An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 28 (1994) no. 2, p. 123-140
@article{M2AN_1994__28_2_123_0,
     author = {Miller, J. J. H. and Wang, Song},
     title = {An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {28},
     number = {2},
     year = {1994},
     pages = {123-140},
     zbl = {0820.65089},
     mrnumber = {1267195},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1994__28_2_123_0}
}
Miller, J. J. H.; Wang, Song. An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 28 (1994) no. 2, pp. 123-140. http://www.numdam.org/item/M2AN_1994__28_2_123_0/

[1] R. E. Bank, D. J. Rose, Some Error Estimates for the Box Method, SIAM J. Numer. Anal., 24, No. 4, 1987, pp. 777-787. | MR 899703 | Zbl 0634.65105

[2] F. Brezzi, P. Marini, P. Pietra, Two-dimensional exponentially fitting and applications to semiconductor device equations, SIAM J. Numer. Anal., 26, 1989, pp. 1342-1355. | MR 1025092 | Zbl 0686.65088

[3] E. Buturla, P. Cottrell, B. M. Grossman, K. A. Salsburg, Finite-Element Analysis of Semiconductor Devices : The FIELDAY Program, IBM J. Res. Develop., 25, No. 4, 1981, pp. 218-231.

[4] B. Delaunay, Sur la sphère vide, Izv. Akad. Nauk. SSSR, Math. and Nat. Sci. Div., No. 6, 1934, pp. 793-800. | Zbl 0010.41101

[5] G. L. Dirichlet, Über die Reduction der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen, J. Reine Angew. Math., 40, No. 3, 1850, pp. 209-227. | Zbl 040.1103cj

[6] H. K. Gummel, A Self-Consistent Iterative Scheme for One-Dimensional Steady State Transistor Calculation, IEEE Trans. Elec. Dev., ED-11, 1964,pp. 455-465.

[7] R. H. Macneal, An Asymmetrical Finite Difference Network, Quart. Appl. Math., 11, 1953, pp. 295-310. | MR 57631 | Zbl 0053.26304

[8] P. A. Markowich, M. Zlámal, Inverse-Average-Type Finite Element Discretisations of Selfadjoint Second-Order Elliptic Problems, Math. Comp., 51,No. 184, 1988, pp. 431-449. | MR 930223 | Zbl 0699.65074

[9] B. J. Mccartin, Discretization of the Semiconductor Device Equations from New Problems and New Solutions for Device and Process Modelling, ed. J.J.H. Miller, Boole Press, Dublin, 1985.

[10] J. J. H. Miller, S. Wang, A Triangular Mixed Finite Element Method for the Stationary Semiconductor Device Equations, M2AN, 25, No. 4, 1991, pp. 441-463. | Numdam | MR 1108585 | Zbl 0732.65114

[11] J. J. H. Miller, S. Wang, A New Non-conforming Petrov-Galerkin Finite Element Method with Triangular Elements for an Advection-Diffusion Problem, IMAJ. Num. Anal., to appear. | Zbl 0806.65111

[12] M. S. Mock, Analysis of a Discretization Algorithm for Stationary Continuity Equations in Semiconductor Device Models, COMPEL, 2, No. 4, 1983, pp. 117-139. | Zbl 0619.65116

[13] M. S. Mock, Analysis of a Discretization Algorithm for Stationary Continuity Equations in Semiconductor Device Models, II, COMPEL, 3, No. 3, 1984, pp. 137-149. | MR 782025 | Zbl 0619.65117

[14] J. T. Oden, J. N. Reddy, An Introduction to the Mathematical Theory of Finite Elements, John Wiley & Son, New York-London-Sydney-Toronto, 1976. | MR 461950 | Zbl 0336.35001

[15] D. Scharfetter, H. K. Gummel, Large-signal analysis of a silicon read diode oscillator, IEEE Trans. Elec. Dev., ED-16, 1969, pp. 64-77.

[16] J. W. Slotboom, Iterative Scheme for 1- and 2-Dimensional D. C.-Transistor, IEEE Trans. Elect. Dev. 24, 1977, pp. 1123-1125.

[17] P. Sonneveld, CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear Systems, SIAM J. Sci. Statist. Comput., 10, 1989, pp. 36-52. | MR 976160 | Zbl 0666.65029

[18] H. A. Van Der Vorst, Bi-CGSTAB : A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems, SIAM J. Sci. Stat. Comput., 13, No. 2, 1992, pp. 631-644. | MR 1149111 | Zbl 0761.65023

[19] W. V. Van Roosbroeck, Theory of Flow of Electrons and Holes in Germanium and Other Semiconductors, Bell Syst. Tech. J., 29, 1950, pp. 560-607.

[20] R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1962. | MR 158502 | Zbl 0133.08602