2.5.5.5 Ridley's Model

The ionized impurity scattering rate has a sharp peak at very low energies. This can cause very high self-scattering rates in Monte Carlo methods described later in this work and long computational times. Although the comprehensive ionized impurity scattering model described above is mostly used in the present work, in some cases it is useful to employ simpler models. One such model is briefly described here.

Assuming statistical screening avoids the problem of the sharp behavior at low energies[52]. In this approach an additional statistical screening mechanism is introduced to cut off the long-range part of the screened Coulomb interaction. The resulting scattering rate is:

$$\lambda_{st.sc}(\vec{k})=\frac{\vert\vec{v}(\vec{k})\vert}{R} \bi... ...biggl(-\lambda_{BH}(\vec{k})\frac{R}{\vert\vec{v}(\vec{k})\vert}\biggr)\biggr),$$ (2.167)

where $\lambda_{BH}$ stands for the scattering rate of the Brooks-Herring model (2.140). This approach allows the number of small-angle scattering events to be reduced and thus reduces the amount of scattering events to be simulated.

S. Smirnov: