Landauer vs. Boltzmann and Full Dispersion vs. Debye Model Evaluation of Lattice Thermal Conductivity

TL;DR

This paper compares full phonon dispersion and simplified models in calculating lattice thermal conductivity of Si and Bi2Te3, introducing a method to extract meaningful phonon mean-free-paths and Debye temperatures.

Contribution

It presents a new approach to extract physically meaningful phonon mean-free-paths and Debye temperatures from thermal conductivity data using full dispersion models.

Findings

Full dispersion approach yields different mean-free-paths than simple estimates.

Two distinct Debye temperatures are necessary for specific heat and thermal conductivity.

The method provides insights into phonon transport properties and model limitations.

Abstract

Using a full dispersion description of phonons, the thermal conductivities of bulk Si and Bi2Te3 are evaluated using a Landauer approach and related to the conventional approach based on the Boltzmann transport equation. A procedure to extract a well-defined average phonon mean-free-path from the measured thermal conductivity and given phonon-dispersion is presented. The extracted mean-free-path has strong physical significance and differs greatly from simple estimates. The use of simplified dispersion models for phonons is discussed, and it is shown that two different Debye temperatures must be used to treat the specific heat and thermal conductivity (analogous to the two different effective masses needed to describe the electron density and conductivity). A simple technique to extract these two Debye temperatures is presented and the limitations of the method are discussed.