Analysis of Lattice Thermal Conductivity

An analysis of thermal conductivity is presented which differs from that of Klemens and of Callaway in that it considers explicitly the conduction by both transverse and longitudinal phonons. This approach is then used to provide a very good fit to the data on silicon from 1.7 to 1300\ifmmode^\circ\else\textdegree\fi{}K and on germanium from 1.7 to 1000\ifmmode^\circ\else\textdegree\fi{}K, and is also used to fit the data on isotropically pure germanium. A comparison of the analysis with that due to Callaway shows that the same results are obtained in the impurity scattering and boundary scattering regions. A discussion of the approximations used in the various analyses is included. A more complete expression for the umklapp scattering relaxation time, valid for materials with a very disperse transverse acoustic phonon spectrum, is derived in an appendix. The question of the validity of the addition of inverse relaxation times and the coupling due to normal three-phonon processes is considered in another appendix.