Ultrasonic-Wave Propagation in Pure Silicon and Germanium

Abstract

Ultrasonic attenuation and velocity measurements have been made in pure germanium and silicon (doping <1014 impurity atoms per cc) and in doped n-type germanium and p-type silicon. The attenuation in pure materials shows a continuous decrease as the temperature is decreased and a very low attenuation below 20°K. These results indicate that the energy losses are accounted for entirely by phonon-phonon interactions. A calculation has been made of these losses, using a model based on the Akheiser effect and incorporating the recently measured third-order elastic moduli of silicon and germanium. For both materials, the calculated values predict correctly the large difference between longitudinal and shear waves and agree quantitatively within 50% with the measured values over the whole temperature range.