A simplified quantum energy-transport model for semiconductors |
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Authors: | Ansgar Jüngel Josipa-Pina Milišić |
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Institution: | 1. Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040 Wien, Austria;2. Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, Croatia |
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Abstract: | 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. |
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