Impurity band tails in quantum-well heterostructures

Abstract

A calculation of the band tailing in heavily $n$-type doped superlattices and single wells is presented. We calculate the density of states in the low-energy tail for ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$-GaAs quantum-well heterostructures using an extension of the semiclassical approach developed by Halperin and Lax for bulk materials. It is found that the density-of-states curve for superlattices is shifted in energy in roughly the same way as the position of the lowest subband edge as the layer width is varied. A similar result is found for single wells. In addition to this the shape of the curve for the heterostructures is changed so that the density of states at low energies is enhanced somewhat relative to that at higher energies. The size of the band tail is quite sensitive to the dopant concentration. The extension of the wave function perpendicular and parallel to the layers depends mainly on the layer width and the energy, respectively. The effects of different choices of the effective mass and the dielectric constant are examined.