2.5.5.2 Two-Ion Scattering

This correction [44,45] to the Brooks-Herring model takes into account the fact that at high impurity concentration the scattering on two ions becomes important. The bare scattering potential is given as:

$$V_{0}(\vec{r})=\frac{Ze}{4\pi\varepsilon}\biggl(\frac{1}{\vert\vec{r}\vert}+\frac{1}{\vert\vec{r}-\vec{R}\vert}\biggr),$$ (2.142)

where $\vert\vec{R}\vert$ is the average distance between impurity centers. The Fourier transform of this potential is equal to:

$$V_{0}(\vec{q})=\int\exp(-i\vec{q}\cdot\vec{r})V_{0}(\vec{r})\,d\vec{r}=\frac{Ze}{\varepsilon\vec{q}^{2}}(1+\exp(-i\vec{q}\cdot\vec{R})).$$ (2.143)

Electrons respond to this potential forming a self-consistent potential which can be described by screening theory. The general screening theory in the presence of the periodic crystal potential is rather complicated. Thus the screening theory for the electron gas is employed here. S. Smirnov: