ABSTRACT
Perhaps the simplest use of photons for the characterization of a semiconductor is linear absorption spectroscopy. A monochromatic photon beam arrives at a semiconductor sample with intensity I0. After passing through the sample, the intensity is I. From the Beer-Lambert Law (Equation 1.25), the optical transmission is given by
(10.1)T I I e x≡ =/ 0 −α
where x is the sample thickness and α is the linear absorption coefficient. The absorbance is defined as
(10.2)Absorbance / = =( ) − ( )log log10 0 10I I T
Equation 10.1 neglects reflection from the sample surfaces. Taking into account multiple reflections from identical surfaces in a vacuum, at normal incidence,
(10.3)
T R e R e R e knx
x x= −( )
+ − ⋅ ( )
1 1 2 2
where the reflectance R is given by Equation 7.8. The cosine term accounts for interference between the multiple reflections. This results in Fabry-Perot interference fringes that have maxima when 2x is a multiple m of the wavelength in the material:
(10.4)2x m n= λ/
In a transmission spectrum, the spacing between adjacent maxima,
(10.5)∆ 1 1 2/ ( )λ( )= / nx
allows one to determine the thickness of the sample if the refractive index n is known. FabryPerot fringes can be seen in Figure 7.9. The amplitude of Fabry-Perot fringes is reduced by absorption, scattering, or surfaces that are rough or nonparallel. Because of these effects, in many situations, multiple reflections are negligible and the denominator in Equation 10.3 can be replaced by 1.
