Abstract
The transient quantum drift diffusion model is derived from the isothermal quantum hydrodynamic model via a zero relaxation time limit. This yields a fourth-order nonlinear parabolic equation for the electron density, which is self-consistently coupled to the Poisson equation for the electrostatic potential. A stability analysis of the linearized system is performed by means of Hilbert space methods, which rely on a generalized Poincaré-type inequality. In the quantum case more states are linearly stable than in the classical one. The linear stability of an implicit Euler discretization for the nonlinear equations is proven and numerical results for a diode are presented, indicating that no maximum principle holds for the linearized system.
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