Role of Three-Phonon Normal Processes in the Phonon Conductivity of an Insulator

Abstract

In the present work the role of three-phonon normal processes is studied in the framework of Callaway’s theory of Phonon conductivity of an insulator under the conditions τ_N⁻¹>τ_R⁻¹, τ_N⁻¹<τ_R⁻¹ and τ_N⁻¹<<τ_R⁻¹ where τ_R⁻¹=τ_B⁻¹+τ_pt⁻¹+τ_U⁻¹. Use also made of a parameter ‘a’, which is a measure of the relative strengths of normal and Umklapp processes and is equal to τ_N⁻¹⁄τ_U⁻¹ in Callaway’s model. It is shown that for τ_N⁻¹<<τ_R⁻¹ and ‘a’ approaching 10⁻³ Callaway’s model gives good description of phonon conductivity of Ge in the temperature range 2 to 100 K. For τ_N⁻¹>>τ_R⁻¹ Callaway’s theory gives not only the smaller values of phonon conductivity but also leads to wrong temperature dependence in the range 20–100 K.