Temperature Dependence of the Ultrasonic Attenuation in Germanium

The ultrasonic attenuation in germanium has been measured as a function of temperature from 300 to 20\ifmmode^\circ\else\textdegree\fi{}K and at frequencies of 4 to 132 Mc/sec. The measurements were made using the pulse-echo technique with longitudinal sound pulses along the [111] direction. At 4 Mc/sec the attenuation was found to be 0.04 dB/cm independent of temperature in contrast with the results of Blitz et al. At $f<10$ Mc/sec the attenuation is dominated by diffraction losses exhibiting a frequency dependence of $\frac{1}{f}$. At $f>30$ Mc/sec the attenuation was found to be due to phonon-phonon losses with a frequency dependence of ${f}^{2}$. Contribution to the attenuation from electron-phonon interactions was found to be negligible and independent of carrier concentration. By using the theory of sound absorption by Woodruff and Ehrenreich involving phonon-phonon interactions, an rms Gr\"uneisen constant is deduced from the experimental data. This rms Gr\"uneisen constant has a temperature dependence similar to the usual thermodynamic temperature-dependent Gr\"uneisen constant.