An adaptive mixed scheme for energy-transport simulations of field-effect transistors

SIAM Journal on Scientific Computing

Volumn 25, Issue 5, 2004, Pages 1698-1716

  Holst, Stefan ^a   Jüngel, Ansgar ^a   Pietra, Paola ^b  

^a UNIVERSITY OF KONSTANZ   (Germany)

^b CNR   (Italy)

Author keywords

Adaptive scheme; Double gate MESFET; Exponential fitting; Mixed finite elements; MOSFET; Semiconductors; Two dimensional

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; ENERGY TRANSFER; FINITE ELEMENT METHOD; GATES (TRANSISTOR); POISSON EQUATION;

ADAPTIVE SCHEME; DOUBLE GATE MESFET; EXPONENTIAL FITTING; MIXED FINITE ELEMENTS;

MOSFET DEVICES;

EID: 6344249180     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827502418215     Document Type: Article

References (49)

1. Y. APANOVICH, P. BLAKEY, R. COTTLE, E. LYUMKIS, B. POLSKY, A. SHUR, AND A. TCHERNIAEV, Numerical simulations of submicrometer devices including coupled nonlocal transport and nonisothermal effects, IEEE Trans. Electr. Dev., 42 (1995), pp. 890-897.
2. D. ARNOLD AND F. BREZZI, Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates, RAIRO Modél. Math. Anal. Numér., 19 (1977), pp. 7-32.
3. R. E. BANK, A. H. SHERMAN, AND A. WEISER, Refinement algorithms and data structures for regular local mesh refinement, in Scientific Computing, R. Steplemen et al., eds., IMACS, New Brunswick, NJ, 1983, pp. 3-17.
4. N. BEN ABDALLAH AND P. DEGOND, On a hierarchy of macroscopic models for semiconductors, J. Math. Phys., 37 (1996), pp. 3308-3333.
5. F. BOSISIO, R. SACCO, F. SALERI, AND E. GATTI, Exponentially fitted mixed finite volumes for energy balance models in semiconductor device simulation, in Proceedings of ENUMATH 97, H. Bock et al., eds., World Scientific, Singapore, 1998, pp. 188-197.
6. F. BREZZI AND M. FORTIN, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991.
7. F. BREZZI, L. MARINI, S. MICHELETTI, P. PIETRA, R. SACCO, AND S. WANG, Discretization of semiconductor device problems, in Numerical Methods for Electrodynamical Problems, Handb. Numer. Anal., W. Schilders and E. ter Maten, eds., North-Holland, Amsterdam, to appear.
8. F. BREZZI, L. MARINI, AND P. PIETRA, Numerical simulation of semiconductor devices, Comput. Methods Appl. Mech. Engrg., 75 (1989), pp. 493-514.
9. F. BREZZI, L. MARINI, AND P. PIETRA, Two-dimensional exponential fitting and applications to drift-diffusion models, SIAM J. Numer. Anal., 26 (1989), pp. 1342-1355.
10. F. BREZZI AND A. RUSSO, Choosing bubbles for advection diffusion problems, Math. Models Methods Appl. Sci., 4 (1994), pp. 571-587.
11. D. CHEN, E. KAN, U. RAVAIOLI, C. SHU, AND R. DUTTON, An improved energy transport model including nonparabolicity and non-Maxwellian distribution effects, IEEE Electr. Dev. Letters, 13 (1992), pp. 26-28.
12. E. CASSAN, S. GALDIN, P. DOLLFUS, AND P. HESTO, Comparison between device simulators for gate current calculation in ultra-thin gate oxide n-MOSFETs, IEEE Trans. Electr. Dev., 83 (2000), pp. 1194-1202.
13. C. CARSTENSEN AND S. JANSCHE, An a posteriori estimate for nonconforming finite element methods, ZAMM Z. Angew. Math. Mech., 78 (1998), pp. S871-S872.
14. M. CROUZEIX AND P. A. RAVIART, Conforming and nonconforming finite element methods for solving the stationary Stokes equations I, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge, 7 (1973), pp. 33-75.
15. E. DARI, R. DURAN, C. PADRA, AND V. VAMPA, A posteriori error estimation for nonconforming finite element methods, RAIRO Modél. Math. Anal. Numér., 30 (1996), pp. 385-400.
16. P. DEGOND, S. GÉNIEYS, AND A. JÜNGEL, A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects, J. Math. Pures Appl. (9), 76 (1997), pp. 991-1015.
17. P. DEGOND, S. GÉNIEYS, AND A. JÜNGEL, A steady-state system in nonequilibrium thermodynamics including thermal and electrical effects, Math. Methods Appl. Sci., 21 (1998), pp. 1399-1413.
18. P. DEGOND, A. JÜNGEL, AND P. PIETRA, Numerical discretization of energy-transport models for semiconductors with nonparabolic band structure, SIAM J. Sci. Comput., 22 (2000), pp. 986-1007.
19. W. FANG AND K. ITO, Existence of stationary solutions to an energy drift-diffusion model for semiconductor devices, Math. Models Methods Appl. Sci., 11 (2001), pp. 827-840.
20. A. FORGHIERI, R. GUERRIERI, P. CIAMPOLINI, A. GNUDI, M. RUDAN, AND G. BACCARANI, A new discretization strategy of the semiconductor equations comprising momentum and energy balance, IEEE Trans. Comp. Aided Design Integr. Circuits Sys., 7 (1988), pp. 231-242.
