Ultrasonic attenuation in pure and doped<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-type silicon

Abstract

The attenuation due to phonon viscosity and thermoelastic phenomena of longitudinal ultrasonic waves propagating along 100 &gt; and 110 &gt; directions and shear waves polarized along 100 &gt; and 1\ifmmode\bar\else\textasciimacron\fi{}10 &gt; directions, has been evaluated for pure and doped $n$-type silicon at 298 \ifmmode^\circ\else\textdegree\fi{}K using second- and third-order elastic moduli through Gr\"uneisen mode $〈\ensuremath{\gamma}〉$, average square Gr\"uneisen constant $〈{\ensuremath{\gamma}}^{2}〉$, and nonlinearity constant $D$. The present theoretical results of pure silicon for longitudinal and shear waves along 100 &gt; direction are in good agreement with the previous experimental results. The phonon viscosity in terms of dislocation-drag coefficient along 100 &gt; and 110 &gt; directions is also discussed.