  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.
