Decoupled and Iterative Method for Numerical solution of Three-Dimensional Density-Gradient Model in Semiconductor Devices Simulation
by
Shih-Ching Lo
National Center for High-Performance Computing
Coauthors: Yiming Li

Numerical solution of a set of semiconductor partial differential equations (PDEs) has been of great interest in these years. Nowadays, the dimension of semiconductor devices, such as MOSFETs is in the regime of nanometer. Quantum mechanical confinement effect becomes an important factor in numerical simulation of semiconductor devices. Among approaches, density-gradient (DG) approach has successfully been proposed to account for the effect of quantum mechanical confinement. A set of DG model involves the Poisson equation, the electron current continuity equation, and the electron quantum corrected density equation to be solved for a specified device domain. With the continuous decrease of device dimensions, one- and two-dimensional simulations are not accurate enough to describe and explore the physical transportation phenomena for electrons and holes in a semiconductor device.

In this work, we iteratively solve the 3D DG model for a given nanoscale semiconductor device, where several physical quantities and convergence properties are discussed. The solution procedure is described briefly as follows. (1) the stop criteria, mesh, output variables and simulated devices are chosen, (2) solving the Poisson equation with density-gradient correction modified potential iteratively, (3) after the Poisson equation is convergent, continuity equations are solved, (4) then, we’ll check the whole system converges or not, (5) and if the whole system converges, then stop computing, otherwise, the Poisson equation and continuity equations should be solved again until the whole system equations converge. All decoupled PDEs to be solved are approximated with the finite element method over 3D domain. This scheme makes sure the solution will be self-consistent. By calculating several essential characteristics of devices, such as the threshold voltage (VTH) and the drain current (ID), the device physical quantities are compared with the results of 1D and 2D simulations by varying channel lengths. Also, the convergence behavior in the inner and outer iteration loops is discussed among 1D, 2D, and 3D simulations.

Date received: February 16, 2005

Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # capm-31.