Quantum hydrodynamic models for semiconductors with and without collisions [Elektronische Ressource] / Josipa Pina Milišić

Quantum Hydrodynamic Models forSemiconductors with and withoutCollisionsDissertationzur Erlangung des GradesDoktor der NaturwissenschaftenAm Fachbereich Physik, Mathematik und Informatikder Johannes Gutenberg-Universit¨at MainzJosipa Pina Miliˇsi´c,geboren in Split (Kroatien)Mainz, 2007Tag der mu¨ndlichen Pru¨fung: 21. August 2007D77 - Mainzer Dissertation3AbstractIn this thesis we study quantum hydrodynamic (QHD) models, particularlythe ones used in semiconductor device modeling. The QHD model consistsof the conservation laws for the particle density, momentum, and energydensity, including quantum corrections from the Bohm potential.We start with a review of the known results on collisionless QHD mod-els derived from the mixed-state Schr¨odinger system or from the Wignerequation. Using the reformulation of the one-dimensional stationary QHDequationswiththelinearpotential asastationary Schr¨odingerequation, thesemi-analytical expressions for current-voltage curves are studied.Further on, we consider viscous stabilizations of the QHD model. The nu-merical viscosity for the upwind finite-difference discretization of the QHDmodel proposed by C. Gardner is computed. On the other side, startingfrom the Wigner equation with the Fokker-Planck collision operator we de-rive the viscous QHD model. This model contains the physical viscosity in-troduced by the collision operator.