On the Nonlinear Theory of Ultrasound Amplification in Semiconductors

Abstract

The nonlinear theory of the amplification of ultrasonic waves of arbitrary amplitude by the electric current in semiconductors is developed in the arproxirnation of small variations of amplitude, shape, and velocity of the wave on the wavelength in space and during the period of oscillation in time. The general equation is derived that determines slow variation of the amplitude of the sound wave of arbitrary shape in space and time, i.e., the continuity equation for sound flux. Also the average local drift velocity of the electrons and the amplitude-dependent correction to the sound velocity are calculated. The "nonlinear" sound absorption coefficient entering the continuity equation, the average drift velocity of the electrons, and the nonlinear correction to the sound velocity are directly calculated in three limiting cases: 1) small sound amplitude; 2) large "overcriticity"; and 3) large sound amplitude. Then the convenient interpolation formulas that are valid for the arbitrary amplitude of the sound wave are found for these quantities. The problem of generation of higher harmonics at the amplification of a sound wave of large amplitude is considered. It is shown that with the growth of the intensity of the wave, the maximum of the amplification coefficient shifts to the lower frequencies. With the use of the derived continuity equation for sound flux, the distributions of the intensity of sound and of the electric field along the specimen are found for the case of stationary sound amplification in a semiconductor. It is shown that in a finite crystal the nonlinear effects accompanying the sound amplification take place only in a restricted (both from below and from above) region of the voltages on the specimen. Also, it is shown that the finite specimen under sound amplification conditions may posses the S-shaped current-voltage curve.