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Volumn 67, Issue 1, 2006, Pages 46-68

Derivation of new quantum hydrodynamic equations using entropy minimization

Author keywords

Current voltage characteristics; Entropy minimization; Finite difference discretization; Moment method; Numerical simulations; Quantum Maxwellian; Quantum moment hydrodynamics; Resonant tunneling diode

Indexed keywords

CURRENT VOLTAGE CHARACTERISTICS; ENTROPY; MATHEMATICAL MODELS; MAXWELL EQUATIONS; NUMERICAL METHODS; OPTIMIZATION;

EID: 33847733017     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/050644823     Document Type: Article
Times cited : (60)

References (31)
  • 1
    • 0000977058 scopus 로고
    • Quantum correction to the equation of state of an electron gas in a semiconductor
    • M. ANCONA AND G. IAFRATE, Quantum correction to the equation of state of an electron gas in a semiconductor, Phys. Rev. B, 39 (1989), pp. 9536-9540.
    • (1989) Phys. Rev. B , vol.39 , pp. 9536-9540
    • ANCONA, M.1    IAFRATE, G.2
  • 2
    • 0000776042 scopus 로고
    • Macroscopic physics of the silicon inversion layer
    • M. ANCONA AND H. TIERSTEN, Macroscopic physics of the silicon inversion layer, Phys. Rev. B, 35 (1987), pp. 7959-7965.
    • (1987) Phys. Rev. B , vol.35 , pp. 7959-7965
    • ANCONA, M.1    TIERSTEN, H.2
  • 3
    • 0022044296 scopus 로고
    • An investigation of steady-state velocity overshoot effects in Si and GaAs devices
    • G. BACCARANI AND M. WORDEMAN, An investigation of steady-state velocity overshoot effects in Si and GaAs devices, Solid-State Electronics, 28 (1985), pp. 407-416.
    • (1985) Solid-State Electronics , vol.28 , pp. 407-416
    • BACCARANI, G.1    WORDEMAN, M.2
  • 4
    • 26344468007 scopus 로고
    • A model for collision processes in gases, I. Small amplitude processes in charged and neutral one-component systems
    • P. BHATNAGAR, E. GROSS, AND M. KROOK, A model for collision processes in gases, I. Small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94 (1954), pp. 511-525.
    • (1954) Phys. Rev , vol.94 , pp. 511-525
    • BHATNAGAR, P.1    GROSS, E.2    KROOK, M.3
  • 5
    • 17144376255 scopus 로고
    • Path integral approach to quantum Brownian motion
    • A. CALDEIRA AND A. LEGGETT, Path integral approach to quantum Brownian motion, Phys. A, 121A (1983), pp. 587-616.
    • (1983) Phys. A , vol.121 A , pp. 587-616
    • CALDEIRA, A.1    LEGGETT, A.2
  • 6
    • 0030127934 scopus 로고    scopus 로고
    • A finite element method for the quantum hydrodynamic model for semiconductor devices
    • Z. CHEN, A finite element method for the quantum hydrodynamic model for semiconductor devices, Comput. Math. Appl., 31 (1996), pp. 17-26.
    • (1996) Comput. Math. Appl , vol.31 , pp. 17-26
    • CHEN, Z.1
  • 7
    • 27744435255 scopus 로고    scopus 로고
    • Quantum hydrodynamic models derived from the entropy principle
    • P. DEGOND, F. MÉHATS, AND C. RINGHOFER, Quantum hydrodynamic models derived from the entropy principle, Contemp. Math., 371 (2005), pp. 107-131.
    • (2005) Contemp. Math , vol.371 , pp. 107-131
    • DEGOND, P.1    MÉHATS, F.2    RINGHOFER, C.3
  • 8
    • 15244345981 scopus 로고    scopus 로고
    • Quantum energy-transport and drift-diffusion models
    • P. DEGOND, F. MÉHATS, AND C. RINGHOFER, Quantum energy-transport and drift-diffusion models, J. Statist. Phys., 118 (2005), pp. 625-665.
