Phonon scattering

Phonons can scatter through several mechanisms as they travel through the material. These scattering mechanisms are: Umklapp phonon-phonon scattering, phonon-impurity scattering, phonon-electron scattering, and phonon-boundary scattering. Each scattering mechanism can be characterised by a relaxation rate 1/ τ {displaystyle au } which is the inverse of the corresponding relaxation time. Phonons can scatter through several mechanisms as they travel through the material. These scattering mechanisms are: Umklapp phonon-phonon scattering, phonon-impurity scattering, phonon-electron scattering, and phonon-boundary scattering. Each scattering mechanism can be characterised by a relaxation rate 1/ τ {displaystyle au } which is the inverse of the corresponding relaxation time. All scattering processes can be taken into account using Matthiessen's rule. Then the combined relaxation time τ C {displaystyle au _{C}} can be written as: The parameters τ U {displaystyle au _{U}} , τ M {displaystyle au _{M}} , τ B {displaystyle au _{B}} , τ ph-e {displaystyle au _{ ext{ph-e}}} are due to Umklapp scattering, mass-difference impurity scattering, boundary scattering and phonon-electron scattering, respectively. For phonon-phonon scattering, effects by normal processes (processes which conserve the phonon wave vector - N processes) are ignored in favor of Umklapp processes (U processes). Since normal processes vary linearly with ω {displaystyle omega } and umklapp processes vary with ω 2 {displaystyle omega ^{2}} , Umklapp scattering dominates at high frequency. τ U {displaystyle au _{U}} is given by: where γ {displaystyle gamma } is the Gruneisen anharmonicity parameter, μ is the shear modulus, V0 is the volume per atom and ω D {displaystyle omega _{D}} is the Debye frequency. For many decades, thermal transport in non-metal solids was considered to be governed by the three-phonon scattering process, and the role of four-phonon and higher-order scattering processes was believed to be negligible. Recent study has shown that the four-phonon scattering can be important for nearly all materials at high temperature, and for certain materials even at room temperature. The predicted significance of four-phonon scattering in boron arsenide was confirmed by experiments.