Models of optical absorption in amorphous semiconductors at the absorption edge — A review and re-evaluation

Abstract

Davis-Mott and Tauc models of optical absorption at the absorption edge in the high absorption coefficient region (α≥10⁴cm⁻¹) are carefully reviewed with regard to their theoretical foundations, assumptions, mathematical derivations, and results. The full implications of these models are exploited, and it is found that the Davis-Mott model for negligible matrix elements between localised states could account for the cubic power law behaviour ofα with photon energyħω of some amorphous semiconductors such as a-Si. A fractional power law to find the optical band gapE _opt, of the form [αħω ∝ (ħω−E _opt)^r; 2≤r≤3] based on Davis-Mott model is proposed in which the indexr can be a function of disorder. The Tauc model has further been extended to the case of negligible matrix elements between localised states, in which the same square power law forα vs.ħω with the same meaning of the optical gap as in the original Tauc model has resulted. A consideration of the case of unequal matrix elements for those transitions between localised states and those between extended states is also included. The meaning ofE _opt has been re-assessed and it is emphasized that it is an extrapolation of delocalised states to the zero of the density of states rather than a threshold energy for the onset of some kind of optical transitions.