1 Introduction 2 The Haynes-Shockley Experiment

α = 4πk
λ , (32)
where λ is the wavelength of the light used.
For normal incidence of light on the sample, the reflection coefficient, R, is related to the refractive
index by
R = (n − 1)2 + k 2
(n + 1) 2 + k 2 (33)
and if the sample thickness is many times the wavelength of the light (i.e. if d ≫ λ), the transmission
coefficient is
T =
(
1 − R 2) e −αd (
1 + k2
n 2 )
. (34)
From these equations it is clear that a measurement of R and T enables the determination of n and k,
and if R and T are measured as a function of wavelength then a complete optical characterisation of
the material is possible. When k 2 ≪ n 2 , which is usually the case for many materials in the wavelength
region of high transparency, equations (33) and (34) aquire a simplified form:
and
T =
R =
(n − 1)2
(n + 1) 2 (35)
(
1 − R 2) e −αd . (36)
Of particular importance to us in this final equation is the absorption coefficient, α. It depends directly
on the electronic band structure of the material involved. For a direct band gap semiconductor,
α = B 1 (hν − E g ) 1/2 (37)
where E g is the band gap energy, whereas for an indirect band gap semiconductor
α = B 2 (hν − E g ± E p ) 2 (38)
where E p is the phonon energy associated with the indirect transition. When E p ≪ E g , then equation
(38) reduces to
α = B 3 (hν − E g ) 2 . (39)
For many amorphous semiconductors, the dependence of α on E follows the relationship
αhν = B 4 (hν − E g ) 2 . (40)
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