    • (2005) J. Statist. Phys , vol.118 , pp. 625-665
    • DEGOND, P.1    MÉHATS, F.2    RINGHOFER, C.3
  • 9
    • 0037837827 scopus 로고    scopus 로고
    • Quantum moment hydrodynamics and the entropy principle
    • P. DEGOND AND C. RINGHOFER, Quantum moment hydrodynamics and the entropy principle, J. Statist. Phys., 112 (2003), pp. 587-628.
    • (2003) J. Statist. Phys , vol.112 , pp. 587-628
    • DEGOND, P.1    RINGHOFER, C.2
  • 10
    • 33847746855 scopus 로고    scopus 로고
    • J. E. DENNIS, JR., AND R. B. SCHNABEL, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM, Philadelphia, 1996.
    • J. E. DENNIS, JR., AND R. B. SCHNABEL, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM, Philadelphia, 1996.
  • 11
    • 0000996833 scopus 로고
    • Form of the quantum potential for use in hydrodynamic equations for semiconductor device modeling
    • D. FERRY AND J.-R. ZHOU, Form of the quantum potential for use in hydrodynamic equations for semiconductor device modeling, Phys. Rev. B, 48 (1993), pp. 7944-7950.
    • (1993) Phys. Rev. B , vol.48 , pp. 7944-7950
    • FERRY, D.1    ZHOU, J.-R.2
  • 12
    • 0028413338 scopus 로고
    • The quantum hydrodynamic model for semiconductor devices
    • C. L. GARDNER, The quantum hydrodynamic model for semiconductor devices, SIAM J. Appl. Math., 54 (1994), pp. 409-427.
    • (1994) SIAM J. Appl. Math , vol.54 , pp. 409-427
    • GARDNER, C.L.1
  • 13
    • 0029482315 scopus 로고
    • Resonant tunneling in the quantum hydrodynamic model
    • C. GARDNER, Resonant tunneling in the quantum hydrodynamic model, VLSI Design, 3 (1995), pp. 201-210.
    • (1995) VLSI Design , vol.3 , pp. 201-210
    • GARDNER, C.1
  • 14
    • 0001719509 scopus 로고    scopus 로고
    • Smooth quantum potential for the hydrodynamic model
    • C. GARDNER AND C. RINGHOFER, Smooth quantum potential for the hydrodynamic model, Phys. Rev. E, 53 (1996), pp. 157-167.
    • (1996) Phys. Rev. E , vol.53 , pp. 157-167
    • GARDNER, C.1    RINGHOFER, C.2
  • 15
    • 0032097932 scopus 로고    scopus 로고
    • Approximation of thermal equilibrium for quantum gases with discontinuous potentials and application to semiconductor devices
    • C. L. GARDNER AND C. RINGHOFER, Approximation of thermal equilibrium for quantum gases with discontinuous potentials and application to semiconductor devices, SIAM J. Appl. Math., 58 (1998), pp. 780-805.
    • (1998) SIAM J. Appl. Math , vol.58 , pp. 780-805
    • GARDNER, C.L.1    RINGHOFER, C.2
  • 16
    • 0033672512 scopus 로고    scopus 로고
    • The Chapman-Enskog expansion and the quantum hydrodynamic model for semiconductor devices
    • C. GARDNER AND C. RINGHOFER, The Chapman-Enskog expansion and the quantum hydrodynamic model for semiconductor devices, VLSI Design, 10 (2000), pp. 415-435.
    • (2000) VLSI Design , vol.10 , pp. 415-435
    • GARDNER, C.1    RINGHOFER, C.2
  • 17
    • 33847727669 scopus 로고    scopus 로고
    • I. GASSER, P. MARKOWICH, D. SCHMIDT, AND A. UNTERREITER, Macroscopic theory of charged quantum fluids, in Mathematical Problems in Semiconductor Physics, P. Marcati, P. A. Markowich, and R. Natalini, eds., Res. Notes Math. Ser. 340, Pitman, Boston, 1995, pp. 42-75.
    • I. GASSER, P. MARKOWICH, D. SCHMIDT, AND A. UNTERREITER, Macroscopic theory of charged quantum fluids, in Mathematical Problems in Semiconductor Physics, P. Marcati, P. A. Markowich, and R. Natalini, eds., Res. Notes Math. Ser. 340, Pitman, Boston, 1995, pp. 42-75.
