Collective elastic waves in piezoelectric semiconductors

A new mode of energy transport in solids is described, which utilizes the interaction between monochromatic elastic vibrations to produce a collective wave traveling with a velocity only slightly slower than the speed of sound. The phenomenon is similar in concept to the propagation of "second sound" in liquid He II. The vibrational state of a solid is first described in terms of a set of quantized lattice harmonic oscillators or phonons. By analogy with the kinetic theory of sound propagation in an ordinary particle gas, it is then shown that a phonon-density wave can propagate in this phonon gas. This corresponds to a wave-like transport of heat through the solid. The conditions for this mode of transport are described and compared to those for the usual diffusion of heat. It is shown that these conditions can be satisfied in piezoelectric semiconductors for a restricted band of phonon frequencies when the electrons drift in an applied field at a speed greater than the speed of sound. The electron-phonon interaction processes which produce this behavior are described graphically, and the frequency and temperature dependence of the interaction is discussed. Experimental observations in photoconducting CdS, a piezo-electric semiconductor, are described which appear to verify these predictions. Pulse propagation experiments at room temperature show a velocity corresponding to the collective mode, and the properties vary as predicted with changes of electron drift velocity and of temperature. A mechanism for the excitation and detection of the collective wave is suggested. The nonlinear processes leading to the generation of elastic waves at harmonics of the input frequency are also described.