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The Hooke's law is perfectly obeyed in perfectly elastic solids, where even a small amplitude wave can propagate with undiminished amplitude and intensity. But, most of the real solids show a deviation from perfectly elastic behaviour, and exhibit "anharmonicity". As a result, a high frequency acoustic wave travelling through real solids gets attenuated. In present work, on the basis of theory of elasticity and making use of higher order elastic constants in solids some aspects of elastic and acoustic properties of semiconductor silicon are studied. Assuming a temperature dependent lattice parameter and non-linearity parameter, D_L, the acoustic wave attenuation is calculated. The losses leading to attenuation are attributed to phonon-phonon interactions. Theoretically calculated values of D_L and attenuation are compared with experimental values of D_L and attenuation obtained by W.P. Mason. A good agreement between the theoretical and experimental values proves the correctness of our approach.

Keywords

Acoustic Wave Attenuation, Longitudinal Waves, Elastic Constants.

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Temperature and Frequency Dependence of Acoustic Attenuation in Pure Semiconductors

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Authors

Sanjay H. Bagade ¹

Affiliations
1 Department of Physics, Bajaj College of Science, Wardha-442 001, IN

Source

Journal of Pure and Applied Ultrasonics, Vol 42, No 3 (2020), Pagination: 66-71

Abstract

Real solids show a deviation from perfectly elastic behavior and exhibit anharmonicity due to existence of zero-point energy, owing to which, a stress wave in the form of high frequency acoustic wave, travelling through it, gets attenuated. In the present work, some acoustic properties of pure semiconductors germanium and silicon, are investigated within temperature range 73-293 K, by making use of second and third order elastic constants. Assuming a temperature dependent non-linearity parameter D_L, D_S, the acoustic wave attenuation 'A' is calculated for longitudinal waves of frequency 286 MHz and 495 MHz and for shear waves of 495 MHz, propagating in pure germanium and silicon. The Akhieser losses leading to attenuation are attributed mainly to phonon-phonon interactions within the solid. Attenuation of high frequency waves is found to be strongly temperature and frequency dependent. Theoretically calculated values of attenuation 'A' show good agreement with experimental values obtained earlier.

Keywords

Acoustic Wave Attenuation, Longitudinal Waves, Shear Waves, Elastic Constants.

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