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Analysis of a diffusive effective mass model for nanowires
1. | Istituto di Matematica Applicata e Tecnologie Informatiche CNR, via Ferrata 1, 27100 Pavia |
2. | UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, INRIA Paris-Rocquencourt, EPI MAMBA, F-75005, Paris, France |
References:
[1] |
N. W. Ashcroft and N. D. Mermin, "Solid State Physics,'' Saunders College Publishing, 1976. |
[2] |
J.-P. Aubin, Un théor\`eme de compacité, C. R. Acad. Sci. Paris, 256 (1963), 5042-5044. |
[3] |
N. Ben Abdallah and L. Barletti, Quantum transport in crystals : Effective-mass theorem and k.p Hamiltonians, Comm. Math. Phys., 307 (2011), 567-607. |
[4] |
N. Ben Abdallah and P. Degond, On a hierarchy of macroscopic models for semiconductors J. Math. Phys., 37 (1996), 3306-3333.
doi: 10.1063/1.531567. |
[5] |
N. Ben Abdallah, C. Jourdana and P. Pietra, An effective mass model for the simulation of ultra-scaled confined devices,, preprint, ().
|
[6] |
N. Ben Abdallah and F. Méhats, On a Vlasov-Schrödinger-Poisson model, Comm. Partial Differential Equations, 29 (2004), 173-206. |
[7] |
N. Ben Abdallah and F. Méhats, Semiclassical analysis of the Schrödinger equation with a partially confining potential, J. Math. Pures Appl. (9), 84 (2005), 580-614.
doi: 10.1016/j.matpur.2004.10.004. |
[8] |
N. Ben Abdallah, F. Méhats and N. Vauchelet, Diffusive transport of partially quantized particles: Existence, uniqueness and long-time behaviour, Proc. Edinb. Math. Soc. (2), 49 (2006), 513-549.
doi: 10.1017/S0013091504000987. |
[9] |
N. Ben Abdallah and M. L. Tayeb, Diffusion approximation for the one dimensional Boltzmann-Poisson system, Discrete Contin. Dyn. Syst. Ser. B, 4 (2004), 1129-1142.
doi: 10.3934/dcdsb.2004.4.1129. |
[10] |
C. Heitzinger and C. Ringhofer, A transport equation for confined structures derived from the Boltzmann equation, Comm. Math. Sci., 9 (2011), 829-857. |
[11] |
A. Henrot, "Extremum Problems for Eigenvalues of Elliptic Operators,'' Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2006. |
[12] |
A. Jüngel, "Transport Equations for Semiconductors,'' Lecture Notes in Physics, 773, Springer-Verlag, Berlin, 2009. |
[13] |
J.-L. Lions, "Équations Différentielles Opérationnelles et Problèmes aux Limites,'' Die Grundlehren der mathematischen Wissenschaften, Bd. 111, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. |
[14] |
P. A. Markowich, C. A. Ringhofer and C. Schmeiser, "Semiconductor Equations,'' Springer-Verlag, Vienna, 1990.
doi: 10.1007/978-3-7091-6961-2. |
[15] |
N. Masmoudi and M. L. Tayeb, Diffusion limit of a semiconductor Boltzmann-Poisson system, SIAM J. Math. Anal., 38 (2007), 1788-1807.
doi: 10.1137/050630763. |
[16] |
M. S. Mock, "Analysis of Mathematical Models of Semiconductor Devices,'' Advances in Numerical Computation Series, 3, Boole Press, Dún Laoghaire, 1983. |
[17] |
P. Pietra and N. Vauchelet, Modeling and simulation of the diffusive transport in a nanoscale Double-Gate MOSFET, J. Comp. Elec., 7 (2008), 52-65.
doi: 10.1007/s10825-008-0253-z. |
[18] |
F. Poupaud, Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers, Asymptotic Anal., 4 (1991), 293-317. |
[19] |
N. Vauchelet, Diffusive limit of a two dimensional kinetic system of partially quantized particles, J. Stat. Phys., 139 (2010), 882-914.
doi: 10.1007/s10955-010-9970-3. |
[20] |
N. Vauchelet, Diffusive transport of partially quantized particles: $L\log L$ solutions, Math. Models Methods Appl. Sci., 18 (2008), 489-510.
