On a steady-state quantum hydrodynamic model for semiconductors

Nonlinear Analysis, Theory, Methods and Applications

Volumn 26, Issue 4, 1996, Pages 845-856

  Zhang, Bo ^a,b   Jerome, Joseph W ^a  

^a NORTHWESTERN UNIVERSITY   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Integro differential equation; Quantum hydrodynamic model; Quantum perturbation

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; HYDRODYNAMICS; INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; SEMICONDUCTOR MATERIALS; THEOREM PROVING;

BERNOULLI FUNCTION; QUANTUM HYDRODYNAMIC MODEL; QUANTUM PERTURBATION;

QUANTUM THEORY;

EID: 0030084587     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(94)00326-D     Document Type: Article

References (15)

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).
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).
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).
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).
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.
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).
13. COURANT R. & FRIEDRICHS K. O., Supersonic Flow and Shock-Waves. J, Wiley and Sons, New York (1967).
14. KINDERLEHRER D. & STAMPACCHIA G., An Introduction to Variational Inequalities and Their Applications. Academic Press, New York (1980).
15. GILBARG D. & TRUDINGER N. S., Elliptic Partial Differential Equations of Second Order. Springer, Berlin (1977).