New approaches in a 3-D one-carrier device solver

Wu, Kechih; Lucas, Robert F.; Wang, Z.-Y.; Dutton, R.W.

doi:10.1109/43.24881

Cited by 16 publications

(7 citation statements)

References 9 publications

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“…The carrier variables are generally preferred to the Slotboom variables since they have better numerical behavior. However, one can now go a step further and look for maps similar to (4.28) defining variables with an even better numerical behavior; for details, see [15].…”

Section: Existence and Computation Of Solutionsmentioning

confidence: 98%

“…The second approach uses the Newton or coupled algorithm and solves at each step of an iterative Newton-Raphson algorithm the three linearized PDEs of (1.1) simultaneously. For a discussion of when the coupled or the uncoupled algorithm is preferred, we refer to [15]. Since the uncoupled algorithm can be viewed as a special case of the coupled algorithm, where the off-diagonal field blocks of the Jacobi matrix are set to zero, we present the coupled solution algorithm for the carrier variables here without considering boundary conditions.…”

Section: Existence and Computation Of Solutionsmentioning

confidence: 99%

“…The drawback with this approach is that when we couple together the solutions of the Poisson and current continuity equations we get an unstable system of equations which tends to oscillate, and it is unusable for most practical applications. The solution to this problem is simple and classical [1,5,15] and consists in using a pointwise mapping between the Slotboom and carrier variables. We suppose a constant intrinsic density n I and define (4.28) with the diagonal matrix D( w) defined by D( w) ij = δ ij w i .…”

Section: Existence and Computation Of Solutionsmentioning

confidence: 99%

See 2 more Smart Citations

A 3D Rectangular Mixed Finite Element Method to Solve the Stationary Semiconductor Equations

Sartoris¹

1998

SIAM J. Sci. Comput.

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A mixed finite element method using rectangular elements is presented to solve the drift-diffusion model of semiconductors. The method, which is, on the one hand, a classical primal mixed finite element method, generalizes the one-dimensional Scharfetter-Gummel scheme to three dimensions in a natural way. The major contribution to a successful implementation of the method is the development of a fast and exact numerical evaluation of exponential fitted integrals, to which considerable attention has been devoted. The essentials of the efficient computation of these integrals are described, with full details to be presented elsewhere. In order to use computer resources parsimoniously, with the help of Lagrange multipliers, admissible bases on irregular rectangular meshes are constructed which allow a local element refinement. To validate the method, the modeling of a three-dimensional magneto transistor is presented.

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Section: Existence and Computation Of Solutionsmentioning

confidence: 98%

Section: Existence and Computation Of Solutionsmentioning

confidence: 99%

Section: Existence and Computation Of Solutionsmentioning

confidence: 99%

See 1 more Smart Citation

A 3D Rectangular Mixed Finite Element Method to Solve the Stationary Semiconductor Equations

Sartoris¹

1998

SIAM J. Sci. Comput.

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“…In [ 13, a formula for a was presented which combines the modification made using GGL with the original a of unity. Through a slight rearrangement of the terms and subtraction of one from it, it can be shown that the modification coefficient to %, ha,,, introduced by GGL can be expressed as -1 D@"v (in deriving these matrix blocks, the independent variable for the continuity equations are the scaled Slotboom variables, see [2]). Interestingly, this scheme is essentially the same as one of the schemes used in [4] where it was rated as somewhat effective.…”

Section: Discussionmentioning

confidence: 99%

“…A block matrix formulation for MSP was presented in [2], it is therefore instructive to find a similar one for GGL. In [ 13, a formula for a was presented which combines the modification made using GGL with the original a of unity.…”

Section: Discussionmentioning

confidence: 99%

Further improvements in decoupled methods for semiconductor device modeling

Obrecht

Heasell

Elmasry

et al.

Proceedings of International Workshop on Numerical Modeling of Processes and Devices for Integrated Circuits: NUPAD V

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Two complementary techniques for accelerating the Gummel iterations are successfully combined to yield an efficient and robust. decoupled nonlinear solution method for semiconductar device simulation. The reasons for this success are explored. The effectiveness of the new method under high level injection, and its robustness in the presence of large time or bias steps should pave the way to its widespread application in multidimensional semiconductor device simulation.

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Two-dimensional non-stationary numerical model for MSM structures

Radunović

Radunovic

1999

Int. J. Numer. Model.

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In this paper the solution of the non‐stationary model for MSM structures is obtained numerically. The two‐dimensional model consists of three singularly perturbed non‐linear partial differential equations. The alternating‐direction method for discretization in time and the non‐oscillatory streamline upwind method on a piecewise uniform grid for discretization in space are used to eliminate the interior and boundary layer oscillations. The described model is used for the analysis of the time response of a GaAs n‐type MSM structure to a Heaviside function form of the applied voltage. For the stationary case the I–V characteristic of the structure is determined. The numerical results confirm that the applied method is convenient for solving convection–diffusion problems. Copyright © 1999 John Wiley & Sons, Ltd.

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New approaches in a 3-D one-carrier device solver

Cited by 16 publications

References 9 publications

A 3D Rectangular Mixed Finite Element Method to Solve the Stationary Semiconductor Equations

A 3D Rectangular Mixed Finite Element Method to Solve the Stationary Semiconductor Equations

Further improvements in decoupled methods for semiconductor device modeling

Two-dimensional non-stationary numerical model for MSM structures

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