  We present a first-principles framework to extract deformation potentials in
Silicon based on density-functional theory (DFT) and density-functional
perturbation theory (DFPT). We compute the electronic band structures, phonon
dispersion relations, and electron-phonon matrix elements to extract
deformation potentials for acoustic and optical phonons. The matrix elements
clearly show the separation between intra- and inter-valley scattering in the
conduction band, and quantify the strength of the scattering events in the
heavy, light, and spit-off bands of the valence band.
