A new exponentially fitted triangular finite element method for the continuity equations in the drift-diffusion model of semiconductor devices

Mathematical Modelling and Numerical Analysis

Volumn 33, Issue 1, 1999, Pages 99-112

  Wang, Song ^a  

^a CURTIN UNIVERSITY   (Australia)

Author keywords

Exponential fitting; Finite element method; Semiconductors

Indexed keywords

EID: 0033449102     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:1999107     Document Type: Article

References (18)

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.
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.
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.
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).
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.
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 Discretisations of Selfadjoint Second-Order Elliptic Problems. Math. Comp. 51 (1988) 431-449.
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 Model. Math. Anal. Numér. 25 (1991) 441-463.
11. J.J.H. Miller and S. Wang, An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations. RAIRO Model Math. Anal. Numer. 28 (1994) 123-140.
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.
13. M.S. Mock, Analysis of a Discretization Algorithm for Stationary Continuity Equations in Semiconductor Device Models. COMPEL 2 (1983) 117-139.
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.
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.