Deterministic modeling of impact ionization with a random-k approximation and the multiband Boltzmann equation

We present here an approach for determining impact ionization coefficients for the spherical multiband model in silicon. Using random-k approximation, the impact ionization rate is determined to reflect the multiband density of states in silicon. To account for the actual density of states, we have solved four coupled Boltzmann transport equations by combining a generalized Legendre polynomial expansion method with numerical techniques using finite differences and sparse matrices. Calculated values for the impact ionization coefficients agree with experiments for electrons in silicon, while being obtained in significantly less CPU time than required by analogous Monte Carlo calculations. Different multiband transport parameter sets are also compared.