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Volumn 98, Issue 3-4, 2000, Pages 835-870

On the convergence of the Boltzmann equation for semiconductors toward the energy transport model

Author keywords

Boltzmann equation; Diffusion; Energy transport model; Entropy dissipation rate; Semiconductor

Indexed keywords


EID: 0034134829     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (23)

References (28)
  • 1
    • 0028446731 scopus 로고
    • Steady-state and transient analysis of submicron devices using energy-balance and simplified hydrodynamic models
    • Y. Apanovich, E. Lyumskis, B. Polsky, A. Shur, and P. Blakey, Steady-state and transient analysis of submicron devices using energy-balance and simplified hydrodynamic models. IEEE Trans. CAD of Integ. Circuits Syst. 13:702-711 (1994).
    • (1994) IEEE Trans. CAD of Integ. Circuits Syst. , vol.13 , pp. 702-711
    • Apanovich, Y.1    Lyumskis, E.2    Polsky, B.3    Shur, A.4    Blakey, P.5
  • 2
    • 50849147116 scopus 로고
    • The nonaecretive radiative transfer equations: Existence of solutions and Rosseland approximation
    • C. Bardos, F. Golse, B. Perthame, and R. Sentis, The nonaecretive radiative transfer equations: Existence of solutions and Rosseland approximation, J. Fund. Anal. 77(2):434-460 (1988).
    • (1988) J. Fund. Anal. , vol.77 , Issue.2 , pp. 434-460
    • Bardos, C.1    Golse, F.2    Perthame, B.3    Sentis, R.4
  • 3
    • 0030537690 scopus 로고    scopus 로고
    • On a hierarchy of macroscopic models for semiconductors
    • N. Ben Abdallah and P. Degond, On a hierarchy of macroscopic models for semiconductors. J. Math. Phys. 37(7):3306-3333 (1996).
    • (1996) J. Math. Phys. , vol.37 , Issue.7 , pp. 3306-3333
    • Ben Abdallah, N.1    Degond, P.2
  • 4
    • 0030186891 scopus 로고    scopus 로고
    • An energy transport model for semiconductors derived from the Boltzmann equation
    • N. Ben Abdallah, P. Degond, and S. Genieys, An energy transport model for semiconductors derived from the Boltzmann equation. J. Stat. Phys. 84(1-2):205-231 (1996).
    • (1996) J. Stat. Phys. , vol.84 , Issue.1-2 , pp. 205-231
    • Ben Abdallah, N.1    Degond, P.2    Genieys, S.3
  • 8
    • 0026735256 scopus 로고
    • An improved energy transport model including nonparabolicily and non-maxwellian distribution effects
    • D. Chen, E. Kan, U. Ravaioli, C. Shu, and R. Dutton, An improved energy transport model including nonparabolicily and non-maxwellian distribution effects, IEEE Electr. Dev. Letters 13:26-28 (1992).
    • (1992) IEEE Electr. Dev. Letters , vol.13 , pp. 26-28
    • Chen, D.1    Kan, E.2    Ravaioli, U.3    Shu, C.4    Dutton, R.5
  • 9
    • 0031115853 scopus 로고    scopus 로고
    • An existence and uniqueness result for the energy transport model in semiconductor theory
    • P. Degond, S. Génieys, and A. Jüngel, An existence and uniqueness result for the energy transport model in semiconductor theory, C. R. Acad. Sci. Sér. I 324:29-34 (1997).
    • (1997) C. R. Acad. Sci. Sér. I , vol.324 , pp. 29-34
    • Degond, P.1    Génieys, S.2    Jüngel, A.3
  • 10
    • 0031185320 scopus 로고    scopus 로고
    • An existence result for strongly coupled parabolic system arising in non equilibrium thermodynamics
    • P. Degond, S. Génieys, and A. Jüngel, An existence result for strongly coupled parabolic system arising in non equilibrium thermodynamics, C. R. Acad. Sci. Sér. I 325:227-232 (1997).
    • (1997) C. R. Acad. Sci. Sér. I , vol.325 , pp. 227-232
    • Degond, P.1    Génieys, S.2    Jüngel, A.3
  • 11
    • 0032183027 scopus 로고    scopus 로고
    • A steady-state system in non equilibrium thermodynamics including thermal and electrical effects
    • P. Degond, S. Génieys, and A. Jüngel, A steady-state system in non equilibrium thermodynamics including thermal and electrical effects. Math. Meth. Appl. Sci. 21:1399-1413 (1998).
    • (1998) Math. Meth. Appl. Sci. , vol.21 , pp. 1399-1413
    • Degond, P.1    Génieys, S.2    Jüngel, A.3
  • 12
    • 0031521314 scopus 로고    scopus 로고
    • A system of parabolic equations in non equilibrium thermodynamics including thermal and electrical effects
    • P. Degond, S. Génieys, and A. Jüngel, A system of parabolic equations in non equilibrium thermodynamics including thermal and electrical effects, J. Math. Pures Appl. 76:991-1015 (1997).
    • (1997) J. Math. Pures Appl. , vol.76 , pp. 991-1015
    • Degond, P.1    Génieys, S.2    Jüngel, A.3
  • 14
    • 0032355337 scopus 로고    scopus 로고
    • Macroscopic models for semiconductor heterostructures
    • P. Degond and C. Schmeiser, Macroscopic models for semiconductor heterostructures. J. Math. Phys. 39(9):4634-4663 (1998).
    • (1998) J. Math. Phys. , vol.39 , Issue.9 , pp. 4634-4663
