Deformation potentials for band-to-band tunneling in silicon and germanium from first principles

The deformation potentials for phonon-assisted band-to-band tunneling (BTBT) in silicon and germanium are calculated using a plane-wave density functional theory code. Using hybrid functionals, we obtain: DTA = 4.1 × 108 eV/cm, DTO = 1.2 × 109 eV/cm, and DLO = 2.2 × 109 eV/cm for BTBT in silicon and DTA = 7.8 × 108 eV/cm and DLO = 1.3 × 109 eV/cm for BTBT in germanium. These values agree with experimentally measured values and we explain why in diodes, the TA/TO phonon-assisted BTBT dominates over LO phonon-assisted BTBT despite the larger deformation potential for the latter. We also explain why LO phonon-assisted BTBT can nevertheless dominate in many practical applications.