Application of the uncertainty principle to electron scattering by phonons in solids

The contribution of the uncertainty principle to the scattering rates of electrons by phonons in non-polar semiconductors is derived and applied to the hot electron problem. It is shown to modify all of the transport integrals to a certain extent and to remove a singularity appearing in the expression for the mobility when expanded in powers of the electric field. This singularity results from the occurrence of an abrupt threshold for the emission by an electron of an optical phonon. The contribution to the mobility of the term in question and its dependence on the energy uncertainty are calculated for conduction in n-type germanium. © 1963.