Finite-element methods in semiconductor device simulation

Barnes, J.J.; Lomax, R.J.

doi:10.1109/t-ed.1977.18880

Cited by 71 publications

(20 citation statements)

References 18 publications

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“…Substituting (14) into (13), noticing that and ignoring the term 0(h)|supp(∆θ i j)| we finally obtain:…”

Section: Theorem 3 Suppose That the Quadrilateral (Hexa Hedral) Meshmentioning

confidence: 99%

“…A practical scheme should be such that the computed terminal currents are conservative. Some authors 14,15 have discussed the evaluation of the terminal currents for their schemes. In the following we do this for our scheme.…”

Section: Evaluation Of the Terminal Currentsmentioning

confidence: 99%

“…Suppose that the hypotheses of Theorem 3 are fulfilled. Let f be the flux solution of Problem (P) and f h the flux given by (14). Then there is a constant c > 0, independent of h, such that where J c and Jhc are given by (18) and (19) respectively.…”

Section: Evaluation Of the Terminal Currentsmentioning

confidence: 99%

“…Furthermore, from the definition of θhc, we know that for this choice we have (θhc = θc. Therefore, substituting such θhc into (19) and using (14) we get:…”

Section: Evaluation Of the Terminal Currentsmentioning

confidence: 99%

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A mixed finite element method for the stationary semiconductor continuity equations

Miller

Wang²,

Wu³

1988

Engineering Computations

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If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation. ABSTRACTWe discuss a finite element approximation of the semiconductor continuity equations based on quadrilateral and hexahedral space discretizations. This method can be regarded as an extension to higher dimensions of the well-known onedimensional Scharfetter-Gummel scheme. The existence, uniqueness and error estimates of the solution is discussed. Using a lumping technique we get a linear system similar to that obtained from the conventional box-scheme. We also discuss the evaluation of the approximate terminal currents, which are shown to be convergent and conservative.

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“…Substituting (14) into (13), noticing that and ignoring the term 0(h)|supp(∆θ i j)| we finally obtain:…”

Section: Theorem 3 Suppose That the Quadrilateral (Hexa Hedral) Meshmentioning

confidence: 99%

Section: Evaluation Of the Terminal Currentsmentioning

confidence: 99%

Section: Evaluation Of the Terminal Currentsmentioning

confidence: 99%

“…Furthermore, from the definition of θhc, we know that for this choice we have (θhc = θc. Therefore, substituting such θhc into (19) and using (14) we get:…”

Section: Evaluation Of the Terminal Currentsmentioning

confidence: 99%

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A mixed finite element method for the stationary semiconductor continuity equations

Miller

Wang²,

Wu³

1988

Engineering Computations

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“…The finite element (FE) method offers distinct advantages in TCAD simulations [2], since it allows the often inherently complex geometries and features of semiconductor devices to be captured where finite difference methods would require unreasonably fine grids. But, in present implementations, severe restrictions are placed on the shape of elements making mesh generation a burdensome task.…”

Section: Introductionmentioning

confidence: 99%

Enriched residual free bubbles for semiconductor device simulation

et al. 2012

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This article outlines a method for stabilising the current continuity equations which are used for semiconductor device simulation. Residual-free bubble functions (RfBF) are incorporated into a finite element (FE) implementation that are able to prevent oscillations which are seen when using the conventional Bubnov-Galerkin FE implementation. In addition, it is shown that the RfBF are able to provide stabilisation with very distorted meshes and curved interface boundaries. Comparison with the commonly used SUPG scheme is made throughout, showing that in the case of 2D problems the RfBF allow faster convergence of the coupled semiconductor device equations, especially in the case of distorted meshes.

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Comparative study of finite element formulations for the semiconductor drift-diffusion equations

Trattles¹,

Johnson²

1997

Int. J. Numer. Meth. Engng.

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A number of transient and steady-state finite element formulations of the semiconductor drift-diffusion equations are studied and compared with respect to their accuracy and efficiency on a simple test structure (the Mock diode). A new formulation, with a consistent interpolation function used to represent the electron and hole carrier densities throughout the set of semiconductor drift-diffusion and Poisson's equations, is introduced. Results highlight the advantages in using consistent interpolation functions showing an increased accuracy in the calculated values and a saving in data storage and execution time. The results also illustrate how the use of different time integration methods affect the number of time steps required during transient simulations. The combination of the fully consistent DFUS with appropriate time integration methods is found to yield a saving of up to 80 per cent of the execution time required for standard spatial/temporal discretization techniques.

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Finite-element methods in semiconductor device simulation

Cited by 71 publications

References 18 publications

A mixed finite element method for the stationary semiconductor continuity equations

A mixed finite element method for the stationary semiconductor continuity equations

Enriched residual free bubbles for semiconductor device simulation

Comparative study of finite element formulations for the semiconductor drift-diffusion equations

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