On the Mobility of Electrons in Pure Non-Polar Insulators

It is pointed out that Peierls' condition for the validity of time-dependent perturbation theory in the determination of the mobility $\mu$ of electrons in crystals can be transformed to the form $\mu >30\mathrm{} \frac{{\mathrm{cm}}^2}{\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{t}-\mathrm{s}\mathrm{e}\mathrm{c}.} \left(\mathrm{at}\mathrm{room}\mathrm{temperature}\right)$ in the case in which the electrons are distributed classically. Since the recent investigations of the mobility of electrons in diamond, silicon, and germanium indicate that the mobility in these materials is at least several times greater than the foregoing limit, it would appear that perturbation methods may be used to discuss the mobility in these materials and possibly in other non-polar insulating materials, such as sulfur.