Thermal Conductivity of Heavily Dopedp-Type InSb at Liquid-Helium Temperatures

The lattice thermal conductivity ${\lambda }_g$ of three heavily doped (${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$) $p$-type samples of InSb has been determined in the temperature range 1.3-4.2 ° K. The data are fitted to a phenomenological model including boundary scattering, Rayleigh scattering due to impurities and isotopes, and the scattering of phonons by charge carriers. That the charge carriers are a significant source of scattering is indicated by a general $T^2$ behavior at the lowest temperatures and by a rapid increase in ${\lambda }_g$ at the higher temperatures because of phonons which have wave-propagation vectors larger than the diameter of the Fermi surface, and which therefore cannot be scattered by charge carriers. A probable screening in the carrier-phonon interaction is apparent from the lowest-temperature behavior of ${\lambda }_g$. In general, a good fit is made using the theories of charge-carrier-phonon interactions developed for the treatment of ultrasonic attenuation.