Modelling, analysis and asymptotics, Lectures from the C, I.M.E. Summer School, 2006. ,
Homogenization of the Schr??dinger Equation and Effective Mass Theorems, Communications in Mathematical Physics, vol.90, issue.1, pp.1-22, 2005. ,
DOI : 10.1007/s00220-005-1329-2
A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations, Commun. Comput. Phys, vol.4, issue.4, pp.729-796, 2008. ,
Carbon nanotube electronics, IEEE Transactions On Nanotechnology, vol.1, issue.4, pp.184-189, 2002. ,
DOI : 10.1109/TNANO.2002.807390
MATHEMATICAL CONCEPTS OF OPEN QUANTUM BOUNDARY CONDITIONS, Transport Theory and Statistical Physics, vol.6, issue.4-6, pp.561-584, 2001. ,
DOI : 10.1080/00411458908204692
Solid State Physics, 1976. ,
Quantum Transport in Crystals: Effective Mass Theorem and K??P Hamiltonians, Communications in Mathematical Physics, vol.98, issue.4, pp.567-607, 2011. ,
DOI : 10.1007/s00220-011-1344-4
Quantum drift-diffusion modeling of spin transport in nanostructures, Journal of Mathematical Physics, vol.51, issue.5, p.53304, 2010. ,
DOI : 10.1063/1.3380530
URL : https://hal.archives-ouvertes.fr/hal-00521507
A 1D coupled Schr??dinger drift-diffusion model including collisions, Journal of Computational Physics, vol.203, issue.1, pp.129-153, 2005. ,
DOI : 10.1016/j.jcp.2004.08.009
A Hybrid Kinetic-Quantum Model for Stationary Electron Transport, Journal of Statistical Physics, vol.90, issue.3-4, pp.627-662, 1998. ,
DOI : 10.1023/A:1023216701688
On a multidimensional Schr??dinger???Poisson scattering model for semiconductors, Journal of Mathematical Physics, vol.41, issue.7, pp.4241-4261, 2000. ,
DOI : 10.1063/1.533397
On a hierarchy of macroscopic models for semiconductors, Journal of Mathematical Physics, vol.37, issue.7, pp.3306-3333, 1996. ,
DOI : 10.1063/1.531567
On a one-dimensional Schr??dinger-Poisson scattering model, Zeitschrift f??r angewandte Mathematik und Physik, vol.48, issue.1, pp.135-155, 1997. ,
DOI : 10.1007/PL00001463
On hierarchy of macroscopic models for semiconductor spintronics ,
DIFFUSIVE TRANSPORT OF PARTIALLY QUANTIZED PARTICLES: EXISTENCE, UNIQUENESS AND LONG-TIME BEHAVIOUR, Proc. Edinb, pp.49513-549, 2006. ,
DOI : 10.1017/S0013091504000987
URL : https://hal.archives-ouvertes.fr/hal-00378536
An accelerated algorithm for 2D simulations of the quantum ballistic transport in nanoscale MOSFETs, Journal of Computational Physics, vol.225, issue.1, pp.74-99, 2007. ,
DOI : 10.1016/j.jcp.2006.11.028
URL : https://hal.archives-ouvertes.fr/hal-00393043
Emission of spin waves by a magnetic multilayer traversed by a current, Physical Review B, vol.54, issue.13, pp.9353-9358, 1996. ,
DOI : 10.1103/PhysRevB.54.9353
Analyse fonctionnelle, Collection Mathématiques Appliquées pour la Ma??triseMa??trise. [Collection of Applied Mathematics for the Master's Degree]. Masson, 1983. ,
Mixed and hybrid finite element methods, of Springer Series in Computational Mathematics, 1991. ,
DOI : 10.1007/978-1-4612-3172-1
Discretization of semiconductor device problems. I. In Handbook of numerical analysis, Handb. Numer. Anal., XIII, vol.XIII, pp.317-441, 2005. ,
Méthodes d'´ eléments finis mixtes et schéma de Scharfetter- Gummel, C. R. Acad. Sci. Paris Sér. I Math, vol.305, issue.13, pp.599-604, 1987. ,
Numerical simulation of semiconductor devices, Proceedings of the Eighth International Conference on Computing Methods in Applied Sciences and Engineering, pp.493-514, 1987. ,
DOI : 10.1016/0045-7825(89)90044-3
Two-Dimensional Exponential Fitting and Applications to Drift-Diffusion Models, SIAM Journal on Numerical Analysis, vol.26, issue.6, pp.1342-1355, 1989. ,
DOI : 10.1137/0726078
Finite element approximation of electrostatic potential in one-dimensional multilayer structures with quantized electronic charge, Computing, vol.45, issue.3, pp.251-264, 1990. ,
High Performance Silicon Nanowire Field Effect Transistors, Nano Letters, vol.3, issue.2, pp.149-152, 2003. ,
DOI : 10.1021/nl025875l
