Self-consistent calculation of ionized impurity scattering in semiconductor quantum wires

TL;DR

This paper presents a self-consistent method to calculate the electron mean free path due to ionized impurity scattering in semiconductor quantum wires, revealing that screening significantly increases the mean free path compared to unscreened models.

Contribution

It introduces an exact self-consistent calculation scheme for impurity scattering in quantum wires using a short-range potential model, improving upon previous approximations.

Findings

Self-consistent screening increases mean free path substantially.

The mean free path scales as the square of the logarithm of the bare mean free path.

The method provides an exact solution within the specified approximations.

Abstract

We calculate the electron elastic mean free path due to ionized impurity scattering in semiconductor quantum wires, using a scheme in which the screened ionized impurity potential and the electron screening self-consistently determine each other. By using a short-range scattering potential model, we obtain an {\sl exact} solution of the self-energy within the self-consistent Born and ``noncrossing" approximations. We find that, compared to the mean free path for the bare unscreened potential $\ell_{\rm bare}$, the calculated mean free path including self-consistent screening $\ell_{\rm sc}$ is {\sl substantially larger}, going as $\ell_{\rm sc} \sim \ell_{\rm bare}[\ln(\ell_{\rm bare})]^2$ for large $\ell_{\rm bare}$.