John D. Dow

Effective-impurity model of optical absorption edges☆

A simple model of an amorphous or disordered semiconductor is presented in which the disorder is approximated by a distribution of effective impurities. In this model the disorder potential in a given region of the semiconductor is characterized by an effective charge, and the optical absorption in that region is calculated. The total absorption is then a statistical average (over effective charge distributions) of the absorption in the presence of a single effective-impurity. Thus the model leads to an expression for e2(ω) as a functional of the density-of-states, which accounts for electron-hole correlations due to both the final-state (exciton) interaction and the spatial fluctuations of the disorder potential. These effects lead to an exponential suppression of the optical absorption in the edge region, beyond that calculated in an uncorrelated non-direct transition model. Finally, the model is complementary to Franz-Keldysh theories of absorption edge shapes and can be used to describe exponential edges in a variety of non-conducting materials.