TY - JOUR
T1 - A Positivity-Preserving Finite Element Method for Quantum Drift-Diffusion Model
AU - Mu , Pengcong
AU - Zheng , Weiying
JO - Journal of Computational Mathematics
VL - 5
SP - 909
EP - 932
PY - 2023
DA - 2023/05
SN - 41
DO - http://doi.org/10.4208/jcm.2206-m2021-0353
UR - https://global-sci.org/intro/article_detail/jcm/21679.html
KW - Quantum drift-diffusion model, Positivity-preserving finite element method, Newton method, FinFET device, High bias voltage.
AB - <p style="text-align: justify;">In this paper, we propose a positivity-preserving finite element method for solving the
three-dimensional quantum drift-diffusion model. The model consists of five nonlinear
elliptic equations, and two of them describe quantum corrections for quasi-Fermi levels.
We propose an interpolated-exponential finite element (IEFE) method for solving the two
quantum-correction equations. The IEFE method always yields positive carrier densities
and preserves the positivity of second-order differential operators in the Newton linearization of quantum-correction equations. Moreover, we solve the two continuity equations
with the edge-averaged finite element (EAFE) method to reduce numerical oscillations of
quasi-Fermi levels. The Poisson equation of electrical potential is solved with standard
Lagrangian finite elements. We prove the existence of solution to the nonlinear discrete
problem by using a fixed-point iteration and solving the minimum problem of a new discrete functional. A Newton method is proposed to solve the nonlinear discrete problem.
Numerical experiments for a three-dimensional nano-scale FinFET device show that the
Newton method is robust for source-to-gate bias voltages up to 9V and source-to-drain
bias voltages up to 10V.</p>