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

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 $\ell_{\rm bare}$.