21. M. FOURNIÉ, Numerical discretization of energy-transport model for semiconductors using high-order compact schemes, Appl. Math. Lett., 15 (2002), pp. 727-734.
22. C. GARDNER, P. LANZKORN, AND D. ROSE, A parallel block iterative method for the hydrodynamic device model, IEEE Trans. Comp. Aided Design Integr. Circuits Sys., 10 (1991), pp. 1187-1192.
23. J. GRIEPENTROG, An application of the implicit function theorem to an energy model of the semiconductor theory, ZAMM Z. Angew. Math. Mech., 79 (1999), pp. 43-51.
24. S. HOLST, A. JÜNGEL, AND P. PIETRA, A mixed finite-element discretization of the energy-transport model for semiconductors, SIAM J. Sci. Comput., 24 (2003), pp. 2058-2075.
25. R. HOPPE AND B. WOHLMUTH, Element-oriented and edge-oriented local error estimators for nonconforming finite element methods, RAIRO Modél. Math. Anal. Numér., 30 (1996), pp. 237-263.
26. R. HOPPE AND B. WOHLMUTH, A comparison of a posteriori error estimators for mixed finite element discretizations by Raviart-Thomas elements, Math. Comp., 68 (1999), pp. 1347-1378.
27. J. JEROME, Analysis of Charge Transport. A Mathematical Study of Semiconductor Devices, Springer-Verlag, Berlin, 1996.
28. J. JEROME AND T. KERKHOVEN, A finite-element approximation theory for the drift diffusion semiconductor model, SIAM J. Numer. Anal., 28 (1991), pp. 403-422.
29. J. JEROME AND C.-W. SHU, Energy models for one-carrier transport in semiconductor devices, in Semiconductors, Part II, IMA Vol. Math. Appl. 59, W. Coughran et al., eds., Springer-Verlag, New York, 1994, pp. 185-207.
30. A. JÜNGEL, Quasi-Hydrodynamic Semiconductor Equations, Birkhäuser, Basel, 2001.
31. A. JÜNGEL AND P. PIETRA, A discretization scheme of a quasi-hydrodynamic semiconductor model, Math. Models Methods Appl. Sci., 7 (1997), pp. 935-955.
32. T. KERKHOVEN AND Y. SAAD, On acceleration methods for coupled nonlinear elliptic systems, Numer. Math., 60 (1992), pp. 525-548.
33. C. LAB AND P. CAUSSIGNAC, An energy-transport model for semiconductor heterostructure devices: Application to AlGaAs/GaAs MODFETs, COMPEL, 18 (1999), pp. 61-76.
34. L. D. MARINI AND P. PIETRA, An abstract theory for mixed approximations of second order elliptic problems, Mat. Apl. Comput., 8 (1989), pp. 219-239.
35. L. D. MARINI AND P. PIETRA, New mixed finite element schemes for current continuity equations, COMPEL, 9 (1990), pp. 257-268.
36. P. A. MARKOWICH, C. A. RINGHOFER, AND C. SCHMEISER, Semiconductor Equations, Springer-Verlag, Vienna, 1990.
37. A. MARROCCO, P. MONTARNAL, AND B. PERTHAME, Simulation of the energy-transport and simplified hydrodynamic models for semiconductor devices using mixed finite elements, in Proceedings of ECCOMAS 96, John Wiley, London, 1996.
38. J. J. MILLER AND S. WANG, A new non-conforming Petrov-Galerkin finite-element method with triangular elements for a singularly perturbated advection-diffusion problem, IMA J. Numer. Anal., 14 (1996), pp. 257-276.
39. P. RAVIART AND J. THOMAS, A Mixed Finite Element Method for Second Order Elliptic Equations, in Mathematical Aspects of the Finite Element Method, Lecture Notes in Math. 606, Springer-Verlag, New York, 1977, pp. 292-315.
40. C. RINGHOFER, An entropy-based finite difference method for the energy transport system, Math. Models Methods Appl. Sci., 11 (2001), pp. 769-796.
41. M. RUDAN, A. GNUDI, AND W. QUADE, A generalized approach to the hydrodynamic model of semiconductor equations, in Process and Device Modeling for Microelectronics, G. Baccarani, ed., Elsevier, Amsterdam, 1993, pp. 109-154.
42. R. SACCO AND F. SALERI, Stabilization of mixed finite elements for convection-diffusion problems, CWI Quarterly, 10 (1997), pp. 301-315.
43. S. SELBERHERR, Analysis and Simulation of Semiconductor Devices, Springer-Verlag, Vienna, 1984.
44. K. SOUISSI, F. ODEH, H. TANG, AND A. GNUDI, Comparative studies of hydrodynamic and energy transport models, COMPEL, 13 (1994), pp. 439-453.
45. R. STRATTON, Diffusion of hot and cold electrons in semiconductor barriers, Phys. Rev., 126 (1962), pp. 2002-2014.
46. S. SZE, Physics of Semiconductor Devices, John Wiley, New York, 1981.
47. R. VERFÜRTH, A Review of a Posteriori Error Estimation and Adaptive Mesh Refinement Techniques, Wiley, Teubner, Germany, 1996.
48. P. VISOCKY, A method for transient semiconductor device simulation using hot-electron transport equations, in Proceedings of the Nasecode X Conference., J. Miller, ed., Boole Press, Dublin, 1994.
49. B. WOHLMUTH, A residual based error estimator for mortar finite element discretizations, Numer. Math., 84 (1999), pp. 143-171.