A THEORY OF ACOUSTOELECTRIC DOMAINS IN PIEZOELECTRIC SEMICONDUCTORS .3. DOMAIN SOLUTION

A model for an acoustoelectric domain is obtained by solving the non-linear growth equations derived previously via the Krylov-Bogoliubov method. It is shown that the shape of the acoustic flux profile is determined by a combination of coherent and incoherent effects, the former arising from a non-linear self-interaction of a single acoustic mode, the latter arising from the interaction of all the random-phase waves in the domain with a space-charge mode. Although a flat-topped region is a possibility, the domain fields and flux intensity required for such a saturation are so high that in most practical cases it is unlikely to occur. The common situation is therefore one in which the flux profile in both edges is hyperbolic and symmetrical, the two hyperbolic wings meeting in the centre to give a cusp of high flux intensity (greater, similar100 w cm-2) and high electric field (greater, similar10 4v/cm-1). The domain travels at the velocity νs(1+K2)1/2 and the field outside the domain is at the threshold (zero net gain). Domain widths are typically 100-1000 μm. Since the field profile is hyperbolic the domain voltage does not converge, which implies some time dependence of profile though this will be weak in many cases. The downward frequency shift of the maximum-gain acoustic modes can be 30% or more. The whole basis of the model is that there is a non-electronic loss mechanism.