A Coupled Schr??dinger Drift-Diffusion Model for Quantum Semiconductor Device Simulations, Journal of Computational Physics, vol.181, issue.1, pp.222-259, 2002. ,
DOI : 10.1006/jcph.2002.7122
An Effective Mass Theorem for the Bidimensional Electron Gas in a Strong Magnetic Field, Communications in Mathematical Physics, vol.66, issue.3, pp.829-870, 2009. ,
DOI : 10.1007/s00220-009-0868-3
URL : https://hal.archives-ouvertes.fr/hal-00378528
High-performance thin-film transistors using semiconductor nanowires and nanoribbons, Nature, vol.425, issue.6955, pp.274-278, 2003. ,
DOI : 10.1038/nature01996
Discrete transparent boundary conditions for the Schrödinger equation, Riv. Mat. Univ. Parma, vol.4, issue.6, pp.57-108, 2001. ,
Diffusion models for spin transport derived from the spinor Boltzmann equation, Communications in Mathematical Sciences, vol.12, issue.3 ,
DOI : 10.4310/CMS.2014.v12.n3.a9
URL : https://hal.archives-ouvertes.fr/hal-00624338
Boundary conditions for open quantum systems driven far from equilibrium, Reviews of Modern Physics, vol.62, issue.3, pp.745-791, 1990. ,
DOI : 10.1103/RevModPhys.62.745
Band Effects on the Transport Characteristics of Ultrascaled SNW-FETs, IEEE Transactions on Nanotechnology, vol.7, issue.6, pp.700-709, 2008. ,
DOI : 10.1109/TNANO.2008.2005777
MIXED FINITE ELEMENT SIMULATION OF HETEROJUNCTION STRUCTURES INCLUDING A BOUNDARY LAYER MODEL FOR THE QUASI???FERMI LEVELS, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.13, issue.4, pp.757-770, 1994. ,
DOI : 10.1108/eb051893
SEMICONDUCTOR DEVICE MODELLING FOR HETEROJUNCTIONS STRUCTURES WITH MIXED FINITE ELEMENTS, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.10, issue.4, pp.425-438, 1991. ,
DOI : 10.1108/eb051718
A transport equation for confined structures derived from the Boltzmann equation, Communications in Mathematical Sciences, vol.9, issue.3, pp.829-857, 2011. ,
DOI : 10.4310/CMS.2011.v9.n3.a8
Perturbation theory for linear operators, 1976. ,
The quantum transmitting boundary method, Journal of Applied Physics, vol.67, issue.10, pp.6353-6359, 1990. ,
DOI : 10.1063/1.345156
Motion of Electrons and Holes in Perturbed Periodic Fields, Physical Review, vol.97, issue.4, pp.869-883, 1955. ,
DOI : 10.1103/PhysRev.97.869
Semiconductor equations, 1990. ,
DOI : 10.1007/978-3-7091-6961-2
Single-walled carbon nanotube electronics, IEEE Transactions On Nanotechnology, vol.1, issue.1, pp.78-85, 2002. ,
DOI : 10.1109/TNANO.2002.1005429
Analysis of mathematical models of semiconductor devices, volume 3 of Advances in Numerical Computation Series, 1983. ,
Diffusion limit of a generalized matrix boltzmann equation for spin-polarized transport ,
Schrödinger-Poisson systems in dimension d ? 3: the whole-space case, Proc. Roy. Soc. Edinburgh Sect. A, pp.1179-1201, 1993. ,
A variational formulation of schr??dinger-poisson systems in dimension d ??? 3, Communications in Partial Differential Equations, vol.71, issue.7-8, pp.1125-1147, 1993. ,
DOI : 10.1080/03605309308820966
Atomistic Modeling of Gate-All-Around Si-Nanowire Field-Effect Transistors, IEEE Transactions on Electron Devices, vol.54, issue.12, pp.3159-3167, 2007. ,
DOI : 10.1109/TED.2007.908883
Modeling and simulation of the diffusive transport in a nanoscale Double-Gate MOSFET, Journal of Computational Electronics, vol.11, issue.10, pp.52-65, 2008. ,
DOI : 10.1007/s10825-008-0253-z
Subband decomposition approach for the simulation of quantum electron transport in nanostructures, Journal of Computational Physics, vol.202, issue.1, pp.150-180, 2005. ,
DOI : 10.1016/j.jcp.2004.07.003
Diffusion approximation of the linear semiconductor Boltzmann equation: analysis of boundary layers, Asymptotic Anal, vol.4, issue.4, pp.293-317, 1991. ,
Semi-classical limits in a crystal with exterior potentials and effective mass theorems., Communications in Partial Differential Equations, vol.21, issue.11, pp.11-121897, 1996. ,
DOI : 10.1080/03605309608821248
Methods of modern mathematical physics, IV -Analysis of operators, 1978. ,
Self-consistent treatment of nonequilibrium spin torques in magnetic multilayers, Physical Review B, vol.67, issue.10, p.104430, 2003. ,
