Amorphous materials

OJL interband transition model for amorphous materials - a brief tutorial

OJL model parameters

The so-called OJL model for interband transitions is due to [S.K.O'Leary, S.R.Johnson, P.K.Lim, J. Appl. Phys., Vol. 82, No.7, 1.October 1997] where expressions for the density of states (DOS) are given for the optical transition from the valence band to the conduction band. Parabolic bands are assumed with tail states exponentially decaying into the band gap as sketched in the following graph:

The original parameters of the OJL density of states model are the energies EV and EC, the 'damping constants' of the valence and conduction band gV and gC, respectively, as well as the masses of the valence and conduction band mV and mC.
The expressions

and

denote the mobility edges of the valence and conduction band, respectively. The mobility ga in the OJL model is therefore given by

The meaning of the term 'mass' in this context is the following: Consider the band structure of a crystal (here: silicon):

The blue rectangle shows a region of one of the conduction bands which may be described by a parabola approximately. That means that the energy is proportional to the square of the wave vector:

This relation between wavevector and energy is similar to the one between momentum p and energy of a classical particle of mass m moving with velocity v (p=mv ):

The coefficient a that determines the curvature of the conduction band can be associated with the inverse mass of a classical particle, which is said to represent an electron in that conduction band:

A small mass corresponds to a large increase of energy with k, i.e. large slopes in the band structure:

On the other hand, a large mass stands for a flat band:

For the optical properties only the joint density of states (JDOS) denoted here as J is important which is a certain combination of the density of states of the valence and conduction band:

The integration collects all possible transitions from the valence band to the conduction band with energy separation equal to the energy of the absorbed photon. It is shown by O'Leary et al. that J can be written as a product of a function which is independent of the masses and a pre-factor (called M here) which contains the masses of the conduction and valence bands besides some constant factors:

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