A triangular mixed finite element method for the stationary semiconductor device equations

 Access to full text

 Full (PDF)

1. [1] R. A. ADAMS, Sobolev Spaces, Academie Press, New York (1975). Zbl0314.46030MR450957
2. [2] I. BABUŠKA, A. K. AZIZ, Survey Lectures on the Mathematical Foundations of the Finite Element Method from The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, Academic Press, New York (1972). Zbl0268.65052MR421106
3. [3] I. BABUŠKA, J. E. OSBORN, Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods, SIAM J. Numer. Anal., 20, No. 3 (1983) 510-536. Zbl0528.65046MR701094
4. [4] R. E. BANK, D. J. ROSE, Some Error Estimates fot the Box Method, SIAM J. Numer. Anal., 24, No. 4 (1987) 777-787. Zbl0634.65105MR899703
5. [5] F. BREZZI, P. MARINI, P. PIETRA, Méthodes d'éléments finis et schema de Scharfetter-Gummel, C. R. Acad. Sci. Paris, 305, Seriel (1987) 599-604. Zbl0623.65131MR917577
6. [6] F. BREZZI, P. MARINI, P. PIETRA, Two-Dimensional Exponential Fitting and Applications to Semiconductor Device Equations, SIAM J. Numer. Anal. 26 (1989) 1342-1355. Zbl0686.65088MR1025092
7. [7] F. BREZZI, L. D. MARINI, P. PIETRANumerical Solution of Semiconductor Devices, Comp. Meth. Appl. Mech. Engin, 75 (1989) 493-514. Zbl0698.76125MR1035759
8. [8] 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) 218-231. 
9. [9] P. G. CIARLET, P. A. RAVIART, General Lagrange and Hermite Interpolation in Rn with Applications to Finite Element Methods, Arch. Rat. Mech. Anal., 46 (1972) 177-199. Zbl0243.41004MR336957
10. [10] B. DELAUNAY, Sur la sphere vide, Izv. Akad. Nauk. SSSR, Math and Nat. Sci. Div., No. 6 (1934) 793-800 Zbl0010.41101
11. [11] G. L. DIRICHLET, Uber die Reduction der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen, J. Reine Angew. Math., 40, No. 3 (1850) 209-227. 
12. [12] V. GIRAULT, P. A. RAVIART, Finite Element Approximation of the Navier-Stokes Equations, Lect. Notes in Math., No. 749, Springer-Verlag (1979). Zbl0413.65081MR548867
13. [13] H. K. GUMMEL, A Self-Consistent Iterative Scheme for One-Dimensional Steady State Transistor Calculation, IEEE Trans. Elec. Dev., ED-11 (1964) 455-465. 
14. [14] B. HEINRICH, Finite difference methods on irregular networks, Birkhauser Verlag, Basel-Boston-Stuttgart (1987). Zbl0623.65096MR875416
15. [15] T IKEDA, Maximum Principle in Finite Element Models for Convection-Diffusion Phenomena, North-Holland (1983) Zbl0508.65049
16. [16] R. H. LI, Generalized Difference Methods for a Nonlinear Dirichlet Problem, SIAM J. Numer. Anal. Vol. 24, No. 1 (1987) 77-88 Zbl0626.65091MR874736
17. [17] R. H. MACNEAL, An Asymmetrical Finite Difference Network, Quart. Appl. Math., 11 (1953) 295-310. Zbl0053.26304MR57631
18. [18] P. A. MARKOWICH, M. ZLÁMAL, Inverse-Average-Type Finite Element Discretisations of Self adjoint Second-Order Elliptic Problems, Math. Comput., 51, No. 184 (1988) 431-449. Zbl0699.65074MR930223
19. [19] 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). 
20. [20] J. J. H. MILLER, S. WANG, C. H. WU, A Mixed Finite Element Method for the Stationary Semiconductor Continuity Equations, Engin. Comput., 5, No. 4 (1988) 285-288. MR1171713
21. [21] M. S. MOCK, Analysis of a Discretization Algorithm for Stationary Continuity Equations in Semiconductor Device Models, COMPEL, Vol. 2, No. 4 (1983) 117-139. Zbl0619.65116
22. [22] J. T. ODEN, J. K. LEE, Theory of Mixed and Hybrid Finite-Element Approximations in Linear Elasticity from IUTAM/IUM Symp. Applications of Methods of Functional Analysis to Problems of Mechanics, Lect. Notes in Math. No. 503, Springer-Verlag (1976). Zbl0361.73031MR670098
23. [23] J. T. ODEN, J. N. REDDY, An Introduction to the Mathematical Theory of Finite Elements, John Wiley & Sons, New York (1976). Zbl0336.35001MR461950
24. [24] W. V. VAN ROOSBROECK, Theory of Flow of Electrons and Holes in Germanium and Other Semiconductors, Bell Syst. Tech. J., 29 (1950) 560-607 
25. [25] R. S. VARGA, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, New Jersey (1962). Zbl0133.08602MR158502

1. J. J. H. Miller, Song Wang, An analysis of the Scharfetter-Gummel box method for the stationary semiconductor device equations
2. Song Wang, A new exponentially fitted triangular finite element method for the continuity equations in the drift-diffusion model of semiconductor devices