Analysis of Lattice Thermal Conductivity

Abstract

An analysis of thermal conductivity is presented which divers 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 6t to the data on silicon from 1.7 to 1300'K and on germanium from 1.7 to 1000'K, and is also used to 6t 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.

Thermal transport in phononic crystals and the observation of coherent phonon scattering at room temperature

“…impurity;j ¼ Do 4 j ðqÞ and t À 1 boundary;j ¼ Ev j ðqÞ=L, respectively, where L is the effective sample length and is a measure of the average distance between boundaries 7,19,21,22 . The constants B, C, D and E measure the fractional influence of these different types of scattering mechanisms in a given sample, and are determined by fitting equation (1) to measured bulk Si data.…”

“…However, the choice of L ¼ L c treats all of the samples identically and is insensitive to the increase in the number of boundaries with the supercell order n. Thus, we also consider an alternate model for deducing an order-dependent sample size L. Noting that phonon scattering events by the inplane air hole boundaries and the cross-plane sample surface boundaries are stochastic rather than mutually exclusive, a Matthiessen's rule-type approach can be used to separate their influence as 1/t boundary,j ¼ 1/t cross-plane,j þ 1/t in-plane,j , with t cross-plane,j ¼ t/v j (q). The in-plane component can be evaluated using an order-dependent effective sample size L n , obtained by geometrically averaging over the relative in-plane boundary separations in a given sample 19 with t in-plane,j ¼ L n /v j (q) (Supplementary Note 2). Alternately, each PnC sample can be viewed as a combination of n(n-1) SC unit cells and n 1 Â 1 unit cells.…”

Ab initioand molecular dynamics predictions for electron and phonon transport in bismuth telluride

“…One is the continuum transport theory ͑or kinetic theory͒, such as BTE, 11,12 which is suitable for fast calculations of large systems. However, this normally needs some parameter input from experiments or other predictions; therefore, its application is limited.…”

Ab initiothermal transport in compound semiconductors

“…Until recent years, full microscopic descriptions of this scattering have been unavailable, and many theories of κ L resorted to simple models involving a number of ad hoc approximations. Among them, the Debye approximation for phonon dispersions was often used, neglecting dispersion in the acoustic branches and ignoring optic phonons altogether, and mode averaged Gruneisen constants were often used to estimate the intrinsic phonon scattering rates [1][2][3][4][5]. Such approximations are of questionable validity, and because such models are typically fit to experimental data, they lack predictive power.…”