3D Finite Element Modeling of Current Densities in Semiconductor Transport with Impact Ionization

TL;DR

This paper introduces two innovative 3D finite element models for simulating current densities in semiconductor devices, demonstrating improved accuracy and stability, especially in impact ionization scenarios.

Contribution

The paper presents two novel 3D finite element methods for drift-diffusion current densities, extending classic formulas and comparing their performance in semiconductor device simulations.

Findings

Method A outperforms in accuracy and stability.

Method A accurately simulates I-V characteristics up to breakdown.

Models effectively incorporate impact ionization in 3D simulations.

Abstract

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.