engleski

Quantum macroscopic models including collisional effects

Due to the growing field of nanotechnology applications, mathematical modeling and simulation of charge transport in semiconductors is today a challenging research area. In order to achieve the efficient fabrication of the electronic devices, it is important to derive quantum models which are physically accurate as well as computationally feasible. The quantum hydrodynamic models seem to fulfill these requests. We derived new quantum hydrodynamic equations from a Wigner-Boltzmann model, using the quantum entropy minimization method recently developed by Degond and Ringhofer. The model consists of conservation equations for the carrier, momentum, and energy densities. The derivation is based on a careful expansion of the quantum Maxwellian in powers of the Planck constant. Compared to the standard quantum hydrodynamic equations derived by Gardner, the new model includes vorticity terms and a dispersive term for the velocity. Numerical current-voltage characteristics of one-dimensional resonant tunneling diode for both the new quantum hydrodynamic equations and Gardner's model are presented. The numerical results indicate that the dispersive velocity term regularizes the solution of the system.

quantum hydrodynamics; entropy minimization; quantum collisions

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