First-principles calculation of phonon-limited mobility in silicon

We introduce a new first-principles method to calculate phonon-scattering-limited electron mobilities. The lifetime of a Bloch state due to scattering is represented by an imaginary electron self-energy which is extracted from the complex band structure of a supercell that contains the phonon vibrations within the frozen-phonon approximation. The phonon vibrations are modeled by a set of configurations generated from a Monte Carlo simulation. Mobility contributions are dominated by electrons on the transverse ellipsoids with low effective mass and long lifetime. The results indicate that high-mobility channels form a conduction network above the percolation threshold. As a result the Matthiessen's rule does not hold for phonon scattering. The overall mobility is evaluated through the configurational average of the percolation-dominant resistor network. The calculated electron mobility agrees with available experimental data.