DOI : 10.1103/PhysRevB.67.104430
Current-driven excitation of magnetic multilayers, Journal of Magnetism and Magnetic Materials, vol.159, issue.1-2, pp.1-7, 1996. ,
DOI : 10.1016/0304-8853(96)00062-5
Effective Mass Theorems for Nonlinear Schr??dinger Equations, SIAM Journal on Applied Mathematics, vol.66, issue.3, pp.820-842, 2006. ,
DOI : 10.1137/050623759
URL : http://arxiv.org/pdf/math-ph/0410017v1.pdf
Adiabatic perturbation theory in quantum dynamics, Lecture Notes in Mathematics, vol.1821, 2003. ,
DOI : 10.1007/b13355
L SOLUTIONS, Mathematical Models and Methods in Applied Sciences, vol.18, issue.04, pp.489-510, 2008. ,
DOI : 10.1142/S0218202508002759
URL : https://hal.archives-ouvertes.fr/hal-00635512
Diffusive Limit of a Two Dimensional Kinetic System of??Partially Quantized Particles, Journal of Statistical Physics, vol.96, issue.3, pp.882-914, 2010. ,
DOI : 10.1007/s10955-010-9970-3
Essential of Semiconductor Physics, 1999. ,
Efficient modeling techniques for atomistic-based electronic density calculations, Journal of Computational Electronics, vol.42, issue.8, pp.427-431, 2008. ,
DOI : 10.1007/s10825-008-0179-5
Mechanisms of Spin-Polarized Current-Driven Magnetization Switching, Physical Review Letters, vol.88, issue.23, p.236601, 2002. ,
DOI : 10.1103/PhysRevLett.88.236601
Spintronics: Fundamentals and applications, Reviews of Modern Physics, vol.76, issue.2, pp.323-410, 2004. ,
DOI : 10.1103/RevModPhys.76.323
Quantum correction to the equation of state of an electron gas in a semiconductor, Physical Review B, vol.39, issue.13, pp.9536-9540, 1989. ,
DOI : 10.1103/PhysRevB.39.9536
Discretization of semiconductor device problems. II. In Handbook of numerical analysis, Handb. Numer. Anal., XIII, vol.XIII, pp.443-522, 2005. ,
Solid State Physics, 1976. ,
A compact double-gate MOSFET model comprising quantum-mechanical and nonstatic effects, IEEE Transactions on Electron Devices, vol.46, issue.8, pp.1656-1666, 1999. ,
DOI : 10.1109/16.777154
Quantum Transport in Crystals: Effective Mass Theorem and K??P Hamiltonians, Communications in Mathematical Physics, vol.98, issue.4, pp.567-607, 2011. ,
DOI : 10.1007/s00220-011-1344-4
On a multidimensional Schr??dinger???Poisson scattering model for semiconductors, Journal of Mathematical Physics, vol.41, issue.7, pp.4241-4261, 2000. ,
DOI : 10.1063/1.533397
On a hierarchy of macroscopic models for semiconductors, J. Math. Phys, vol.37, issue.7, pp.3306-3333, 1996. ,
An energy-transport model for semiconductors derived from the Boltzmann equation, Journal of Statistical Physics, vol.5, issue.1-2, pp.205-231, 1996. ,
DOI : 10.1007/BF02179583
On a one-dimensional Schr??dinger-Poisson scattering model, Zeitschrift f??r angewandte Mathematik und Physik, vol.48, issue.1, pp.135-155, 1997. ,
DOI : 10.1007/PL00001463
On the convergence of the Boltzmann equation for semiconductors toward the energy transport model, J. Statist. Phys, vol.98, pp.3-4835, 2000. ,
Diffusion approximation for the one dimensional Boltzmann- Poisson system. Discrete Contin, Dyn. Syst. Ser. B, vol.4, issue.4, pp.1129-1142, 2004. ,
Kinetic equations and asymptotic theory, Series in Appl. Math, vol.4, 2000. ,
URL : https://hal.archives-ouvertes.fr/hal-00538692
On spherical harmonics expansion type modelsfor electron-phonon collisions, Mathematical Methods in the Applied Sciences, vol.43, issue.3, pp.247-271, 2003. ,
DOI : 10.1002/mma.353
Analyse fonctionnelle, Collection Mathématiques Appliquées pour la Ma??triseMa??trise. [Collection of Applied Mathematics for the Master's Degree]. Masson, 1983. ,
Discretization of semiconductor device problems. I. In Handbook of numerical analysis, Handb. Numer. Anal., XIII, vol.XIII, pp.317-441, 2005. ,
Numerical simulation of tunneling effects in nanoscale semiconductor devices using quantum corrected drift-diffusion models, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.19-22, pp.19-222193, 2006. ,
DOI : 10.1016/j.cma.2005.05.007
