**Coupling between phonon-phonon and phonon-impurity scattering: A
critical revisit of the spectral Matthiessen's rule**

TL Feng and B Qiu and XL Ruan, PHYSICAL REVIEW B, 92, 235206 (2015).

DOI: 10.1103/PhysRevB.92.235206

The spectral Matthiessen's rule is commonly used to calculate the total phonon scattering rate when multiple scattering mechanisms exist. Here we predict the spectral phonon relaxation time tau of defective bulk silicon using normal mode analysis based on molecular dynamics and show that the spectral Matthiessen's rule is not accurate due to the neglect of the coupling between anharmonic phonon-phonon scattering tau(-1)(a) a and phonon-impurity scattering tau(-1)(i) . As a result, the spectral Matthiessen's rule underestimates the total phonon scattering rate and hence overestimates the thermal conductivity kappa of mass-doped and Ge- doped silicon by about 20-40%. We have also directly estimated this coupling scattering rate, so-called coupled five-phonon scattering tau(couple)-(1) couple, and achieved good agreement between tau(-1)(a) + tau(-1)(i) + tau(-1)(couple) couple and the total scattering rate tau(-1)(tot).

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