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On a steady-state quantum hydrodynamic model for semiconductors. (English) Zbl 0882.76105

This paper develops a simplified one-dimensional hydrodynamic-like quantum model for the steady states of a semiconductor. It is a pure-state, single carrier transport model. The governing equations are self-consistent, in the sense that the electric field, which forms the forcing term in the momentum equation, is determined by the coupled Poisson equations. The novelty of the method (which may be extended to two-dimensional cases) is that it reduces the system of equations to an integro-differential equation with a set of boundary conditions, among which a condition is nonstandard and is equivalent to specifying the quantum potential at the current inflow boundary.
Reviewer: I.Bena (Iaşi)

MSC:

76Y05 Quantum hydrodynamics and relativistic hydrodynamics
81Q15 Perturbation theories for operators and differential equations in quantum theory
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References:

[1] Ancona, M. G.; Iafrate, G. J., Quantum correction to the equation of state of an electron gas in a semiconductor, Phys. Rev., B39, 9536-9540 (1989)
[2] Ancona, M. G.; Tiersten, H. F., Macroscopic physics of the silicon inversion layer, Phys. Rev., B35, 7959-7965 (1987)
[3] Grubin, H. L.; Kreskovsky, J. P., Quantum moment balance equations and resonant tunnelling structures, Solid-State Elec., 32, 1071-1075 (1989)
[4] Gardner, C. L., The quantum hydrodynamic model for semiconductor devices, SIAM J. appl. Math., 54, 409-427 (1994) · Zbl 0815.35111
[5] Chen, Z.; Cockburn, B.; Gardner, C. L.; Jerome, J. W., Quantum hydrodynamic simulation of hysteresis in the resonant tunneling diode, J. Comp. Phys., 117, 274-280 (1995) · Zbl 0833.76033
[6] Kluksdahl, N. C.; Kriman, A. M.; Ferry, D. K.; Ringhofer, C., Self-consistent study of the resonant tunneling diode, Phys. Rev., B39, 7720-7735 (1989)
[7] Gamba, I. M., Stationary transonic solutions of a one-dimensional hydrodynamic model for semiconductors, Communs partial diff. Eqns, 17, 553-577 (1992) · Zbl 0748.35049
[8] Zhang, B., Convergence of the Godunov scheme for a simplified one-dimensional hydrodynamic model for semiconductor devices, Communs math. Phys., 157, 1-22 (1993) · Zbl 0785.76053
[9] Gardner, C. L.; Jerome, J. W.; Rose, D. J., Numerical methods for the hydrodynamic device model: subsonic flow, IEEE Trans Comp. Des. Int. Circ. Sys., CAD-8, 501-507 (1989)
[10] Fatemi, E.; Jerome, J.; Osher, S., Solution of the hydrodynamic device model using high-order nonoscillatory shock capturing algorithms, IEEE Trans Comp. Des. Int. Circ. Sys., CAD-10, 232-244 (1991)
[11] Gamba I.M., Personal communication.; Gamba I.M., Personal communication.
[12] Lax, P. D.; Levermore, C. D., The small dispersion limit for the Korteweg-de Vries equation I, Communs pure appl. Math., 36, 253-290. (1983) · Zbl 0532.35067
[13] Courant, R.; Friedrichs, K. O., (Supersonic Flow and Shock-Waves (1967), J. Wiley and Sons: J. Wiley and Sons Cambridge) · Zbl 0041.11302
[14] Kinderlehrer, D.; Stampacchia, G., (An Introduction to Variational Inequalities and Their Applications (1980), Academic Press: Academic Press New York) · Zbl 0457.35001
[15] Gilbarg, D.; Trudinger, N. S., (Elliptic Partial Differential Equations of Second Order (1977), Springer: Springer New York) · Zbl 0361.35003
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