3D Finite Element Modeling of Current Densities in Semiconductor Transport with Impact Ionization
This work provides a 3D extension of the classic 1D Scharfetter-Gummel method for semiconductor device simulation, addressing a known bottleneck in modeling current densities in 3D.
The paper proposes two novel 3D finite element models for electron and hole drift-diffusion current densities, with method A showing best performance in physical accuracy and numerical stability, and accurately computing I-V characteristics until drain-to-bulk junction breakdown in a 3D n-MOS transistor simulation including impact ionization.
In this article we propose two novel 3D finite element models, denoted method A and B, for electron and hole Drift-Diffusion (DD) current densities. Method A is based on a primal-mixed formulation of the DD model as a function of the quasi-Fermi potential gradient, while method B is a modification of the standard DD formula based on the introduction of an artificial diffusion matrix. Both methods are genuine 3D extensions of the classic 1D Scharfetter-Gummel difference formula. The proposed methods are compared in the 3D simulation of a p-n junction diode and of a p-MOS transistor in the on-state regime. Results show that method A provides the best performance in terms of physical accuracy and numerical stability. Method A is then used in the 3D simulation of a n-MOS transistor in the off-state regime including the impact ionization generation mechanism. Results demonstrate that the model is able to accurately compute the I-V characteristic of the device until drain-to-bulk junction breakdown.