larger than the actual values when the cell is operated near maximum power point.
R d (~)
0.3295 0.0834 0.0209 0.0093
5 10 20 30
Wyeth [2] (0% deviation)
(lines cm - 1 )
Grid structure
0.358 0.084 0.0205 0.009
Rd (~-~)
Handy [1 ]
8.64 0.71 --1.91 --3.22
(%)
Deviation 0.3749 0.0843 0.0210 0.0093
R d (~) 13.77 1.07 0.47 0.00
(%)
Deviation
Flat and Milnes [5]
0.3839 0.0965 0.0241 0.010
R d (~) 16.41 15.70 15.31 15.05
(%)
Deviation
Chambouleyron [4]
0.5625 0.1406 0.0351 0.0156
R d (~)
Wolf [3]
Percentage deviation in the values of the diffused layer resistance R d c o m p u t e d using different models (pit = 500 ~1[])
TABLE 1
70.71 68.58 67.94 67.74
(%)
Deviation
198 100.0~i ' - - - - - - - . ~ ~
~
IOO'/. AT F~s = O.O O H M ALL INTENSITIES
ooL
'i S U N
b
.
Y
/
%
_J
/ I ///
"~\
EL
30"0 1 25.0 O.01
I
___
0.02 TOTAL
[ 0.05 SERIES
I .......... ~.___ 0.1 0.2 RESISTANCE
I O.5
I
1 1.0
(OHMS)
YzX
T~
O SPACE
O BETWEEN
TWO
GRID
LINES
Fig. 2. Relative fill factor vs. total series resistance at different levels of illumination. Fig. 3. Potential distribution between two grid lines: - - , d i t i o n ; - - , near the maximum power point.
under the short-circuit con-
It can be stated that the different models of diffused layer resistance c o m p u t a t i o n e x c e p t t h a t in r e f . 3 p r o d u c e n e g l i g i b l e d e v i a t i o n in t h e c o m p u t a t i o n o f t h e m a x i m u m d e r i v a b l e p o w e r f r o m t h e cell. T h e a u t h o r s a r e g r a t e f u l t o P r o f e s s o r B. R. N a g f o r his i n t e r e s t in t h i s work.
References
1 2 3 4
R . J . Handy, S o l i d - S t a t e Electron., 10 (1967) 765. N. C. Wyeth, S o l i d - S t a t e Electron., 2 0 (1977) 629. M. Wolf, Proc. I R E , 48 (1960) 1246. I. Chambouleyron, Proc. Int. Conf. o n P h o t o v o l t a i c Solar Energy, L u x e m b o u r g , S e p t e m b e r 2 7 - 30, 1977, Reidel, Dordrecht, 1977, p. 987. 5 A. Flat and A. G. Milnes, Sol. Energy, 2 3 (1979) 289. 6 M. A. Green, S o l i d - S t a t e Electron., 2 0 (1977) 265.
. X