TEMPERATURE DEPENDENCE OF PHONON-PHONON INTERACTION IN SILICON

Abstract
The generation of a second harmonic of an initially sinusoidal ultrasonic wave can be considered as collinear interaction between two identical phonons to produce the sum frequency phonon. This phenomenon has been studied in considerable detail, and the studies have led to a technique for measuring harmonic amplitudes and calculating anharmonic coupling coefficients in terms of second- and third-order elastic constants. Measurements have been made on silicon, and have resulted for the first time in a complete set of third-order elastic constants at temperatures between 3°K and 300°K. Results are presented for silicon between 3°K and 300°K and a comparison is made between TOE constants calculated by using our data in the Keating theory and TOE constants evaluated by combining our data and those of Beattie and Schirber.