Variation of Mobility with Electric Field in Nondegenerate Semiconductors

In a recent communication Sclar has discussed the nature of ionized-impurity scattering when the product of the carrier wave number and the distance at which the scattering potential is cut off is much less than unity. Sclar has studied the mobility under these conditions but has neglected the influence of lattice scattering and electric field. In this communication the author has studied the variation of mobility with electric field, taking lattice scattering into account.For semiconductors of low impurity concentration at usual temperatures, the product of the carrier wave number and the distance at which the scattering potential is cut off is much larger than unity. In this case Conwell has given a theory for the variation of mobility with electric field, assuming a δ-function distribution for free electrons in a semiconductor. Her theory predicts a net zero-field mobility which at first increases with decreasing impurity mobility. This conclusion is physically untenable and leads one to doubt the assumptions implied in the theory. The assumption of a δ-function distribution seems to be the least reliable. Hence the author has repeated the calculations by choosing a Maxwellian distribution of electron velocities, appropriate to a temperature, which in general is different from that of the phonon distribution. This leads to a net zero-field mobility monotonically decreasing with decreasing impurity mobility which is reasonable enough. Other interesting results at variance with Conwell's treatment have also been obtained.