Nonlinear Theory of Current Saturation in Piezoelectric Semiconductors

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Abstract
A nonlinear theory is given of the current saturation in cadmium sulfide at room temperature when the drift velocity of electrons exceeds the velocity of sound. The constitutive equations consist of the coupled Boltzmann equations for conduction electrons and amplified phonons. The classical expressions are used for the amplification of phonons and the linear loss of amplified phonons by thermal phonons. Although a three-phonon process via a nonlinear interaction with electrons is taken into account, the expression for the “nonlinear relaxation time” involves an adjustable parameter. When a reasonable value of the parameter is chosen, the theory explains semiquantitatively (1) the current-voltage characteristics, (2) the decay time of current from ohmic to saturation values, and (3) the characteristics of acoustoelectric-after-current.