engleski

A simplified quantum energy-transport model for semiconductors

The existence of global-in-time weak solutions to a quantum energy-transport model for semiconductors is proved. The equations are formally derived from the quantum hydrodynamic model in the large-time and small- velocity regime. They consist of a nonlinear parabolic fourth-order equation for the electron density, including temperature gradients ; an elliptic nonlinear heat equation for the electron temperature ; and the Poisson equation for the electric potential. The equations are solved in a bounded domain with periodic boundary conditions. The existence proof is based on an entropy-type estimate, exponential variable transformations, and a fixed-point argument. Furthermore, we discretize the equations by central finite differences and present some numerical simulations of a one-dimensional ballistic diode.

Quantum energy-transport equations; quantum semiconductors; existence of solutions; parabolic nonlinear fourth-order equation

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