Search Results
Analysis of electronic models for solar cells including energy resolved defect densities
2010, Glitzky, Annegret
We introduce an electronic model for solar cells including energy resolved defect densities. The resulting drift-diffusion model corresponds to a generalized van Roosbroeck system with additional source terms coupled with ODEs containing space and energy as parameters for all defect densities. The system has to be considered in heterostructures and with mixed boundary conditions from device simulation. We give a weak formulation of the problem. If the boundary data and the sources are compatible with thermodynamic equilibrium the free energy along solutions decays monotonously. In other cases it may be increasing, but we estimate its growth. We establish boundedness and uniqueness results and prove the existence of a weak solution. This is done by considering a regularized problem, showing its solvability and the boundedness of its solutions independent of the regularization level.
An electronic model for solar cells including active interfaces and energy resolved defect densities
2011, Glitzky, Annegret
We introduce an electronic model for solar cells taking into account heterostructures with active interfaces and energy resolved volume and interface trap densities. The model consists of continuity equations for electrons and holes with thermionic emission transfer conditions at the interface and of ODEs for the trap densities with energy level and spatial position as parameters, where the right hand sides contain generation-recombination as well as ionization reactions. This system is coupled with a Poisson equation for the electrostatic potential. We show the thermodynamic correctness of the model and prove a priori estimates for the solutions to the evolution system. Moreover, existence and uniqueness of weak solutions of the problem are proven. For this purpose we solve a regularized problem and verify bounds of the corresponding solution not depending on the regularization level.
Analysis of a spin-polarized drift-diffusion model
2008, Glitzky, Annegret
We introduce a spin-polarized drift-diffusion model for semiconductor spintronic devices. This coupled system of continuity equations and a Poisson equation with mixed boundary conditions in all equations has to be considered in heterostructures. We give a weak formulation of this problem and prove an existence and uniqueness result for the instationary problem. If the boundary data is compatible with thermodynamic equilibrium the free energy along the solution decays monotonously and exponentially to its equilibrium value. In other cases it may be increasing but we estimate its growth. Moreover we give upper and lower estimates for the solution.
Existence of bounded steady state solutions to spin-polarized drift-diffusion systems
2008, Glitzky, Annegret, Gärtner, Klaus
We study a stationary spin-polarized drift-diffusion model for semiconductor spintronic devices. This coupled system of continuity equations and a Poisson equation with mixed boundary conditions in all equations has to be considered in heterostructures. In 3D we prove the existence and boundedness of steady states. If the Dirichlet conditions are compatible or nearly compatible with thermodynamic equilibrium the solution is unique. The same properties are obtained for a space discretized version of the problem: Using a Scharfetter-Gummel scheme on 3D boundary conforming Delaunay grids we show existence, boundedness and, for small applied voltages, the uniqueness of the discrete solution.
Optimal and pressure-independent L2 velocity error estimates for a modified Crouzeix-Raviart Stokes element with BDM reconstructions
2014, Brennecke, Christian
Nearly all inf-sup stable mixed finite elements for the incompressible Stokes equations relax the divergence constraint. The price to pay is that a priori estimates for the velocity error become pressure-dependent, while divergence-free mixed finite elements deliver pressure-independent estimates. A recently introduced new variational crime using lowest-order Raviart-Thomas velocity reconstructions delivers a much more robust modified Crouzeix-Raviart element, obeying an optimal pressure-independent discrete H1 velocity estimate. Refining this approach, a more sophisticated variational crime employing the lowest-order BDM element is proposed, which also allows proving an optimal pressure-independent L2 velocity error. Numerical examples confirm the analysis and demonstrate the improved robustness in the Navier-Stokes case.