Hexahedron-Based Control Volume Finite Element Method for Fully Coupled Nonlinear Drift-Diffusion Transport Equations in Semiconductor Devices

Abstract

We present a new stabilized 3-D control volume finite element method (FEM) for massively parallel simulation of drift-diffusion transport in semiconductor devices. This new solver employs unstructured hexahedral elements, thus leading to a very efficient scheme; both Poisson and current continuity equations are discretized with control volume FEM, and thus, the accuracy and stability are improved. Furthermore, a fully coupled Newton’s method is applied to solve these nonlinear equations, thus remarkably increasing the numerical stability. Then, we apply this new solver to simulate diode, MOSFET, and multifinger MOSFET devices. Numerical results indicate that the hexahedron-based method requires fewer iterative numbers, and its computing speed is 3.44–4.61 times faster than the tetrahedron-based counterpart. Moreover, our fully coupled Newton’s method permits constant iterative numbers, showing strong numerical stability even when the drain voltage is 160 V.