doi: 10.1142/S0218202508002759. |
[21] |
T. Wenckebach, "Essential of Semiconductor Physics,'' Wiley, Chichester, 1999. |
show all references
References:
[1] |
N. W. Ashcroft and N. D. Mermin, "Solid State Physics,'' Saunders College Publishing, 1976. |
[2] |
J.-P. Aubin, Un théor\`eme de compacité, C. R. Acad. Sci. Paris, 256 (1963), 5042-5044. |
[3] |
N. Ben Abdallah and L. Barletti, Quantum transport in crystals : Effective-mass theorem and k.p Hamiltonians, Comm. Math. Phys., 307 (2011), 567-607. |
[4] |
N. Ben Abdallah and P. Degond, On a hierarchy of macroscopic models for semiconductors J. Math. Phys., 37 (1996), 3306-3333.
doi: 10.1063/1.531567. |
[5] |
N. Ben Abdallah, C. Jourdana and P. Pietra, An effective mass model for the simulation of ultra-scaled confined devices,, preprint, ().
|
[6] |
N. Ben Abdallah and F. Méhats, On a Vlasov-Schrödinger-Poisson model, Comm. Partial Differential Equations, 29 (2004), 173-206. |
[7] |
N. Ben Abdallah and F. Méhats, Semiclassical analysis of the Schrödinger equation with a partially confining potential, J. Math. Pures Appl. (9), 84 (2005), 580-614.
doi: 10.1016/j.matpur.2004.10.004. |
[8] |
N. Ben Abdallah, F. Méhats and N. Vauchelet, Diffusive transport of partially quantized particles: Existence, uniqueness and long-time behaviour, Proc. Edinb. Math. Soc. (2), 49 (2006), 513-549.
doi: 10.1017/S0013091504000987. |
[9] |
N. Ben Abdallah and M. L. Tayeb, Diffusion approximation for the one dimensional Boltzmann-Poisson system, Discrete Contin. Dyn. Syst. Ser. B, 4 (2004), 1129-1142.
doi: 10.3934/dcdsb.2004.4.1129. |
[10] |
C. Heitzinger and C. Ringhofer, A transport equation for confined structures derived from the Boltzmann equation, Comm. Math. Sci., 9 (2011), 829-857. |
[11] |
A. Henrot, "Extremum Problems for Eigenvalues of Elliptic Operators,'' Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2006. |
[12] |
A. Jüngel, "Transport Equations for Semiconductors,'' Lecture Notes in Physics, 773, Springer-Verlag, Berlin, 2009. |
[13] |
J.-L. Lions, "Équations Différentielles Opérationnelles et Problèmes aux Limites,'' Die Grundlehren der mathematischen Wissenschaften, Bd. 111, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. |
[14] |
P. A. Markowich, C. A. Ringhofer and C. Schmeiser, "Semiconductor Equations,'' Springer-Verlag, Vienna, 1990.
doi: 10.1007/978-3-7091-6961-2. |
[15] |
N. Masmoudi and M. L. Tayeb, Diffusion limit of a semiconductor Boltzmann-Poisson system, SIAM J. Math. Anal., 38 (2007), 1788-1807.
doi: 10.1137/050630763. |
[16] |
M. S. Mock, "Analysis of Mathematical Models of Semiconductor Devices,'' Advances in Numerical Computation Series, 3, Boole Press, Dún Laoghaire, 1983. |
[17] |
P. Pietra and N. Vauchelet, Modeling and simulation of the diffusive transport in a nanoscale Double-Gate MOSFET, J. Comp. Elec., 7 (2008), 52-65.
doi: 10.1007/s10825-008-0253-z. |
[18] |
F. Poupaud, Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers, Asymptotic Anal., 4 (1991), 293-317. |
[19] |
N. Vauchelet, Diffusive limit of a two dimensional kinetic system of partially quantized particles, J. Stat. Phys., 139 (2010), 882-914.
doi: 10.1007/s10955-010-9970-3. |
[20] |
N. Vauchelet, Diffusive transport of partially quantized particles: $L\log L$ solutions, Math. Models Methods Appl. Sci., 18 (2008), 489-510.
doi: 10.1142/S0218202508002759. |
[21] |
T. Wenckebach, "Essential of Semiconductor Physics,'' Wiley, Chichester, 1999. |
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