Impact Ionization in $\beta-Ga_2O_3$

A theoretical investigation of extremely high field transport in an emerging wide-bandgap material $\beta-Ga_2O_3$ is reported from first principles. The signature high-field effect explored here is impact ionization. Interaction between a valence-band electron and an excited electron is computed from the matrix elements of a screened Coulomb operator. Maximally localized Wannier functions (MLWF) are utilized in computing the impact ionization rates. A full-band Monte Carlo (FBMC) simulation is carried out incorporating the impact ionization rates, and electron-phonon scattering rates. This work brings out valuable insights on the impact ionization coefficient (IIC) of electrons in $\beta-Ga_2O_3$. The isolation of the $\Gamma$ point conduction band minimum by a significantly high energy from other satellite band pockets play a vital role in determining ionization co-efficients. IICs are calculated for electric fields ranging up to 8 MV/cm for different crystal directions. A Chynoweth fitting of the computed IICs is done to calibrate ionization models in device simulators.