    • Degond, P.1    Schmeiser, C.2
  • 15
    • 0001035667 scopus 로고
    • Entropy dissipation rate and convergence in kinetic equations
    • L. Desvillettes, Entropy dissipation rate and convergence in kinetic equations. Comm. Math. Phys. 123:687-702 (1989).
    • (1989) Comm. Math. Phys. , vol.123 , pp. 687-702
    • Desvillettes, L.1
  • 16
    • 0002306354 scopus 로고
    • Ordinary differential equations, transport theory and Sobolev spaces
    • R. Di Perna and P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98(3):511-547 (1989).
    • (1989) Invent. Math. , vol.98 , Issue.3 , pp. 511-547
    • Di Perna, R.1    Lions, P.-L.2
  • 17
    • 21844494298 scopus 로고
    • Kinetic models and quantum effects: A modified Boltzmann equation for Fermi Dirac particles
    • J. Dolbeault, Kinetic models and quantum effects: A modified Boltzmann equation for Fermi Dirac particles. Arch. Rat. Mech. Anal. 127(2):101-131 (1994).
    • (1994) Arch. Rat. Mech. Anal. , vol.127 , Issue.2 , pp. 101-131
    • Dolbeault, J.1
  • 19
    • 0002021149 scopus 로고    scopus 로고
    • Energy transport model for a nondegenerate semiconductor. Convergence of the Filbert expansion in the linearized case
    • S. Génieys, Energy transport model for a nondegenerate semiconductor. Convergence of the Filbert expansion in the linearized case, Asympt. Anal. 17(4):279-308 (1998).
    • (1998) Asympt. Anal. , vol.17 , Issue.4 , pp. 279-308
    • Génieys, S.1
  • 20
    • 45549114712 scopus 로고
    • Regularity of the moments of the solution of a transport equation
    • F. Golse, P. L. Lions, B. Perthame, and R. Sentis, Regularity of the moments of the solution of a transport equation, J. Fund. Anal. 77:110-125 (1988).
    • (1988) J. Fund. Anal. , vol.77 , pp. 110-125
    • Golse, F.1    Lions, P.L.2    Perthame, B.3    Sentis, R.4
  • 21
    • 84974759770 scopus 로고
    • Limite fluide des equations de Boltzmann des semiconducteurs pour une statistique de Fermi-Dirae
    • F. Golse and F. Poupaud, Limite fluide des equations de Boltzmann des semiconducteurs pour une statistique de Fermi-Dirae. Asympt. Anal. 6:135-160 (1992).
    • (1992) Asympt. Anal. , vol.6 , pp. 135-160
    • Golse, F.1    Poupaud, F.2
  • 22
    • 21144478445 scopus 로고
    • Initial boundary value problems for Boltzmann equation. Global existence of weak solutions
    • K. Hamdache, Initial boundary value problems for Boltzmann equation. Global existence of weak solutions, Arch. Rat. Mech. Anal. 119:309-151 (1992).
    • (1992) Arch. Rat. Mech. Anal. , vol.119 , pp. 309-1151
    • Hamdache, K.1
  • 23
    • 0002018639 scopus 로고    scopus 로고
    • Simulation of the energy-transport and simplified hydrodynamic models for semiconductor devices using mixed unite elements
    • London, John Wiley
    • A. Marrocco, P. Montarnal, and B. Perthame, Simulation of the energy-transport and simplified hydrodynamic models for semiconductor devices using mixed unite elements, Proceedings ECCOMAS 96, London, 1996, John Wiley.
    • (1996) Proceedings ECCOMAS 96
    • Marrocco, A.1    Montarnal, P.2    Perthame, B.3
  • 24
    • 0002224298 scopus 로고    scopus 로고
    • Convergence of moment methods for linear kinetic equations
    • C. Schmeiser and A. Zwirchmayr, Convergence of moment methods for linear kinetic equations, SIAM J. Numer. Anal. 36(1):74-88 (1999).
    • (1999) SIAM J. Numer. Anal. , vol.36 , Issue.1 , pp. 74-88
    • Schmeiser, C.1    Zwirchmayr, A.2
  • 25
    • 0028444676 scopus 로고
    • Comparative studies of hydrodynamic and energy transport models
    • K. Souissi, F. Odeh, H. Tang, and A. Gnudi, Comparative studies of hydrodynamic and energy transport models, COMPEL 13:439-453 (1994).
    • (1994) COMPEL , vol.13 , pp. 439-453
    • Souissi, K.1    Odeh, F.2    Tang, H.3    Gnudi, A.4
  • 26
    • 36149018649 scopus 로고
    • Diffusion of hot and cold electrons in semiconductor barriers
    • R. Stratton, Diffusion of hot and cold electrons in semiconductor barriers, Phys. Rev. 126:2002-2014 (1962).
    • (1962) Phys. Rev. , vol.126 , pp. 2002-2014
    • Stratton, R.1
  • 27
    • 0003887517 scopus 로고
    • Studies in Mathematics and its Applications North-Holland
    • R. Temam, Navier-Stokes Equations, Studies in Mathematics and its Applications (North-Holland, 1984).
    • (1984) Navier-Stokes Equations
    • Temam, R.1
  • 28
    • 0001614518 scopus 로고
    • On an entropy dissipation inequality for the Boltzmann equation
    • B. Wennberg, On an entropy dissipation inequality for the Boltzmann equation, C. R. Acad. Sci. Sér. I 315(13):1441-1446 (1992).
    • (1992) C. R. Acad. Sci. Sér. I , vol.315 , Issue.13 , pp. 1441-1446
    • Wennberg, B.1


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