Adaptive Local Mesh Refinement for Steady State and Transient Simulation of Semiconductor Devices

We propose an adaptive non-conforming mesh refinement technique for two dimensional semiconductor device simulation on triangular meshes to increase the numerical accuracy in regions of interest. To capture the solution with large gradient in thin layers, three physics-based cell refinement indicators are proposed to effectively locate critical areas around junctions, electrodes and the boundaries of space charge regions respectively. The local conservation property of finite volume Scharfetter-Gummel scheme is preserved after refinement by proper control volume discretization and interpolation rule even with hanging nodes. Steady state and transient simulation results showed that the meshes are properly refined and the numerical error is reduced.