Optical Absorption in Amorphous Semiconductors: The Independent Band Model and its Experimental Basis

Abstract

A major source of information on the electronic properties of amorphous semiconductors is experimental data on the optical properties close to the absorption edge. An important theoretical tool in interpreting this data is a simple physical model for the optical absorption which was introduced about twenty years ago.¹ This model which can be described as the “independent band model”² assumes that the amorphous semiconductor has no positional order but that its valence and conduction band wave functions are linear functions of Bloch functions of a corresponding “virtual” crystal. Based on these assumptions, a simple formula for the magnitude and spectral dependence of the imaginary part of the complex dielectric constant (ɛ₂(E)) can be derived which depends on the optical matrix element of the “virtual” crystal and the density of states of the amorphous semiconductor. This formula has been used to define an optical gap, as well as to derive the energy dependence of the conduction and valence band density of states.³ Despite its wide spread use, the assumptions of the independent band model have yet to be critically examined. For example, there have been relatively few attempts to relate the matrix element of this model to those of the corresponding “virtual” crystal.⁴ Indeed there have been few attempts to identify the “virtual” crystal at all! Furthermore, while the model has been often used to predict the spectral dependence of ɛ₂ from models for the density of states, the magnitude of ɛ₂ has been relatively ignored until recently.⁵