Thermodynamic design of energy models of semiconductor devices

In this preprint a system of evolution equations for energy models of a semiconductor device is derived on an deductive way from a generally accepted expression for the free energy. Only first principles like the entropy maximum principle and the principle of partial local equilibrium are applied. Particular attention is paid to include the electrostatic potential self-consistently. Dynamically ionized trap levels and models with carrier temperatures are regarded. The system of evolution equations is compatible with the corresponding entropy balance equation that contains a positively definite entropy production rate

Modelling and simulation of power devices for high-voltage integrated circuits

Process and device simulators turned out to be important tools in the design of high-voltage integrated circuits and in the development of their technology. The main goal of this project was the improvement of the device simulator WIAS-TeSCA in order to simulate different power devices in high-voltage integrated circuits developed by the industrial partner. Some simulation results are presented. Furthermore, we discuss some aspects of the mathematics of relevant model equations which device and process simulations are based on

On Stationary Schrödinger-Poisson Equations

We regard the Schrödinger-Poisson system arising from the modelling of an electron gas with reduced dimension in a bounded up to three-dimensional domain and establish the method of steepest descent. The electrostatic potentials of the iteration scheme will converge uniformly on the spatial domain. To get this result we investigate the Schrödinger operator, the Fermi level and the quantum mechanical electron density operator for square integrable electrostatic potentials. On bounded sets of potentials the Fermi level is continuous and boundeq, and the electron density operator is monotone and Lipschitz continuous. - As a tool we develop a Riesz-Dunford functional calculus for semibounded self-adjoint operators using paths of integration which enclose a real half axis

Multi-dimensional modeling and simulation of semiconductor nanophotonic devices

Self-consistent modeling and multi-dimensional simulation of semiconductor nanophotonic devices is an important tool in the development of future integrated light sources and quantum devices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically explore their optimization potential. The efficient implementation of multi-dimensional numerical simulations for computer-aided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in device-scale modeling of quantum dot based single-photon sources and laser diodes by self-consistently coupling the optical Maxwell equations with semiclassical carrier transport models using semi-classical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multi-dimensional geometries, we have developed a novel hp-adaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multi-scale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameter-embedding techniques to solve the drift-diffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on various applications, including vertical-cavity surface-emitting lasers, grating couplers and single-photon sources

Remarks on the Convex Analysis of the Energy Model of Semiconductor Devices

Gajewski and Gröger used a convex thermodynamic potential, the free energy, in the analysis of the drift-diffusion model. We consider an energy model as an example of a system in which the temperature is a dynamic variable. In such systems the free energy is no convex functional. We introduce an approach to the transient problem for the model which is based on convex functionals which are related to the entropy and its conjugate potential and which allow the application of the tools of convex analysis. A semi-implicit method for the initial-boundary value problem arises on a rather natural way and basic estimates are proved for the solutions