A new exponentially fitted triangular finite element method for the continuity equations in the drift-diffusion model of semiconductor devices
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 33 (1999) no. 1, p. 99-112
@article{M2AN_1999__33_1_99_0,
     author = {Wang, Song},
     title = {A new exponentially fitted triangular finite element method for the continuity equations in the drift-diffusion model of semiconductor devices},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {33},
     number = {1},
     year = {1999},
     pages = {99-112},
     zbl = {0961.82030},
     mrnumber = {1685746},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1999__33_1_99_0}
}
Wang, Song. A new exponentially fitted triangular finite element method for the continuity equations in the drift-diffusion model of semiconductor devices. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 33 (1999) no. 1, pp. 99-112. http://www.numdam.org/item/M2AN_1999__33_1_99_0/

[1] D.N. De G. Allen, R.V. Southwell, Relaxation methods applied to determine the motion, in two dimensions, of a viscous fluid past a fixed cylinder. Quart. J. Mech. Appl Math. 8 (1955) 129-145. | MR 70367 | Zbl 0064.19802

[2] R.E. Bank, J.F. Bürgler, W. Fichtner, R.K. Smith, Some upwinding techniques for finite element approximations of convection-diffusion equations. Numer. Math. 58 (1990) 185-202. | MR 1069278 | Zbl 0713.65066

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

[4] E. Buturla, P. Cottrell, B.M. Grossman, K.A. Salsburg, Finite Element Analysis of Semiconductor Devices: The FIELDAY Program. IBM J. Res. Develop. 25, (1981) 218-231.

[5] P.G. Ciarlet, The finite element method for elliptic problems. North-Holland, Amsterdam (1978). | MR 520174 | Zbl 0383.65058

[6] C.J. Fitzsimons, J.J.H. Miller, S. Wang, C.H. Wu, Hexahedral finite elements for the stationary semiconductor device equations. Comp. Meth. Appl. Mech. Engrg. 84 (1990) 43-57. | MR 1082819 | Zbl 0725.65119

[7] H.K. Gummel, A self-consistent iterative scheme for one-dimensional Steady State Transistor Calculation. IEEE Trans. Elec. Dev. 11 (1964) 455-465.

[8] P.A. Markowich, M. Zlámal, Inverse-Average-Type Finite Element Discrétisations of Selfadjoint Second-Order Elliptic Problems. Math. Comp. 51 (1988) 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. J.J.H. Miller Ed. Boole Press, Dublin (1985).

[10] J.J.H. Miller and S. Wang, A Triangular Mixed Finite Element Method for the Stationary Semiconductor Device Equations. RAIRO Modél. Math. Anal. Numér. 25 (1991) 441-463. | Numdam | MR 1108585 | Zbl 0732.65114

[11] J.J.H. Miller and S. Wang, An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations. RAIRO Modél. Math. Anal. Numér. 28 (1994) 123-140. | Numdam | MR 1267195 | Zbl 0820.65089

[12] J.J.H. Miller and S. Wang, A tetrahedral mixed finite element method for the stationary semiconductor continuity equations. SIAM J. Numer. Anal. 31 (1994) 196-216. | MR 1259972 | Zbl 0797.65106

[13] M.S. Mock, Analysis of a Discretization Algorithm for Stationary Continuity Equations in Semiconductor Device Models. COMPEL 2 (1983) 117-139. | Zbl 0619.65116

[14] D. Scharfetter and H.K. Gummel, Large-signal analysis of a silicon read diode oscillator. IEEE Trans. Elec. Dev. 16 (1969) 64-77.

[15] M. Sever, Discretization of time-dependent continuity equations. Proceedings of the 6th International NASECODE Conference. J.J.H. Miller Ed. Boole Press, Dublin (1988) 71-83. | MR 1066495 | Zbl 0800.65022

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

[17] S.M. Sze, The physics of semiconductor devices, 2nd ed. John Wiley & Sons, New York (1981).

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