Variation of the electron-phonon mobility with carrier density for highly doped and highly excited semiconductors

We study the response, to a small electric field, of a doped semiconductor or an optically excited electron-hole plasma, as a function of carrier density and temperature. We limit the discussion to the case of nonpolar semiconductors such as Ge and Si and include the screening of the electron-phonon interaction by the carriers, which are considered as classical as well as degenerate. We show that the behavior of the relaxation time τ(n) is much more complex than a simple increase due to electron-phonon interaction screening. For optical phonons, τ goes through a maximum, which is reached in the degenerate limit, and finally decreases when the density n continues to increase. For acoustical phonons we predict that, with increasing n, τ goes first to a maximum, then decreases to a minimum, reached for n∼${10}^{19}$ ${\mathrm{cm}}^3$ in the case of Ge at 20 K, and finally increases again for very large densities and low temperatures.