Quasi-Fermi-Based Charge Transport Scheme for Device Simulation in Cryogenic, Wide Bandgap, and High-Voltage Applications

Abstract

We present a novel approach to solving the transport problem in semiconductors. We reformulate the drift-diffusion (DD) equations in terms of the quasi-Fermi-energies as solution variables; a drastic increase in numerical stability is achieved, which permits the simulation of devices at cryogenic temperatures as well as wide bandgap devices using double precision arithmetic, instead of extended precision arithmetic which would otherwise be required to solve these applications using regular DD.

Multi-scale simulations of two dimensional material based devices: the NanoTCAD ViDES suite

“… ). In NanoTCAD ViDES the current density, J , is defined using the quasi-Fermi level approach [ 29 ], which has been demonstrated to be numerically more stable and accurate than charge-based implementations [ 30 ]: where and are position-dependent anisotropic electron and hole mobility, n and p are the carrier densities of electrons and holes respectively, and and are the spatial-dependent quasi-Fermi levels. The carrier densities are determined by the specific Fermi-Dirac integral, which depends on the channel material dispersion relationship and the dimension (1D, 2D, 3D) of the channel region of the device under study.…”

“…∇J = 0 ). In NanoTCAD ViDES the current density, J, is defined using the quasi-Fermi level approach [29], which has been demonstrated to be numerically more stable and accurate than charge-based implementations [30]:…”