Phonon Conductivity of InAs

Abstract

The low-temperature thermal conductivity $K$ of undoped $n$-type InAs has been measured between 5 and 300 \ifmmode^\circ\else\textdegree\fi{}K, and analyzed on the basis of three different approaches, each including boundary-effect, mass-difference-scattering, and phonon-phonon processes. Various required parameters, mainly the phonon frequencies at zone boundary, have been deduced for InAs from known values of these parameters in the III-V compounds Si and Ge. Callaway's expression of $K$ is found to give satisfactory agreement from low temperature up to temperatures slightly beyond the maximum. At low temperatures boundary and mass-difference scattering predominate. The Holland two-mode formulation explains the temperature dependence of $K$ in the entire temperature range by emphasizing the predominant contribution of transverse phonons at low and high temperatures. The more elaborate approach, two-mode heat conduction using three-phonon relaxation times deduced from Guthrie's analysis and a quadratic relation ($q,\ensuremath{\omega}$), suggests that at high temperatures the contribution of longitudinal phonons to $K$ becomes comparable to that of transverse phonons. Moreover, four-phonon processes have been tentatively included in order to fit the experimental data in the higher-temperature range. It appears that no conclusion as to the relative contributions of transverse and longitudinal phonons may at present be satisfactorily established for InAs at high temperature.