Band Tails and Disordered Potentials

Abstract

It has long been known that the density of states in a semiconductor decays expo nentially into the gap. This tail in the density of states is caused by impurities in the atomic lattice that creates localized states with energies in the gap region. By modeling the impurities as a correlated Gaussian disorder potential, it is possible to utilize path integrals to calculate the density of states in the tails. In this thesis, I examine how the form of the dispersion relation of the band affects the band tail when compared to a standard parabolic dispersion |k|2. I find that for monomial dispersions |k| q with powers higher than q = 2 there does not exist any region with a purely exponential decay, only regions where it decays quicker. For double-well dispersions I find that the density of states decays in a slightly different, but still comparable way to monomial dispersion.