Numerical study of quantum hydrodynamic model for semiconductors

Abstract

This paper presents a numerical study of the one-dimensional quantum hydrodynamic equations, introducing the quantum hydrodynamic model (QHD) for semiconductors. In the case of QHD, numerical solution of the Schrödinger equation must present higher oscillations as the scaled Planck constant ε becomes smaller ( 2 3 10 10 ~ − − ÷ ε ). The numerical studies for general case and for particular isothermal, stationary case are given. Finally, we present different graphical solutions for particle and current densities, in both cases and for different values ofε . Graphical representations allow observing an increasing amplitude of solution oscillations of particle and current densities as ε becomes smaller. For the stationary case one can see that current density remains constant irrespective ofε choice.