High-field approximations of the energy-transport model for semiconductors with non-parabolic band structure

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 52, Issue 6, 2001, Pages 1053-1070

  Degond, Pierre ^a   Jüngel, Ansgar ^b  

^a UNIVERSITÉ PAUL SABATIER   (France)

^b UNIVERSITY OF KONSTANZ   (Germany)

Author keywords

Chapman Enskog method; High field drift diffusion models; Non parabolic band; Semiconductors

Indexed keywords

EID: 0035541515     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001583     Document Type: Article

References (20)

1. N. Ben Abdallah and P. Degond, On a hierarchy of macroscopic models for semiconductors. J. Math. Phys. 37 (1996), 3308-3333.
2. N. Ben Abdallah, P. Degond, and S. Génieys, An energy-transport model for semiconductors derived from the Boltzmann equation. J. Stat. Phys. 84 (1996), 205-231.
3. N. Ben Abdallah, P. Degond, P. Markowich, and C. Schmeiser, High field approximations of the spherical harmonics expansion model for semiconductors. Z. Angew. Math. Phys. 52 (2001), 201-230.
4. F. Brezzi, L. Marini, and P. Pietra, Two-dimensional exponential fitting and applications to drift-diffusion models. SIAM J. Num. Anal. 26 (1989), 1342-1355.
5. C. Cercignani, I. Gamba, D. Levermore, A high field approximation to a Boltzmann-Poisson system in bounded domains. Appl. Math. Lett. 4, (1997), 111-118.
6. D. Chen, E. Kan, U. Ravaioli, C. Shu, and R. Dutton, An improved energy transport model including nonparabolicity and non-Maxvellian distribution effects. IEEE Electr. Dev. Letters 13 (1992), 26-28.
7. P. Degond, Mathematical modelling of microelectronics semiconductor devices, in AMS/IP Studies in Advanced Mathematics, vol 15, AMS and International Press, 77y-110, 2000.
8. P. Degond, S. Génieys, and A. Jüngel, A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects. J. Math. Pures Appl. 76 (1997), 991-1015.
9. P. Degond, A. Jüngel, and P. Pietra, Numerical discretization of energy-transport model for semiconductors with non-parabolic band structure. SIAM J. Sci. Comp. 22 (2000), 986-1007.
10. P. Dmitruk, A. Paul, and L. Reyna, High electric field approximation to charge transport in semiconductor devices. Appl. Math. Lett. 5 (1992), 99-102.
11. C. Jacoboni and P. Lugli, The Monte Carlo Method for Semiconductor Device Simulation. Springer, Wien 1989.
12. A. Jüngel, Quasi-hydrodynamic Semiconductor Equations. Progress in Nonlinear Differential Equations and Its Applications. Birkhäuser, Basel 2001.
13. E. Kane, Band structure of indium-antimonide. J. Phys. Chem. Solids 1 (1957), 249.
14. E. Lyumkis, B. Polsky, A. Shur, and P. Visocky, Transient semiconductor device simulation including energy balance equation. Compel 11 (1992), 311-325.
15. P. A. Markowich, C. Ringhofer, C. Schmeiser, Semiconductor Equations. Springer, Wien 1990.
16. F. Poupaud, Runaway phenomena and fluid approximation under high fields in semiconductor kinetic theory. Z. Angew. Math. Mech. 72 (1992), 359-372.
17. C. Schmeiser and A. Zwirchmayr, Elastic and drift-diffusion limits of electron-phonon interaction in semiconductors. Math. Models Meth. Appl. Sci. 8 (1998), 37-53.
18. S. Selberherr, Analysis and Simulation of Semiconductor Devices. Springer, Wien 1984.
19. R. Stratton, Diffusion of hot and cold electrons in semiconductor barriers. Phys. Rev. 126 (1962), 2002-2014.
20. D. Ventura, A. Gnudi, G. Baccarani, and F. Odeh, Multidimensional spherical harmonics expansion of Boltzmann equation for transport in semiconductors. Appl. Math. Lett. 5 (1992), 85-90.