The Boltzmann equation and its applications, 1988. ,
DOI : 10.1007/978-1-4612-1039-9
Energy-Transport Models for Charge Carriers Involving Impact Ionization in Semiconductors, Transport Theory and Statistical Physics, vol.32, issue.2, pp.99-132, 2003. ,
DOI : 10.1081/TT-120019039
Quantum-corrected drift-diffusion models for transport in semiconductor devices, Journal of Computational Physics, vol.204, issue.2, pp.533-561, 2005. ,
DOI : 10.1016/j.jcp.2004.10.029
AN INFINITE SYSTEM OF DIFFUSION EQUATIONS ARISING IN TRANSPORT THEORY: THE COUPLED SPHERICAL HARMONICS EXPANSION MODEL, Mathematical Models and Methods in Applied Sciences, vol.11, issue.05, pp.903-932, 2001. ,
DOI : 10.1142/S0218202501001173
An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes, Journal of Computational Physics, vol.221, issue.1, pp.226-249, 2007. ,
DOI : 10.1016/j.jcp.2006.06.027
URL : https://hal.archives-ouvertes.fr/hal-00020907
Isothermal Quantum Hydrodynamics: Derivation, Asymptotic Analysis, and Simulation, Multiscale Modeling & Simulation, vol.6, issue.1, pp.246-272, 2007. ,
DOI : 10.1137/06067153X
URL : https://hal.archives-ouvertes.fr/hal-00364875
On quantum hydrodynamic and quantum energy transport models, Communications in Mathematical Sciences, vol.5, issue.4, pp.887-908, 2007. ,
DOI : 10.4310/CMS.2007.v5.n4.a8
URL : https://hal.archives-ouvertes.fr/hal-00368759
A Note on the Energy-Transport Limit of the Semiconductor Boltzmann Equation, Transport in transition regimes, pp.137-153, 2000. ,
DOI : 10.1007/978-1-4613-0017-5_8
Quantum Energy-Transport and Drift-Diffusion Models, Journal of Statistical Physics, vol.126, issue.3-4, pp.3-4625, 2005. ,
DOI : 10.1007/s10955-004-8823-3
URL : https://hal.archives-ouvertes.fr/hal-00378549
Quantum hydrodynamic models derived from the entropy principle, Nonlinear partial differential equations and related analysis, pp.107-131, 2005. ,
DOI : 10.1090/conm/371/06850
URL : https://hal.archives-ouvertes.fr/hal-00366178
A Note on quantum moment hydrodynamics and the entropy principle, Comptes Rendus Mathematique, vol.335, issue.11, pp.587-628, 2003. ,
DOI : 10.1016/S1631-073X(02)02595-5
Transport in nanostructures, 1997. ,
Sur les ??quations diff??rentielles lin??aires ?? coefficients p??riodiques, Annales scientifiques de l'??cole normale sup??rieure, vol.12, issue.2, pp.47-88, 1883. ,
DOI : 10.24033/asens.220
On the basic equations for carrier transport in semiconductors, Journal of Mathematical Analysis and Applications, vol.113, issue.1, pp.12-35, 1986. ,
DOI : 10.1016/0022-247X(86)90330-6
Band-Structure Effects in Ultrascaled Silicon Nanowires, IEEE Transactions on Electron Devices, vol.54, issue.9, pp.2243-2254, 2007. ,
DOI : 10.1109/TED.2007.902901
Limite fluide deséquationsdeséquations de Boltzmann des semi-conducteurs pour une statistique de Fermi-Dirac, Asymptotic Anal, vol.6, issue.2, pp.135-160, 1992. ,
A derivation of the isothermal quantum hydrodynamic equations using entropy minimization, ZAMM, vol.40, issue.11, pp.806-814, 2005. ,
DOI : 10.1002/zamm.200510232
Derivation of New Quantum Hydrodynamic Equations Using Entropy Minimization, SIAM Journal on Applied Mathematics, vol.67, issue.1, pp.46-68, 2006. ,
DOI : 10.1137/050644823
Moment closure hierarchies for kinetic theories, Journal of Statistical Physics, vol.23, issue.5-6, pp.1021-1065, 1996. ,
DOI : 10.1007/BF02179552
Motion of Electrons and Holes in Perturbed Periodic Fields, Physical Review, vol.97, issue.4, pp.869-883, 1955. ,
DOI : 10.1103/PhysRev.97.869
The stationary semiconductor device equations, 1986. ,
Semiconductor equations, 1990. ,
DOI : 10.1007/978-3-7091-6961-2
Diffusion Limit of a Semiconductor Boltzmann???Poisson System, SIAM Journal on Mathematical Analysis, vol.38, issue.6, pp.1788-1807, 2007. ,
DOI : 10.1137/050630763
On equations describing steady-state carrier distributions in a semiconductor device, Communications on Pure and Applied Mathematics, vol.11, issue.6, pp.781-792, 1972. ,
DOI : 10.1002/cpa.3160250606
