Parallel Multigrid Methods for the Continuity Equations in Semiconductor Device Simulation
نویسندگان
چکیده
Here n, p denote the electron, hole density, respectively Jn, Jp the electron, hole current, μ the related mobilities, R the recombination/generation. The Poisson equation relates the electrostatic potential u to the total charge density (D is the net doping concentration, ε is the dielectric permittivity). Contact models result in different boundary conditions. For existence and uniqueness (close to equilibrium only) of weak solutions see [3], [6], for instance. Introducing the variables e−v, e(n = e−v) yields
منابع مشابه
Semiconductor Device Simulation by a New Method of Solving Poisson, Laplace and Schrodinger Equations (RESEARCH NOTE)
In this paper, we have extended and completed our previous work, that was introducing a new method for finite differentiation. We show the applicability of the method for solving a wide variety of equations such as Poisson, Lap lace and Schrodinger. These equations are fundamental to the most semiconductor device simulators. In a section, we solve the Shordinger equation by this method in sever...
متن کامل3D Biconjugate Gradient-Multi Grid Coupling Schemes for Field Equations in Semiconductor Device Simulation
A significant portion of the time required for simulating full three-dimensional (3D) charge transport in semiconductor devices using particle-based methods is spent solving the necessary field equations. Two highly effective, iterative techniques available for solving largesparse systems of equations are the conjugate gradient (CG) method and the multigrid (MG) method. In this work, variants o...
متن کاملFinite Element Simulation of Semiconductor Devices on Multiprocessor Computers
{ In this work we describe a methodology for solving the basic set of state stationary semiconductor device equations. We present a new iterative method for the solution using nite elements of the non linear Poisson equation and use a Conjugate Gradient type method for solving the non symmetric continuity equations. The parallelization of this approach and its projection onto a multiprocessor s...
متن کاملBehavioral Modeling and Simulation of Semiconductor Devices and Circuits Using VHDL-AMS
During the past few years, a lot of work has been done on behavioral models and simulation tools. But a need for modeling strategy still remains. The VHDL-AMS language supports the description of analog electronic circuits using Ordinary Differential Algebraic Equations (ODAEs), in addition to its support for describing discrete-event systems. For VHDL-AMS to be useful to the analog design ...
متن کاملA Multigrid Preconditioner for the Semiconductor Equations
A multigrid preconditioned conjugate gradient algorithm is introduced into a semiconductor device modeling code DANCIR This code simulates a wide variety of semiconductor devices by numerically solving the drift di usion equations The most time consuming aspect of the simulation is the solution of three linear systems within each iteration of the Gummel method The original version of DANCIR use...
متن کامل