Variation of Nonlinearity Parameter and Acoustic Attenuation with Temperature in Few Semiconductors

Abstract

Acoustic attenuation coefficient per unit frequency square has been calculated for pure semiconductors like silicon and germanium, as well as for mixed semiconductors like gallium arsenide (III–V group) and tin telluride (IV–VI group), for longitudinal waves travelling along the \(\left\langle {100} \right\rangle \) crystallographic axis, within the temperature range 80–300 K. Second-order elastic constants of the materials are used to calculate the average Gruneisen parameter \(\left\langle {{{\gamma }}_{i}^{j}} \right\rangle \), using which the nonlinearity parameter D_L has been calculated for different temperatures. The knowledge of D_L is used for calculation of acoustic attenuation coefficient per unit frequency square due to phonon–phonon interaction \({{\left[ {{{{\alpha }} \mathord{\left/ {\vphantom {{{\alpha }} {{{f}^{2}}}}} \right. \kern-0em} {{{f}^{2}}}}} \right]}_{{\text{L}}}}\) and thermoelastic losses \({{\left[ {{{{\alpha }} \mathord{\left/ {\vphantom {{{\alpha }} {{{f}^{2}}}}} \right. \kern-0em} {{{f}^{2}}}}} \right]}_{{{\text{th}}}}}\). Acoustic attenuations are found to be temperature dependent and increases with it. The magnitude of acoustic attenuation per unit frequency square due to phonon–phonon interactions is greater than that due to thermoelastic losses. The magnitude of acoustic attenuation for the investigated semiconductors is in the order Si < Ge < GaAs < SnTe. It is observed that anharmonicity of the solids which give rise to phonon–phonon interaction is the dominant cause of acoustic attenuation of propagating waves. The acoustic attenuation of propagating waves is found to be proportional to the molecular weights of semiconductors.