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: D(TA) = 4.1 x 10⁸ eV/cm, D(TO) = 1.2 x 10⁹ eV/cm, and D(LO) = 2.2 x 10⁹ eV/cm for BTBT in silicon and D(TA) = 7.8 x 10⁸ eV/cm and D(LO) = 1.3 x 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.