We develop numerical solution schemes for semiconductor device models based on mapped discretization strategies and curvilinear, nonuniform grids. Such grids typically arise in adaptive ...redistribution schemes, and they offer several advantages when gridding irregular domain shapes or resolving complex solution profiles. We consider the hydrodynamic class of equations as a representative model for carrier transport. A mathematical transformation of variables is used to map the device equations from the physical coordinate system to a reference system in which the numerical discretization is performed. We develop a Scharfetter–Gummel type of discretization, formulated in the mapped reference domain, for the current density and energy flux terms in the transport model. The solution of the mapped discrete system is carried out in a fully-coupled, implicit form, and nonsymmetric gradient-type iterative strategies are used for solving the algebraic systems. Numerical results demonstrating the performance of the scheme with and without mesh adaptation are presented for test problems.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Efficient numerical simulation techniques based on iterative and multigrid concepts are developed for solving coupled, nonlinear, reaction-diffusion systems. The solution approach is developed in a ...general setting and then applied to specific reaction-diffusion systems that give rise to complex dynamical patterns. The numerical strategy is based on semidiscretizing the coupled equations using a finite-difference formulation, with time integration of the resulting system of ordinary differential equations. Iterative and multigrid strategies are used to improve integration efficiency and to accelerate convergence. Numerical experiments are carried out to demonstrate the performance of the methods.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
In this study, we consider a mathematical model and numerical treatment for the aggregate alkali reaction in fluid leaching processes. This subject is of special interest in analysis of concrete dams ...in civil engineering and the numerical investigations carried out here are directed towards a better understanding of the model and process in this context. Of particular interest are effects of surface imperfection on the subsequent coupled moisture transport and the reactive formation of gel in the granular porous medium. The numerical experiments also consider the influence of periodic and nonperiodic inhomogeneities in material diffusivity properties.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Rapid prototyping tools that combine powerful numerics with a flexible applications interface can play a significant role in micro-scale modeling and simulation. We demonstrate this idea using the ...PROPHET simulator. In the first part of the investigations we extend the simulator's capability to allow analysis of carrier transport in deep submicron MOSFETs using a hydrodynamic model. The model is numerically implemented within PROPHET's dial-an-operator framework by adding certain "flux'' routines. Once implemented, the model becomes available for use in any number of spatial dimensions. We present results for MOSFET type test problems in one and two dimensions. The second application area that we explore here using the same simulator is micro-thermal analysis. The implementation of the thermal equation in PROPHET is demonstrated and results are presented for a test problem in three dimensions.
An efficient numerical solution scheme based on a new mapped finite difference discretization and iterative strategies is developed for submicron semiconductor devices. As a representative model we ...consider a nonparabolic hydrodynamic system. The discretization is formulated in a mapped reference domain, and incorporates a transformed Scharfetter-Gummel treatment for the current density and energy flux. This permits the use of graded, nonuniform curvilinear grids in the physical domain of interest, which has advantages when gridding irregular domain shapes or grading meshes for steep solution profiles. The solution of the discrete system is carried out in a fully coupled, implicit form, and nonsymmetric gradient-type iterative strategies are investigated. Numerical results demonstrating the performance and reliability of the scheme are presented for test problems.
A mathematical framework has been developed for numerical analysis and simulation of applications in superconducting microelectronics. The approach is similar to those used successfully in ...semiconductor modeling. Here we investigate semidiscrete simulation of the time dependent Ginzburg-Landau equations. Several interesting numerical and modeling issues regarding the structure of the solutions and their sensitivity to the data and mesh resolution are described using results from a representative problem.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
We investigate numerical integration, preconditioning, iterative solution and multigrid strategies for a class of réaction-diffusion systems used for modeling nonequilibrium phosphorus diffusion in ...silicon. These problems typically yield stiff systems of equations, and their efficient numerical simulation requires the use of stable integration strategies along with fast, robust algebraic system solvers. We compare the numerical performance of semi-implicit Runge-Kutta methods in conjunction with several standard nonsymmetric iterative solvers and multigrid methods. Our results demonstrate that block-diagonal preconditioning with node-based assembly of the discrete system dramatically improves the performance of iterative solvers. Numerical studies also reveal some interesting new aspects regarding the choice of integration schemes when using iterative methods to solve the linear systems. Unlike the case of direct solvers, where higher-order integration methods typically yield higher computational efficiency, the use of iterative solvers can significantly change or even reverse this trend.
Special numerical techniques for the efficient and accurate solution of fluid flow and certain other transport processes are investigated. These include adaptive redistribution and optimization of ...computational grids, multigrid techniques for convection-diffusion problems, and multigrid time-marching methods for non-stationary and nonlinear problems. The grid optimization strategy is based on constructing and minimizing a mathematical objective function which defines the desired grid properties. For convection-diffusion problems, it is demonstrated that standard multigrid techniques fail when the coarse grids violate mesh-size restrictions. A variety of alternate multigrid strategies are explored, including artificial dissipation, fine grid pre-elimination, self-adjoint formulation, defect correction, and combination with grid redistribution. Multilevel techniques are also developed for time-dependent problems, including evolution problems with non-steady or transient solutions, and steady-state problems solved with artificial time-marching. Both explicit and implicit integration schemes are investigated, and it is shown that significant performance improvements can be gained with the use of multigrid. These techniques are implemented and tested on representative model problems as well as practical applications of current research interest. The grid investigations involve optimization in model problems, and in large-scale 3-D aircraft wing-body configurations. The multigrid applications range from model convection-diffusion problems, to time-dependent problems, to coupled nonlinear problems in two major application areas. The first application involves simulating spatio-temporal patterns in a coupled, nonlinear, reaction-diffusion problem that models the behavior of the Belousov-Zhabotinskii reaction. This multi-species reaction, which exhibits intricate patterns in laboratory experiments, has attracted considerable interest in the field of nonlinear dynamics. The numerical simulation of this problem is carried out using the above multigrid strategies, and it is shown that considerable speedup can be achieved. The other main application involves the simulation of sub-micron semiconductor devices using a new hydrodynamic transport model. This is a very complex application, and many of its modeling and simulation aspects remain a subject of ongoing research. The present work has yielded preliminary results, including significant performance gains for a representative MOSFET structure in 1-D. The software for these applications is optimized to yield high performance on vector supercomputers such as the Cray Y-MP. This is demonstrated, in particular, for the applications involving time-stepping, where computational efficiency is of crucial importance.
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