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A two-dimensional finite element analysis of the stationary semiconductor device equations Chavez, Patrick Pablo


The ability to model the steady-state field inside active structures, such as a transistor, is an important aspect of monolithic microwave integrated circuit (MMIC) design. This paper focuses on such an active zone of semiconductor material, and presents a finite element analysis of the classical semiconductor equations. The semiconductor equations are very nonlinear and govern the potential and carrier density distributions in semiconductor materials. A previously developed finite element method (FEM) formulation of these equations, referred to as the current conservation model, is re-introduced and re-derived with compact matrix notation. It is shown how this formulation can be solved with the Newton-Raphson iterative scheme. Then, a newly developed FEM formulation, referred to as the advection-diffusion model, of the continuity equations is described in detail. It is shown by example how this formulation solved with Gummel's iterative technique is very numerically robust. These two different solution methods of the steady-state system of coupled Poisson and continuity equations are combined into a final solution algorithm that exploits their strengths. As a specific example, GaAs MESFETs are the focus of implementation, and the resulting potential field and carrier density distributions are used, to calculate various MESFET parameters such as electrode currents, voltage gain, capacitances, and conductances. Finally, various extensions to the FEM approach involving the application of the method of moments (MoM) are briefly discussed and partially demonstrated. These extensions are intended to compensate for the assumptions and simplifications, mainly with respect to the artificial boundary conditions, used in the original stand-alone FEM formulations.

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