Crystal Dynamics of Gallium Arsenide

Abstract

The dispersion relation for the normal modes of vibration propagating along the [$\ensuremath{\zeta}00$], [$\ensuremath{\zeta}\ensuremath{\zeta}\ensuremath{\zeta}$], and [$0\ensuremath{\zeta}\ensuremath{\zeta}$] directions in a single crystal of pure gallium arsenide at 296\ifmmode^\circ\else\textdegree\fi{}K has been determined by neutron spectrometry. The frequencies (units ${10}^{12}$ cps) of specific modes are (a) (0,0,0): $\mathrm{TP} 8.02\ifmmode\pm\else\textpm\fi{}0.08$, $\mathrm{LO} 8.55\ifmmode\pm\else\textpm\fi{}0.20$; (b) (1,0,0): $\mathrm{TO} 7.56\ifmmode\pm\else\textpm\fi{}0.08$, $\mathrm{TA} 2.36\ifmmode\pm\else\textpm\fi{}0.015$, $\mathrm{LO} 7.22\ifmmode\pm\else\textpm\fi{}0.15$, $\mathrm{LA} 6.80\ifmmode\pm\else\textpm\fi{}0.06$; (c) (0.5,0.5,0.5): $\mathrm{TO} 7.84\ifmmode\pm\else\textpm\fi{}0.12$, $\mathrm{TA} 1.86\ifmmode\pm\else\textpm\fi{}0.02$, $\mathrm{LO} 7.15\ifmmode\pm\else\textpm\fi{}0.07$, $\mathrm{LA} 6.26\ifmmode\pm\else\textpm\fi{}0.10$. The results are analysed in terms of the dipole approximation model. Although a fairly complex version of this model provides a satisfactory description of most of the data, certain significant discrepancies remain. These indicate that the neglect of quadrupole interactions is a serious weakness of the dipole approximation model.