  • 18
    • 0024930617 scopus 로고
    • Quantum moment balance equations and resonant tunneling structures
    • H. GRUBIN AND J. KRESKOVSKY, Quantum moment balance equations and resonant tunneling structures, Solid-State Electronics, 32 (1989), pp. 1071-1075.
    • (1989) Solid-State Electronics , vol.32 , pp. 1071-1075
    • GRUBIN, H.1    KRESKOVSKY, J.2
  • 19
    • 16644368793 scopus 로고    scopus 로고
    • Analysis of the viscous quantum hydrodynamic equations for semiconductors
    • M. GUALDANI AND A. JÜNGEL, Analysis of the viscous quantum hydrodynamic equations for semiconductors, European J. Appl. Math., 15 (2004), pp. 577-595.
    • (2004) European J. Appl. Math , vol.15 , pp. 577-595
    • GUALDANI, M.1    JÜNGEL, A.2
  • 21
    • 27744473992 scopus 로고    scopus 로고
    • A derivation of the isothermal quantum hydrodynamic equations using entropy minimization
    • A. JÜNGEL AND D. MATTHES, A derivation of the isothermal quantum hydrodynamic equations using entropy minimization, Z. Angew. Math. Mech., 85 (2005), pp. 806-814.
    • (2005) Z. Angew. Math. Mech , vol.85 , pp. 806-814
    • JÜNGEL, A.1    MATTHES, D.2
  • 24
    • 33747894095 scopus 로고    scopus 로고
    • Numerical approximation of the viscous quantum hydrodynamic model for semiconductors
    • A. JÜNGEL AND S. TANG, Numerical approximation of the viscous quantum hydrodynamic model for semiconductors, Appl. Numer. Math., 56 (2006), pp. 899-915.
    • (2006) Appl. Numer. Math , vol.56 , pp. 899-915
    • JÜNGEL, A.1    TANG, S.2
  • 25
    • 0030534703 scopus 로고    scopus 로고
    • Moment closure hierarchies for kinetic theories
    • C. LEVERMORE, Moment closure hierarchies for kinetic theories, J. Statist. Phys., 83 (1996), pp. 1021-1065.
    • (1996) J. Statist. Phys , vol.83 , pp. 1021-1065
    • LEVERMORE, C.1
  • 26
    • 34250913931 scopus 로고
    • Quantentheorie in hydrodynamischer form
    • E. MADELUNG, Quantentheorie in hydrodynamischer form, Z. Physik, 40 (1927), pp. 322-326.
    • (1927) Z. Physik , vol.40 , pp. 322-326
    • MADELUNG, E.1
  • 27
    • 0033348545 scopus 로고    scopus 로고
    • Weak limits of the quantum hydrodynamic model
    • P. PIETRA AND C. POHL, Weak limits of the quantum hydrodynamic model, VLSI Design, 9 (1999), pp. 427-434.
    • (1999) VLSI Design , vol.9 , pp. 427-434
    • PIETRA, P.1    POHL, C.2
  • 28
  • 29
    • 0004124616 scopus 로고    scopus 로고
    • Quantum Effects in MOS Devices
    • Hartung-Gorre, Konstanz, Germany
    • A. WETTSTEIN, Quantum Effects in MOS Devices, Series in Microelectronics 94, Hartung-Gorre, Konstanz, Germany, 2000.
    • (2000) Series in Microelectronics , vol.94
    • WETTSTEIN, A.1
  • 30
    • 0035249575 scopus 로고    scopus 로고
    • Quantum device-simulation with the density-gradient model on unstructured grids
    • A. WETTSTEIN, A. SCHENK, AND W. FICHTNER, Quantum device-simulation with the density-gradient model on unstructured grids, IEEE Trans. Electron. Dev., 48 (2001), pp. 279-284.
    • (2001) IEEE Trans. Electron. Dev , vol.48 , pp. 279-284
    • WETTSTEIN, A.1    SCHENK, A.2    FICHTNER, W.3
  • 31
    • 33745014742 scopus 로고
    • On the quantum correction for thermodynamic equilibrium
    • E. WIGNER, On the quantum correction for thermodynamic equilibrium, Phys. Rev., 40 (1932), pp. 749-759.
    • (1932) Phys. Rev , vol.40 , pp. 749-759
    • WIGNER, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.