Nonlinear Thoery of Ultrasonic Wave Amplification and Current Saturation in Piezoelectric Semiconductors

Abstract

A nonlinear theory based on numerical calculation is developed for the amplification of ultrasonic waves in piezoelectric semiconductors. The theory is one-dimensional and applies to semiconductors at room temperature in which the mean free path of the carriers is small compared with the acoustic wavelength. To provide a physical understanding of the problem, the following quantities are investigated in detail: (1) the carrier and the piezoelectric potential distributions and their relative phases, (2) the harmonic content of the elastic wave caused by the electronic interaction, (3) the acoustoelectric current and the nonuniform distribution of the dc electric field in the crystal, and (4) the effect of nonelectronic loss. As the intensity of the elastic wave increases, the drift velocity of the carriers starts from the Ohmic velocity and gradually decreases to the speed of sound. Similarly, the acoustic gain expressed in nepers per unit distance starts from the small-signal value and decreases slowly toward zero. The results obtained for the current and gain saturations described above in various conditions of amplification are presented in universal curves. We find that the current saturation occurs because the carriers are trapped in the troughs of the large piezoelectric potential excited by the elastic wave and are forced to move along with the wave at the speed of sound. We also show that this concept of the current saturation is entirely consistent with the calculation of the acoustoelectric current. Later, in a study of the acoustoelectric current and the Weinreich relation by means of simple power relations, we calculate the efficiency for the conversion of electronic energy to elastic energy. Among other findings we show that in a nonlinear theory, the Weinreich relation can be written for each harmonic independently. Finally, the theory is applied to various phenomena of acoustoelectric origin. Several simulation calculations are made for the propagation of high-field domains, and they verify the phenomena of "pinned" domains and the associated damped current oscillations observed experimentally in photoconductive CdS. Good agreement is also obtained between the present theory and the existing measurements of gain saturation.