Quantifying doping-dependent electron-phonon scattering rates in silicon by inelastic x-ray scattering and first-principles lattice dynamics

A quantitative understanding of the electron-phonon interaction is important, particularly for the thermal management of electronic devices, which are built mostly on doped silicon. Here, we performed inelastic x-ray scattering measurements on electron-doped and hole-doped bulk silicon crystals along $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}X$ and directly quantified the mode- and momentum-dependent electron-phonon scattering rates of the optical phonon modes. We found the electron-phonon interaction as has been indicated; in electron-doped silicon, phonon scattering by this interaction occurs around 0.3 $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}X$ for the longitudinal phonon mode, supporting the $g$-type intervalley scattering. In hole-doped silicon, a nonzero scattering rate is observed only in the vicinity of the zone center. The experimental results quantitatively agree with the calculations, which also explain the experimental results of the thermal conductivity.