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/${\displaystyle \tau }$ 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 ${\displaystyle \tau _{C}}$ can be written as:

${\displaystyle {\frac {1}{\tau _{C}}}={\frac {1}{\tau _{U}}}+{\frac {1}{\tau _{M}}}+{\frac {1}{\tau _{B}}}+{\frac {1}{\tau _{\text{ph-e}}}}}$

The parameters ${\displaystyle \tau _{U}}$, ${\displaystyle \tau _{M}}$, ${\displaystyle \tau _{B}}$, ${\displaystyle \tau _{\text{ph-e}}}$ are due to Umklapp scattering, mass-difference impurity scattering, boundary scattering and phonon-electron scattering, respectively.