Naslov
A simplified quantum energy-transport model for semiconductors

Autori
Juengel, Ansgar ; Milišić, Josipa Pina

Izvornik
Nonlinear Analysis: Real World Applications (1468-1218) 12 (2011); 1033-1046

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Quantum energy-transport equations; Quantum semiconductors; Existence of solutions; Parabolic nonlinear fourth-order equation

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA