Thomas-Fermi dielectric screening in semiconductors

Thomas-Fermi (TF) screening in metals has been widely studied in the literature many years ago. It is shown in this paper that the same TF equation can be handled with different boundary conditions to describe screening in semiconductors. Explicit results for the wave-number-dependent dielectric function $\epsilon \left(\overrightarrow{\mathrm{k}}\right)$ and for the spatial dielectric function $\epsilon \left(\overrightarrow{\mathrm{r}}\right)$ are obtained in simple analytical form. A detailed comparison is done with the existing literature for diamond, Si, and Ge. TF dielectric functions are found to be in excellent agreement with either Penn model and random-phase approximation dielectric functions.