Asymptotical models and numerical schemes for quantum systems, 2005. ,
Schrödinger-Poisson systems in dimension d ? 3: the whole-space case, Proc. Roy. Soc. Edinburgh Sect. A, pp.1179-1201, 1993. ,
A variational formulation of schr??dinger-poisson systems in dimension d ??? 3, Communications in Partial Differential Equations, vol.71, issue.7-8, pp.1125-1147, 1993. ,
DOI : 10.1080/03605309308820966
Atomistic Modeling of Gate-All-Around Si-Nanowire Field-Effect Transistors, IEEE Transactions on Electron Devices, vol.54, issue.12, pp.3159-3167, 2007. ,
DOI : 10.1109/TED.2007.908883
Semiconductor device modelling from the numerical point of view, International Journal for Numerical Methods in Engineering, vol.2, issue.4, pp.763-838, 1987. ,
DOI : 10.1002/nme.1620240408
Modélisation et simulations numériques du transport quantique ballistique dans les nanostructures semi-conductrices, 2001. ,
Diffusion approximation of the linear semiconductor Boltzmann equation: analysis of boundary layers, Asymptotic Anal, vol.4, issue.4, pp.293-317, 1991. ,
Large-signal analysis of a silicon Read diode oscillator, IEEE Transactions on Electron Devices, vol.16, issue.1, pp.64-77, 1969. ,
DOI : 10.1109/T-ED.1969.16566
Semiconductor physics. An introduction, 2004. ,
Scaling theory for double-gate SOI MOSFET's, IEEE Transactions on Electron Devices, vol.40, issue.12, pp.402326-2329, 1993. ,
DOI : 10.1109/16.249482
A Review of Mathematical Topics in Collisional Kinetic Theory, Handbook of mathematical fluid dynamics, pp.71-305, 2002. ,
DOI : 10.1016/S1874-5792(02)80004-0
Quantum Semiconductor Structures, 1991. ,
Essential of Semiconductor Physics [1] G. Allaire and A. Piatnitski. Homogenization of the Schrödinger equation and effective mass theorems, Comm. Math. Phys, vol.258, issue.1, pp.1-22, 1999. ,
Carbon nanotube electronics, IEEE Transactions On Nanotechnology, vol.1, issue.4, pp.184-189, 2002. ,
DOI : 10.1109/TNANO.2002.807390
Solid State Physics, 1976. ,
Quantum Transport in Crystals: Effective Mass Theorem and K??P Hamiltonians, Communications in Mathematical Physics, vol.98, issue.4, pp.567-607, 2011. ,
DOI : 10.1007/s00220-011-1344-4
AN EFFECTIVE MASS MODEL FOR THE SIMULATION OF ULTRA-SCALED CONFINED DEVICES, Mathematical Models and Methods in Applied Sciences, vol.22, issue.12 ,
DOI : 10.1142/S021820251250039X
URL : https://hal.archives-ouvertes.fr/hal-00848960
High Performance Silicon Nanowire Field Effect Transistors, Nano Letters, vol.3, issue.2, pp.149-152, 2003. ,
DOI : 10.1021/nl025875l
An Effective Mass Theorem for the Bidimensional Electron Gas in a Strong Magnetic Field, Communications in Mathematical Physics, vol.66, issue.3, pp.829-870, 2009. ,
DOI : 10.1007/s00220-009-0868-3
URL : https://hal.archives-ouvertes.fr/hal-00378528
High-performance thin-film transistors using semiconductor nanowires and nanoribbons, Nature, vol.425, issue.6955, pp.274-278, 2003. ,
DOI : 10.1038/nature01996
Band Effects on the Transport Characteristics of Ultrascaled SNW-FETs, IEEE Transactions on Nanotechnology, vol.7, issue.6, pp.700-709, 2008. ,
DOI : 10.1109/TNANO.2008.2005777
Perturbation theory for linear operators, 1976. ,
DOI : 10.1007/978-3-662-12678-3
Motion of Electrons and Holes in Perturbed Periodic Fields, Physical Review, vol.97, issue.4, pp.869-883, 1955. ,
DOI : 10.1103/PhysRev.97.869
Single-walled carbon nanotube electronics, IEEE Transactions On Nanotechnology, vol.1, issue.1, pp.78-85, 2002. ,
DOI : 10.1109/TNANO.2002.1005429
Atomistic Modeling of Gate-All-Around Si-Nanowire Field-Effect Transistors, IEEE Transactions on Electron Devices, vol.54, issue.12, pp.3159-3167, 2007. ,
DOI : 10.1109/TED.2007.908883
Semi-classical limits in a crystal with exterior potentials and effective mass theorems., Communications in Partial Differential Equations, vol.21, issue.11, pp.11-121897, 1996. ,
DOI : 10.1080/03605309608821248
Effective Mass Theorems for Nonlinear Schr??dinger Equations, SIAM Journal on Applied Mathematics, vol.66, issue.3, pp.820-842, 2006. ,
DOI : 10.1137/050623759
