Ionized-Impurity-Limited Mobility ofα-Sn in the Random-Phase Approximation

A calculation of the ionized-impurity-limited mobility of a ${\Gamma }_8$ conduction band is performed, using a random-phase-approximation dielectric function and taking into account the effects of band nonparabolicity and $p$-like character of the wave function on the scattering calculation. The results are compared with measured mobilities of Sb-doped $\alpha$-Sn. It is shown that, assuming singly ionized donor impurities, the calculated results are grossly larger than the experimental values. The results are somewhat better for doubly ionized impurities. It is pointed out that the results of a calculation using a concentration-independent dielectric constant are in excellent agreement with experiment over the whole range of accessible concentration. These results indicate that, if the impurities are singly ionized Sb, the random-phase approximation considerably overestimates the interband polarization.