AMaSiS 2018 Workshop: Abstracts

Poster Challenges for drift-diffusion simulations of semiconductors: A comparative study of different discretization philosophies

Patricio Farrell${}^{\mathbf{\text{(1)}}}$ and Dirk Peschka${}^{\mathbf{\text{(2)}}}$,

(1) TU Hamburg-Harburg, Institut für Mathematik

(2) Weierstrass Institute for Applied Analysis and Stochastics, Berlin

In this talk we present results of a comparative study, where we analyze and benchmark the error and the convergence order of finite difference, finite-element as well as Voronoi finite-volume discretization schemes for the drift-diffusion equations describing charge transport in bulk semiconductor devices, i.e., the van Roosbroeck system

$-\nabla \cdot (\epsilon \nabla \psi )=q(C+p-n),$

$-\nabla \cdot q{\mu }_{n}n\nabla {\phi }_n=+qR,$

$-\nabla \cdot q{\mu }_{p}p\nabla {\phi }_p=-qR.$

The relation between the quasi-Fermi levels ${\phi }_n,{\phi }_p$ and the densities $n,p$ of electrons and holes is given by the equation of state $n=N_{c}F({\eta }_n)$ and $p=N_{v}F({\eta }_p)$ where ${\eta }_n=(\psi -{\phi }_n-q{E}_c)/U_T$ and ${\eta }_p=({\phi }_p-\psi +q{E}_v)/U_T$. Three common challenges, that can corrupt the precision of numerical solutions of the van Roosbroeck system, will be discussed: boundary layers of the quasi-Fermi potentials at Ohmic contacts, discontinuties in the doping profile, and corner singularities in L-shaped domains. The influence on the order of convergence is assessed for each computational challenge and the different discretization schemes. Additionally, we provide an analysis of the inner boundary layer asymptotics near Ohmic contacts to support our observations.