Adiabatic perturbation theory in quantum dynamics, Lecture Notes in Mathematics, vol.1821, 2003. ,
DOI : 10.1007/b13355
WKB-Based Schemes for the Oscillatory 1D Schr??dinger Equation in the Semiclassical Limit, SIAM Journal on Numerical Analysis, vol.49, issue.4, pp.1436-1460, 2011. ,
DOI : 10.1137/100800373
On a one-dimensional Schr??dinger-Poisson scattering model, Zeitschrift f??r angewandte Mathematik und Physik, vol.48, issue.1, pp.135-155, 1997. ,
DOI : 10.1007/PL00001463
Mathematical analysis of the two-band Schrödinger model, Math. Methods Appl. Sci, issue.10, pp.311131-1151, 2008. ,
An accelerated algorithm for 2D simulations of the quantum ballistic transport in nanoscale MOSFETs, Journal of Computational Physics, vol.225, issue.1, pp.74-99, 2007. ,
DOI : 10.1016/j.jcp.2006.11.028
URL : https://hal.archives-ouvertes.fr/hal-00393043
Multiscale simulation of transport in an open quantum system: resonances and WKB interpolation, J. Comput. Phys, vol.213, issue.1, pp.288-310, 2006. ,
Computing the steady states for an asymptotic model of quantum transport in resonant heterostructures, Journal of Computational Physics, vol.219, issue.2, pp.644-670, 2006. ,
DOI : 10.1016/j.jcp.2006.04.008
Far from equilibrium steady states of 1D-Schr??dinger???Poisson systems with quantum wells I, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.25, issue.5, pp.937-968, 2008. ,
DOI : 10.1016/j.anihpc.2007.05.007
Far from equilibrium steady states of 1D- Schrödinger-Poisson systems with quantum wells, II. J. Math. Soc. Japan, issue.1, pp.6165-106, 2009. ,
Finite element approximation of electrostatic potential in one-dimensional multilayer structures with quantized electronic charge, Computing, vol.45, issue.3, pp.251-264, 1990. ,
Boundary conditions for open quantum systems driven far from equilibrium, Reviews of Modern Physics, vol.62, issue.3, pp.745-791, 1990. ,
DOI : 10.1103/RevModPhys.62.745
Band Effects on the Transport Characteristics of Ultrascaled SNW-FETs, IEEE Transactions on Nanotechnology, vol.7, issue.6, pp.700-709, 2008. ,
DOI : 10.1109/TNANO.2008.2005777
Band-Structure Effects in Ultrascaled Silicon Nanowires, IEEE Transactions on Electron Devices, vol.54, issue.9, pp.2243-2254, 2007. ,
DOI : 10.1109/TED.2007.902901
Analysis of a diffusive effective mass model for nanowires, Kinetic and Related Models, vol.4, issue.4 ,
DOI : 10.3934/krm.2011.4.1121
URL : https://hal.archives-ouvertes.fr/hal-00593984
ARPACK User's Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods ,
The quantum transmitting boundary method, Journal of Applied Physics, vol.67, issue.10, pp.6353-6359, 1990. ,
DOI : 10.1063/1.345156
Hierarchical simulation of transport in silicon nanowire transistors, Journal of Computational Electronics, vol.69, issue.3, pp.415-418, 2008. ,
DOI : 10.1007/s10825-008-0242-2
Band structure and transport properties of carbon nanotubes using a local pseudopotential and a transfer-matrix technique, Carbon, vol.42, issue.10, pp.2057-2066, 2004. ,
DOI : 10.1016/j.carbon.2004.04.017
Numerical analysis of a multiscale finite element scheme for the resolution of the stationary Schr??dinger equation, Numerische Mathematik, vol.66, issue.1, pp.625-652, 2008. ,
DOI : 10.1007/s00211-007-0132-8
Modeling and simulation of the diffusive transport in a nanoscale Double-Gate MOSFET, Journal of Computational Electronics, vol.11, issue.10, pp.52-65, 2008. ,
DOI : 10.1007/s10825-008-0253-z
Transient simulations of a resonant tunneling diode, Journal of Applied Physics, vol.92, issue.4, pp.1987-1994, 2002. ,
DOI : 10.1063/1.1494127
Subband decomposition approach for the simulation of quantum electron transport in nanostructures, Journal of Computational Physics, vol.202, issue.1, pp.150-180, 2005. ,
DOI : 10.1016/j.jcp.2004.07.003
Implicitly Restarted Arnoldi/Lanczos Methods for Large Scale Eigenvalue Calculations, Institute for Computer Applications in Science and Engineering, 1996. ,
DOI : 10.1007/978-94-011-5412-3_5
