Abstract
A non-linear theory using the Krylov-Bogoliubov method is developed of the growth and propagation of an acoustoelectric wave and its interaction with a space charge mode, in which the non-linearity derives solely from the drift current. First order differential equations are derived which describe the space and time development of non-linearities and it is shown that these propagate with a well-defined velocity which we have called the non-linear interaction velocity. In the case considered this velocity is near to the piezoelectrically stiffened velocity of sound νs(1 + K2)½. A general expression for the acoustoelectric current is obtained and the importance of a non-electronic loss mechanism for providing an excess field under conditions of zero linear gain is pointed out. Coupled first-order differential equations are derived which describe the time-independent travelling space profiles of the amplitude and wavelength shift of the acoustic mode, and the amplitude of the space charge mode. The waveform of the acoustic wave contains principally only the first (fundamental) and second harmonics and has a saw-tooth appearance. Comparison with a numerical computation shows that this harmonic content is surprisingly successful even in the case of substantial carrier bunching. The theory is generalized to include an arbitrary number of random-phase acoustic modes with essentially the same frequency and acoustoelectric properties. This has the effect of enhancing the acoustoelectric field, increasing the interaction with the space charge mode and making the wavelenth increase more rapidly with amplitude.
Published Version
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