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|Title:||Quasi-Newton and Multigrid Methods for Semiconductor Device Simulation|
|Department / Program:||Computer Science|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|Abstract:||A finite difference approximation to the semiconductor device equations using the Bernoulli function approximation to the exponential function is described, and the robustness of this approximation is demonstrated. Sheikh's convergence analysis of Gummel's method and quasi-Newton methods is extended to a nonuniform mesh and the Bernoulli function discretization. It is proved that Gummel's method and the quasi-Newton methods for the scaled carrier densities and carrier densities converge locally for sufficiently smooth problems.
A new numerical method for semiconductor device simulation is also presented. The device is covered with a relatively coarse nonuniform grid, and Newton's method is applied globally over the entire grid and locally over critical rectangular grid subsets where the residual is large until a solution of moderate accuracy is obtained. Rectangular subgrids of the critical subgrids are then refined by mesh-halving into coextensive sets of grids, and an accurate solution is obtained on the finest subgrids by applying the multigrid method directly to the corresponding sets of nonlinear difference equations. The method is fast because the Newton iteration is applied mainly to small critical regions of the device and the multigrid method significantly reduces the time required to obtain an accurate solution on the finest grids in these regions. The method is applied to a short-channel MOSFET and is shown to compare favorably with conventional methods.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984.
|Date Available in IDEALS:||2014-12-15|