Efficient modeling techniques for atomistic-based electronic density calculations, Journal of Computational Electronics, vol.42, issue.8, pp.427-431, 2008. ,
DOI : 10.1007/s10825-008-0179-5
Solid State Physics, 1976. ,
Un théorème de compacité, C. R. Acad. Sci. Paris, vol.256, pp.5042-5044, 1963. ,
Quantum Transport in Crystals: Effective Mass Theorem and K??P Hamiltonians, Communications in Mathematical Physics, vol.98, issue.4, pp.567-607, 2011. ,
DOI : 10.1007/s00220-011-1344-4
On a hierarchy of macroscopic models for semiconductors, J. Math. Phys, vol.37, issue.7, pp.3306-3333, 1996. ,
AN EFFECTIVE MASS MODEL FOR THE SIMULATION OF ULTRA-SCALED CONFINED DEVICES, Mathematical Models and Methods in Applied Sciences, vol.22, issue.12 ,
DOI : 10.1142/S021820251250039X
URL : https://hal.archives-ouvertes.fr/hal-00848960
On a Vlasov-Schrödinger-Poisson model, Comm. Partial Differential Equations, vol.29, issue.12, pp.173-206, 2004. ,
Semiclassical analysis of the Schrödinger equation with a partially confining potential, J. Math. Pures Appl, vol.84, issue.95, pp.580-614, 2005. ,
DIFFUSIVE TRANSPORT OF PARTIALLY QUANTIZED PARTICLES: EXISTENCE, UNIQUENESS AND LONG-TIME BEHAVIOUR, Proc. Edinb, pp.49513-549, 2006. ,
DOI : 10.1017/S0013091504000987
URL : https://hal.archives-ouvertes.fr/hal-00378536
Diffusion approximation for the one dimensional Boltzmann-Poisson system. Discrete Contin, Dyn. Syst. Ser. B, vol.4, issue.4, pp.1129-1142, 2004. ,
A transport equation for confined structures derived from the Boltzmann equation, Communications in Mathematical Sciences, vol.9, issue.3, pp.829-857, 2011. ,
DOI : 10.4310/CMS.2011.v9.n3.a8
Extremum problems for eigenvalues of elliptic operators, Frontiers in Mathematics . Birkhäuser Verlag, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00087731
Analysis of a diffusive effective mass model for nanowires, Kinetic and Related Models, vol.4, issue.4 ,
DOI : 10.3934/krm.2011.4.1121
URL : https://hal.archives-ouvertes.fr/hal-00593984
Semiconductor equations, 1990. ,
DOI : 10.1007/978-3-7091-6961-2
Diffusion Limit of a Semiconductor Boltzmann???Poisson System, SIAM Journal on Mathematical Analysis, vol.38, issue.6, pp.1788-1807, 2007. ,
DOI : 10.1137/050630763
Analysis of mathematical models of semiconductor devices, volume 3 of Advances in Numerical Computation Series, 1983. ,
Modeling and simulation of the diffusive transport in a nanoscale Double-Gate MOSFET, Journal of Computational Electronics, vol.11, issue.10, pp.52-65, 2008. ,
DOI : 10.1007/s10825-008-0253-z
Diffusion approximation of the linear semiconductor Boltzmann equation: analysis of boundary layers, Asymptotic Anal, vol.4, issue.4, pp.293-317, 1991. ,
L SOLUTIONS, Mathematical Models and Methods in Applied Sciences, vol.18, issue.04, pp.489-510, 2008. ,
DOI : 10.1142/S0218202508002759
URL : https://hal.archives-ouvertes.fr/hal-00635512
Diffusive Limit of a Two Dimensional Kinetic System of??Partially Quantized Particles, Journal of Statistical Physics, vol.96, issue.3, pp.882-914, 2010. ,
DOI : 10.1007/s10955-010-9970-3
Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates, ESAIM: Mathematical Modelling and Numerical Analysis, vol.19, issue.1, pp.7-32, 1985. ,
DOI : 10.1051/m2an/1985190100071
Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods, SIAM Journal on Numerical Analysis, vol.20, issue.3, pp.510-536, 1983. ,
DOI : 10.1137/0720034
PETSc users manual, 2010. ,
Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries, Modern Software Tools in Scientific Computing, pp.163-202, 1997. ,
DOI : 10.1007/978-1-4612-1986-6_8
A 1D coupled Schr??dinger drift-diffusion model including collisions, Journal of Computational Physics, vol.203, issue.1, pp.129-153, 2005. ,
DOI : 10.1016/j.jcp.2004.08.009
A Hybrid Kinetic-Quantum Model for Stationary Electron Transport, Journal of Statistical Physics, vol.90, issue.3-4, pp.627-662, 1998. ,
DOI : 10.1023/A:1023216701688
On a one-dimensional Schr??dinger-Poisson scattering model, Zeitschrift f??r angewandte Mathematik und Physik, vol.48, issue.1, pp.135-155, 1997. ,
