On the shape of the absorption tail in amorphous solids

Abstract

A simple theoretical model is presented in which the exponential shape of the optical absorption tail of amorphous solids is attributed t o elastic (or density) fluctuations in the band gap. The proposed mechanism ascribes this spectral dependence of the absorption coefficient to electronic transitions between states lying at different sites of the sample.

Effect of mechanical stress on the absorption band tail of cubic boron nitride thin films synthesized by inductively coupled radio-frequency plasma chemical vapour deposition

“…Mechanical stress in the grain-boundary regions of polycrystalline films may result in electrostatic fluctuations in the band gap E g as has been discussed earlier by several authors [24][25][26][27]. The basic idea is the existence of a finite probability for transitions between states lying at different energy levels within the band gap of a polycrystalline sample.…”

“…There are two components of corresponding to intrinsic disorder or defect states ( in ) and to thermal or phonon-induced disorder ( T ). The explicit form of is given by [24,25,30] …”

“…0 (at an effective temperature T *) respectively. Now the general form of the absorption coefficient M ðp!Þ arising from mechanical stress may be expressed as [24,25] M ðp!Þ % where D(E g )dE g is proportional to the number of microcrystallites per unit volume and P(E) is the probability of indirect transitions within the regions of the sample in which the energy gaps lie between E g and E g þ dE g . Assuming the form of P(E) given by [24,25], we have…”

“…In order to calculate the absorption from mechanical stress in the c-BN films, we consider the variation of E g at various sites of the specimen, which may be represented by the following distribution function [24,25] DðE g Þ % exp À ðE g À " The disorder parameter indicates the RMS value of antiparallel displacements of the valance and conduction band edges from the corresponding positions in an ideal lattice. There are two components of corresponding to intrinsic disorder or defect states ( in ) and to thermal or phonon-induced disorder ( T ).…”

“…The resultant residual strain (a/a) is related to the parameter Á by the empirical relation [24,25]:…”