Page 49 - Advances in Renewable Energies and Power Technologies

22 CHAPTER 1 Solar Cells and Arrays: Principles, Analysis, and Design

superposition of the dark solar cell characteristics and the illuminated cell with short
circuit. This superposition principle is almost valid for all commercial solar cells.
For experimental solar cells, this principle may not be valid because of the pro-
nounced effect of metal semiconductor contacts and the nonlinear effect of illumi-
nation on the dark characteristics. Here, it will be assumed that the superposition
principle is applicable. The dark current of the solar cell was treated in detail in
Section 1.3. It remains to be determined how the short circuit current is caused by
the incident solar radiation.
Assuming a photogeneration rate g ph at an arbitrary point x from the edge of the
field region and a minority carrier lifetime s n in the p-side, one can express the excess
photogenerated electron concentration as
Dn ¼ Dp ¼ g ph s (1.23)
Assuming s is constant, one can determine an average Dn knowing the average
photogeneration rate g ph such that

Dn ¼ g ph s n (1.24)
Then the collected electron charges Q n from the p-side by diffusion can be written as

Q n ¼ qADnL n ¼ qAg ph s n L n (1.25)
where L n is the diffusion length of electrons in the p-side. Then the current from the
p-side

Q n
I n ¼ ¼ qAg ph L n (1.26)
s n
Similarly, the current from the n-side

Q p
I p ¼ ¼ qAg ph L p (1.27)
s p
The current from the field region

I fr ¼ qAg ph W scr (1.28)
where W scr is the field region width.
Now, summing up all current components, we get the cell short circuit current I sc
I sc ¼ I ph ¼ qAg ph ðL n þ L p þ W scr Þ¼ qAg ph W eff (1.29)
where W eff is the effective thickness of the solar cell.
The spectral irradiance I(x) decreases exponentially as explained in Section 1.2,
then, the photon flux F ph at any point x can be obtained by dividing Eq. (1.8) by E ph ,

F ph ¼ F ph ð0Þe ax (1.30)
To get the photons DF ph absorbed in an incremental distance dx at x

DF ph ¼ F ph ðxÞ F ph ðx þ dxÞ