Page 154 - A Comprehensive Guide to Solar Energy Systems

Chapter 8 • Photovoltaics: The Basics 155

A comparison of the absorption coefficient on photon energy of CdTe (direct band
structure) and si (indirect band structure) is shown in Fig. 8.3.
As shown earlier, electron–hole pairs are generated when photon energy hν > W g . In
this way, the carrier concentration n is higher than the concentration n 0 corresponding to
the thermal equilibrium. The difference ∆n = n − n 0 is called excess carrier concentration
(∆n = ∆p because electron–hole pairs are generated).
Let suppose that each absorbed photon can generate β electron–hole pairs. For a pho-
ton with energy hν < W g , no electron–hole pairs are generated and β = 0. For absorbed
photons with energy hν > W g , β = 1 is generally expected. note that high energy photons
may generate more than one electron–hole pair if the kinetic energy given to a generated
free electron or hole is higher than 2W g . Then, following an impact with a neutral atom, it
may generate another electron–hole pair. (This effect may be considerable only for semi-
conductors with a narrow bandgap.) The excess carrier generation rate G depends on the
band structure, the wavelength λ (the photon energy), and the flux of the photons Φ(λ). At
a distance x from the surface, it can be expressed by

∆ 
 dn
λ
)(
)(
(
)
()
λ = () ()
Gx (; λ =    = α λβ λ Φ x;) αλ βλ Φ ()exp[ − α λ x]. (8.5) G(x;λ)=d∆ndtgen=α(λ)β(λ)Φ(x;λ)=
0
 dt gen α(λ)β(λ)Φ 0 (λ)exp[−α(λ)x].
From eq. (8.5) it follows that the generation rate strongly depends on the wavelength
and intensity of the incident light (and also on the semiconductor material). under condi-
tions of solar radiation, the total generation rate in a distance x from the surface can be
expressed by

FIGURE 8.3 A comparison of absorption coefficients of silicon and CdTe (after Ref. [7]).