A compact formula for the density of states in a quantum well

TL;DR

This paper derives a compact formula for the density of states in a quantum well with inelastic scattering, incorporating various scattering mechanisms and reducing to known results in certain limits.

Contribution

It introduces a new formula for the density of states in quantum wells that accounts for inelastic scattering and unifies different scattering processes through a single parameter.

Findings

The formula includes effects of phonons, impurities, and interface roughness.

It reduces to the Breit-Wigner result for low incoherent scattering rates.

Provides a practical way to calculate density of states in real quantum well structures.

Abstract

In this paper we derive a formula for the density of states in the presence of inelastic scattering in the quantum well of a double barrier structure as a function of a characteristic time of the motion of electrons (namely, the round trip time in the well) and of transmission probabilities for the whole structure and for each barrier. In the model we use the scattering processes due to phonons, impurities, and interface roughness, are taken into account by a unique fenomenological parameter, the mean free path, which plays the role of a relaxation length. We also show that, for lower rates of incoherent processes, the derived formula reduces to the one obtained by means of the Breit-Wigner formalism.