Acoustoelectric interaction in degenerately doped piezoelectric semiconductors

The acoustoelectric gain constant is calculated quantum mechanically for arbitrary degeneracy of the electron gas. The requirements of energy and momentum conservation in individual electron‐phonon interactions result in a rather sharp reduction of the gain factor when the acoustic wave number exceeds the characteristic linear extension of the electron distribution in reciprocal space. A simple two‐band model is developed to describe effects of impurity banding upon the acoustoelectric interaction. According to this model, impurity banding enhances the acoustoelectric coupling and widens the active acoustic spectrum. These effects are associated with the increased density of states near the conduction‐band edge and with the presence of electrons of higher momentum effective mass than the conduction‐band electrons. At low temperatures it becomes possible for the linear gain factor as a function of acoustic frequency to have two maxima.