A high order multi-resolution WENO numerical scheme for solving viscous quantum hydrodynamic model for semiconductor devices
Tài liệu tham khảo
Ancona, 1989, Quantum correction to the equation of state of an electron gas in a semiconductor, Phys Rev B, 39, 9536, 10.1103/PhysRevB.39.9536
Zhou, 1992, Simulation of ultra-small GaAs MESFET using quantum moment equations, IEEE Trans Electron Devices, 39, 473, 10.1109/16.123465
Wettstein, 2000, Quantum e registered ects in MOS devices
Degond, 2003, Quantum moment hydrodynamics and the entropy principle, J Stat Phys, 112, 587, 10.1023/A:1023824008525
Gardner, 1994, The quantum hydrodynamic model for semiconductor devices, SIAM J Appl Math, 54, 409, 10.1137/S0036139992240425
Markowich, 1990
Jungel, 2001, Quasi-hydrodynamic semiconductor equations
Buot, 1990, Lattice WeylWigner formulation of exact many-body quantum-transport theory and applications to novel solid-state quantum-based devices, Phys Rev B, 42, 9429, 10.1103/PhysRevB.42.9429
Argyres, 1992, Quantum kinetic equations for electrons in high electric and phonon fields, Phys Lett A, 171, 373, 10.1016/0375-9601(92)90660-E
Eu, 1994, Quantum kinetic theory of irreversible thermodynamics: Low-density gases, Phys Rev E, 50, 4380, 10.1103/PhysRevE.50.4380
Frommlet, 1999, A Wigner function approach to phonon scattering, VLSI Des, 9, 339, 10.1155/1999/30381
Lui, 2007, Local discontinuous Galerkin methods for moment models in device simulations: Performance assessment and two-dimensional results, Appl Numer Math, 57, 629, 10.1016/j.apnum.2006.07.027
Hoseinzadeh, 2017, J Mater Sci, Mater Electron, 28, 14855, 10.1007/s10854-017-7357-9
Jungel, 2006, Numerical approximation of the viscous quantum hydrodynamic model for semiconductors, Appl Numer Math, 1, 19
Gualdani, 2004, Analysis of the viscous quantum hydrodynamic equations for semiconductors, European J Appl Math, 15, 577, 10.1017/S0956792504005686
Gualdani, 2003, Exponential decay in time of solutions of the viscous quantum hydrodynamic equations, J Appl Math, 16, 1273
Jungel, 2007, Physical and numerical viscosity for quantum hydrodynamics, Comm Math Phys, 5, 447
Chen, 2007, The viscous model of quantum hydrodynamics in several dimensions, Math Models Methods Appl Sci, 17, 1065, 10.1142/S0218202507002200
Dreher, 2008, The transient equations of viscous quantum hydrodynamics, Math Models Methods Appl Sci, 31, 391, 10.1002/mma.918
Gamba, 2009, Global existence of solutions to one-dimensional viscous quantum hydrodynamic equations, J Differ Equ, 247, 3117, 10.1016/j.jde.2009.09.001
Nisar, 2018, Application of kinetic flux vector splitting scheme for solving viscous quantum hydrodynamical model of semiconductor devices, Res Phys, 11, 629
Zhu, 2018, A new type of multi-resolution WENO schemes with increasingly higher order of accuracy, J Comput Phys, 375, 659, 10.1016/j.jcp.2018.09.003
Liu, 1994, Weighted essentially non-oscillatory schemes, J Comput Phys, 115, 200, 10.1006/jcph.1994.1187
Jiang, 1996, Efficient implementation of weighted ENO schemes, J Comput Phys, 126, 202, 10.1006/jcph.1996.0130
Harten, 1991, 23665
Dahmen, 2001, Multiresolution schemes for conservation laws, Numer Math, 88, 399, 10.1007/s211-001-8009-3
Gasser I et al. Macroscopic theory of charged quantum fluids. In: Marcati P, editor. Mathematical problems in semiconductor physics. 1995. p. 42-75.
Petruccioli, 2014, Correspondence principle versus Planck-type theory of the atom, Arch Hist Exact Sci, 68, 599, 10.1007/s00407-014-0137-5
Caldeira, 1983, Path integral approach to quantum brownian motion, Phys A, 121, 587, 10.1016/0378-4371(83)90013-4
Arnold, 2000
Castella, 2000, Fokker-Planck equations as scaling limits of reversible quantum systems, J Stat Phys, 100, 543, 10.1023/A:1018667323830
Shu, 2003, High-order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD, Int J Comput Fluid Dyn, 30, 107, 10.1080/1061856031000104851
Shu, 2009, High order weighted essentially nonoscillatory schemes for convection dominated problems, SIAM Rev, 51, 82, 10.1137/070679065