1 Answers
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 \tau } 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 \tau _{C}} can be written as:
The parameters τ U {\displaystyle \tau _{U}} , τ M {\displaystyle \tau _{M}} , τ B {\displaystyle \tau _{B}} , τ ph-e {\displaystyle \tau _{\text{ph-e}}} are due to Umklapp scattering, mass-difference impurity scattering, boundary scattering and phonon-electron scattering, respectively.