3D finite element modeling and simulation of industrial semiconductor devices including impact ionization

Abstract

In this article we address the numerical study of 3D semiconductor devices for applications in electronics industry including charge generation phenomena due to impact ionization. With this aim, we propose two novel 3D finite element (FE) models (methods 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. Method A is a Galerkin FE approximation of the density current (written in generalized ohmic form) where the harmonic average of the electrical conductivity is used instead of the standard average while method B is a genuine 3D extension of the classic 1D Scharfetter-Gummel difference formula interpreted as a stabilized Galerkin FE approximation with the use of an ‘optimal’ artificial diffusion. 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 outperforms method B in 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 impact ionization. Results demonstrate that the model is able to accurately compute the I-V characteristic of the device until drain-to-bulk junction breakdown.