Model Of Hole-Initiated Impact-Ionization Rate In Alpha-Quartz For A Full Band Monte Carlo Simulation

The hole-initiated impact-ionization rate in alpha-quartz was investigated using both an energy band structure and the corresponding pseudowave functions, which are derived from a self-consistent nonlocal pseudopotential method. The ionization probability is calculated formally from Fermi's golden rule in a straightforward way. The matrix elements for the ionization transition were evaluated from the band structure and the corresponding pseudowave functions. The matrix elements include both direct and the exchange terms with umklapp terms associated with the periodic part of the Bloch function. The hole-initiated impact-ionization rate is discussed with emphasis on both the anisotropy (wave-vector dependence of the primary hole) associated with the band structure and the contribution of the umklapp process to the impact-ionization rate. In contrast to the Keldysh formula, which has a power exponent of 2, the computed impact-ionization rates are fitted to an analytical formula that has a power exponent of 6.7, which originates from the complexity of the alpha-quartz band structure. We have found that primary holes that exist in the eighth and ninth valence bands labeled from the lowest valence band in ascending order especially contribute to the subthreshold region of ionization. In addition, we show the average energies of the secondary holes and electrons generated at the moment of transition as a function of the initial hole energy. (C) 2003 American Institute of Physics.