3D Biconjugate Gradient-Multi Grid Coupling Schemes for Field Equations in Semiconductor Device Simulation

A significant portion of the time required for simulating full three-dimensional (3D) charge transport in semiconductor devices using particle-based methods is spent solving the necessary field equations. Two highly effective, iterative techniques available for solving largesparse systems of equations are the conjugate gradient (CG) method and the multigrid (MG) method. In this work, variants of the CG and MG methods are self-consistently coupled to a particle-based full-band simulator and are applied to model small, 3D structures. Detailed analyses of both performance and solver robustness are presented for different algorithmic configurations. Hybrid strategies using various coupling schemes for improving overall performance behavior of the Poisson solver are also discussed.