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

with V T ¼ the thermal voltage ¼ k B T/q. Mobility and the diffusion constant are
properties of the semiconductor materials that depend on temperature and doping.

2.4 RECOMBINATION MECHANISMS AND MINORITY CARRIER
LIFETIME
The recombination is an intrinsic property of any semiconductor material. In this
process, the electron meets a hole and completes a broken bond. Both are going
to be lost. There are different recombination mechanisms: the band to band radiative
recombination, the band impurity band ShockleyeReadeHall nonradiative recom-
bination, and Auger recombination. Every mechanism has its specific rate equations
[11]. Fig. 1.9 illustrates the fact that an excess of electrons and holes Dn ¼ Dp dis-
appears after an average s.
So, the recombination rate is (Dn/s). Any electron hole pair can survive only on
the average the lifetime. As they move continuously, electrons and holes travel
certain specific distance in their life time called the diffusion length L. The diffusion
p ffiffiffiffiffiffi
length is given by L ¼ Ds. This length is an important property controlling the so-
lar cell performance. For silicon, it amounts to 1e500 mm.

2.5 OPTICAL PROPERTIES
We are interested in understanding the response of the semiconductor to light, i.e.,
the photoelectric effect. If a light beam is incident on a semiconductor material, part
of the light energy will be reflected, a part will be absorbed inside the material after
refraction, and the remaining part will be transmitted. According to energy conser-
vation law, we can write
I ¼ R þ A þ T (1.6)
Here, I is the incident light energy, R the reflected, A the absorbed and T the
transmitted parts. Reflection occurs because of the change of the wave impedance
p ffiffiffiffiffiffiffi
Z w ¼ m (where m and ε are the permeability and permittivity of the medium,
= ε
respectively), which changes at the surface of the material. The reflectance r is given
by
2
jZ w Z wa j
r ¼ (1.7)
jZ w þ Z wa j

FIGURE 1.9
Illustration of the decay of an excess of electrons and holes.