DOI : 10.1007/PL00001463
AN EFFECTIVE MASS MODEL FOR THE SIMULATION OF ULTRA-SCALED CONFINED DEVICES, Mathematical Models and Methods in Applied Sciences, vol.22, issue.12 ,
DOI : 10.1142/S021820251250039X
URL : https://hal.archives-ouvertes.fr/hal-00848960
Mixed and hybrid finite element methods, of Springer Series in Computational Mathematics, 1991. ,
DOI : 10.1007/978-1-4612-3172-1
Méthodes d'´ eléments finis mixtes et schéma de Scharfetter-Gummel, C. R. Acad. Sci. Paris Sér. I Math, vol.305, issue.13, pp.599-604, 1987. ,
Numerical simulation of semiconductor devices, Proceedings of the Eighth International Conference on Computing Methods in Applied Sciences and Engineering, pp.493-514, 1987. ,
DOI : 10.1016/0045-7825(89)90044-3
Two-Dimensional Exponential Fitting and Applications to Drift-Diffusion Models, SIAM Journal on Numerical Analysis, vol.26, issue.6, pp.1342-1355, 1989. ,
DOI : 10.1137/0726078
COMSOL Multiphysics, a simulation software environment facilitating all steps in the modeling process ,
A Coupled Schr??dinger Drift-Diffusion Model for Quantum Semiconductor Device Simulations, Journal of Computational Physics, vol.181, issue.1, pp.222-259, 2002. ,
DOI : 10.1006/jcph.2002.7122
Semiconductor Simulations Using a Coupled Quantum Drift???Diffusion Schr??dinger???Poisson Model, SIAM Journal on Applied Mathematics, vol.66, issue.2, pp.554-572, 2005. ,
DOI : 10.1137/040610805
MIXED FINITE ELEMENT SIMULATION OF HETEROJUNCTION STRUCTURES INCLUDING A BOUNDARY LAYER MODEL FOR THE QUASI???FERMI LEVELS, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.13, issue.4, pp.757-770, 1994. ,
DOI : 10.1108/eb051893
SEMICONDUCTOR DEVICE MODELLING FOR HETEROJUNCTIONS STRUCTURES WITH MIXED FINITE ELEMENTS, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.10, issue.4, pp.425-438, 1991. ,
DOI : 10.1108/eb051718
Analysis of a diffusive effective mass model for nanowires, Kinetic and Related Models, vol.4, issue.4 ,
DOI : 10.3934/krm.2011.4.1121
URL : https://hal.archives-ouvertes.fr/hal-00593984
Semiconductor equations, 1990. ,
DOI : 10.1007/978-3-7091-6961-2
Modeling and simulation of the diffusive transport in a nanoscale Double-Gate MOSFET, Journal of Computational Electronics, vol.11, issue.10, pp.52-65, 2008. ,
DOI : 10.1007/s10825-008-0253-z
Density-matrix-based algorithm for solving eigenvalue problems, Physical Review B, vol.79, issue.11, p.115112, 2009. ,
DOI : 10.1103/PhysRevB.79.115112
A mixed finite element method for 2-nd order elliptic problems, Proc. Conf., Consiglio Naz, pp.292-315, 1975. ,
DOI : 10.1007/BF01436186
On a model of magnetization switching driven by a spin current: modelization and numerical simulations ,
Emission of spin waves by a magnetic multilayer traversed by a current, Physical Review B, vol.54, issue.13, pp.9353-9358, 1996. ,
DOI : 10.1103/PhysRevB.54.9353
Spin-polarized currents in ferromagnetic multilayers, Journal of Computational Physics, vol.224, issue.2, pp.699-711, 2007. ,
DOI : 10.1016/j.jcp.2006.10.029
Mathematical and numerical studies of non linear ferromagnetic materials, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, issue.3, pp.593-626, 1999. ,
DOI : 10.1051/m2an:1999154
URL : https://hal.archives-ouvertes.fr/inria-00073669
Self-consistent treatment of nonequilibrium spin torques in magnetic multilayers, Physical Review B, vol.67, issue.10, p.104430, 2003. ,
DOI : 10.1103/PhysRevB.67.104430
Current-driven excitation of magnetic multilayers, Journal of Magnetism and Magnetic Materials, vol.159, issue.1-2, pp.1-7, 1996. ,
DOI : 10.1016/0304-8853(96)00062-5
Anatomy of spin-transfer torque, Physical Review B, vol.66, issue.1, p.14407, 2002. ,
DOI : 10.1103/PhysRevB.66.014407
A Gauss???Seidel Projection Method for Micromagnetics Simulations, Journal of Computational Physics, vol.171, issue.1, pp.357-372, 2001. ,
DOI : 10.1006/jcph.2001.6793
Mechanisms of Spin-Polarized Current-Driven Magnetization Switching, Physical Review Letters, vol.88, issue.23, p.236601, 2002. ,
DOI : 10.1103/PhysRevLett.88.236601