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Design and implementation of a three-dimensional general purpose semiconductor device simulator


Gernot Heiser

    School of Computer Science and Engineering
    Sydney 2052, Australia


Since the early work by Gummel in the 1960s, numerical simulation of semiconductor devices has developed into an indispensable tool for device engineers. So far, most device simulations have been one or two dimensional. With continuously shrinking device features truly three-dimensional (3d) treatment of the semiconductor becomes necessary.

A few 3d device simulation programs exist since the early 1980s, but their applicability is limited by the fact that they cannot simulate really general device geometries. They all use grids that are tensor-products of one- and two-dimensional meshes, which leaves little flexibility in modelling the third dimension.

This thesis describes the design and implementation of Second, a general-purpose, 3d semiconductor device simulator. Second solves the traditional drift-diffusion equations of the semiconductor. The partial differential equations are discretized with the box method on a general 3d mesh consisting of a mixture of tetrahedra, quadrilateral pyramids, triangular prisms, and parallel epipeds. The one dimensional Scharfetter-Gummel scheme is used for integrating the current relations along grid edges. Decoupled (Gummel) and coupled (Newton) methods are implementeded for linearizing the discrete equations. Iterative methods (preconditioned conjugate-gradient type algorithms) are used for the solution of the linear systems. A time discretization with automatic time step control, based on an estimate of the local truncation error, is used for transient simulations. Physical models implemented include doping and field dependent carrier mobilities, surface scattering, band gap narrowing, and generation and recombination models with doping dependent carrier life times.

The flexibility of Second is demonstrated on a few case studies. One is an investigation of parasitic MOSFETs in a trench isolated sub-micron n-MOS device. This study demonstrates how design rules may be drawn up based on the results of 3d device simulations. A second example investigates latchup in CMOS devices and contains a comparison between two- and three-dimensional simulation results. A third case is a study of the switching behaviour of a bipolar transistor.

BibTeX Entry

    author           = {Gernot Heiser},
    note             = {Diss.\ ETH No.\ 9382. Published by Hartung Gorre Verlag, Konstanz, Germany, Series in
                        Microelectronics, vol 13, ISBN 3-89191-440-7},
    paperUrl         = {},
    school           = {ETH Z{\"u}rich},
    title            = {Design and Implementation of a Three-Dimensional General Purpose Semiconductor Device Simulator},
    year             = {1991}