A Robust Algorithm for Microscopic Simulation of Avalanche Breakdown in Semiconductor Devices

Avalanche breakdown can occur during switching of power devices and is difficult to simulate due to its abrupt onset and strong nonlinear behavior. In addition, it severely degrades the numerical robustness of deterministic solvers for the Boltzmann equation (BE), on which the transport simulations are based. A continuation method is therefore introduced, with which robust and efficient simulation of avalanche breakdown is possible. To this end, the generation rate of the secondary electron/hole pairs due to impact ionization is multiplied with a parameter alpha. Due to this new degree of freedom in the transport equation, voltage as well as current can be specified simultaneously. The final solution is obtained by modifying the voltage or current in such a way that this parameter alpha becomes one. This approach stabilizes the simulation, improves the numerical robustness of the discrete BE, and avoids divergent solutions. Furthermore, efficient frozen-field simulations of avalanche breakdown become possible. The results are presented for a 1-D p-n junction and a 2-D vertical power MOSFET.