  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 for all possible
processes. 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 degenerate bands of the valence band. We then use
an advanced numerical Boltzmann transport equation (BTE) simulator that couples
DFT electronic structures and energy/momentum-dependent scattering rates to
compute the transport properties for electrons and holes. By incorporating
ionized impurity scattering as well, we calculate the n-type and p-type
mobility versus carrier density and make comparisons to experiments, indicating
excellent agreement. The fact that the method we present uses well-established
theoretical tools and requires the extraction of only a limited number of
matrix elements, makes it generally computationally very attractive, especially
for semiconductors with a large unit cell and lower symmetry.
