Thermal Conductivity of Heavily Doped<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi></mml:math>-Type InSb at Liquid-Helium Temperatures

Abstract

The lattice thermal conductivity ${\ensuremath{\lambda}}_{g}$ of three heavily doped (${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$) $p$-type samples of InSb has been determined in the temperature range 1.3-4.2 \ifmmode^\circ\else\textdegree\fi{} 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 ${\ensuremath{\lambda}}_{g}$ 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 ${\ensuremath{\lambda}}_{g}$. In general, a good fit is made using the theories of charge-carrier-phonon interactions developed for the treatment of ultrasonic attenuation.