Coupling between Phonon-Phonon and Phonon-Impurity Scattering: A Critical Revisit of the Spectral Matthiessen's Rule

摘要

The spectral Matthiessen's rule is commonly used to calculate the totalphonon scattering rate when multiple scattering mechanisms exist. Here wepredict the spectral phonon relaxation time $\tau$ of defective bulk siliconusing normal mode analysis based on molecular dynamics, and show that thespectral Matthiessen's rule is not accurate due to the neglect of the couplingbetween anharmonic phonon-phonon scattering $\tau_a^{-1}$ and phonon-impurityscattering $\tau_i^{-1}$. As a result, the spectral Matthiessen's ruleunderestimates the total phonon scattering rate, and hence overestimates thethermal conductivity $\kappa$ of mass-doped and Ge-doped silicon by about20-40%. We have also directly estimated this coupling scattering rate, socalled coupled five-phonon scattering $\tau_{\rm couple}^{-1}$, and achievedgood agreement between $\tau_a^{-1}+\tau_i^{-1}+\tau_{\rm couple}^{-1}$ and thetotal scattering rate $\tau_{tot}^{-1}$.