Page 51 - Advances in Renewable Energies and Power Technologies

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

Recalling that F ph ¼ I/E ph , one gets
Ið0Þe ax 1
Z
l c
g pht ¼ 1 e aW eff dl (1.36)
0 E ph W eff
Combining Eqs. (1.29) and (1.36) we obtain the short circuit current, which is
termed also as the photocurrent, i.e.,
l c Ið0Þe ax 1
Z
I sc ¼ I ph ¼ qAg pht W eff ¼ qA 1 e aW eff dl (1.37)
0 E ph
If the solar cell is designed such that (aW eff ) > 1 and a is dependent of l, Eq. (1.37)
simplifies to
e ax 1 Z l c
I scm ¼ qA lIð0Þdl (1.38)
hc 0
with E ph ¼ hc/l. For the highest efficiency, the dead layer under the top surface
x 1 ¼ 0. Then the highest collected short circuit current from the cell can be
written as

1 Z l c
I scm ¼ qA lIð0Þdl (1.39)
hc 0
To determine the maximum photocurrent, I scm one integrates the area under the
curve of lI(0). To use the spectral irradiance curve one has to subtract from it the
reflected part of the light such that

1 Z l c
I scm ¼ qA lð1 rÞIð0Þdl (1.40)
hc 0
It is clear from Fig. 1.19 that as l c increases, the integral increases and conse-
quently I scm . Hence, silicon collects more photons than gallium arsenide and the
short circuit current for the Si-cells is larger than that for GaAs. I ph amounts to
2
30e40 mA/cm for a single-crystal silicon solar cell at AM1.
From the foregoing analysis of the photocurrent of a solar cell, we conclude that
1. as the energy gap of the material decreases, I ph increases,
2. the dead layer directly under the top surface is very harmful for the photons with
high absorption coefficient a, because they will be mainly absorbed in this layer.
This is true for the energetic photons with high a for all materials,
3. photons with lower a, the low energy photons, must be given sufficient material
thickness to be absorbed, i.e., W eff 1/a,
4. therefore, the lowest a determines the thickness of the solar cell,
5. the reflectance of the surface must be decreased to increase the photocurrent,
ideally r ¼ 0, and
6. the solar cell has also certain spectral response where the spectral photocurrent
depends on the wavelength of the incident light as a depends on l.