An isotropic material is usually described by two optical constants: the refractive index (n) and the extinction coefficient (k). They are related via the complex refractive index (nc) byThe absorption coefficient oL(~o), which is a function of the angular frequency of radiation (w), is related to k and the wavelength ()0 byThe fundamental absorption band of crystalline semiconductors possesses a relatively sharp structure. This is not the case in many amorphous thin films and glasses for which the optical absorption edge is less abrupt and less well-defined. At high absorption levels (o~ > 104 cm -1) 0l is a function of the energy of the incident light (he0), the optical bandgap (Eopt) of the material. These parameters are related by [1,2]
oihco = B(ho9-gopt) r (3)where B is a constant equal to 4ZrOo/ncEe, Cro is the extrapolated d.c. conductivity at T = ~, c is the speed of light, E~ is a measure of the width of the tails of localized states in the bandgap and r is a number between 1 and 3, the exact value of which depends on the optical absorption process. At lower levels of absorption (1 < o~ -< 10 4 cm -1) the absorption edge extends over four orders of magnitude and is described by [3] ol(co) = ol o exp (hr~/Ee)where o~ 0 is a constant.