Finite-element discretization of 3D energy-transport equations for semiconductors

In this thesis a mathematical model was derived that describes the charge and energy transport in semiconductor devices like transistors. Moreover, numerical simulations of these physical processes are performed. In order to accomplish this, methods of theoretical physics, functional analysis, numerical mathematics and computer programming are applied. After an introduction to the status quo of semiconductor device simulation methods and a brief review of historical facts up to now, the attention is shifted to the construction of a model, which serves as the basis of the subsequent derivations in the thesis. Thereby the starting point is an important equation of the theory of dilute gases. From this equation the model equations are derived and specified by means of a series expansion method. This is done in a multi-stage derivation process, which is mainly taken from a scientific paper and which does not constitute the focus of this thesis. In the following phase we specify the mathematical setting and make precise the model assumptions. Thereby we make use of methods of functional analysis. Since the equations we deal with are coupled, we are concerned with a nonstandard problem. In contrary, the theory of scalar elliptic equations is established meanwhile. Subsequently, we are preoccupied with the numerical discretization of the equations. A special finite-element method is used for the discretization. This special approach has to be done in order to make the numerical results appropriate for practical application. By a series of transformations from the discrete model we derive a system of algebraic equations that are eligible for numerical evaluation. Using self-made computer programs we solve the equations to get approximate solutions. These programs are based on new and specialized iteration procedures that are developed and thoroughly tested within the frame of this research work. Due to their importance and their novel status, they are explained and demonstrated in detail. We compare these new iterations with a standard method that is complemented by a feature to fit in the current context. A further innovation is the computation of solutions in three-dimensional domains, which are still rare. Special attention is paid to applicability of the 3D simulation tools. The programs are designed to have justifiable working complexity. The simulation results of some models of contemporary semiconductor devices are shown and detailed comments on the results are given. Eventually, we make a prospect on future development and enhancements of the models and of the algorithms that we used.

New design of polyphenylene dendrimers for full-color light-emitting diodes

Dendritic systems, and in particular polyphenylene dendrimers, have recently attracted considerable attention from the synthetic organic chemistry community, as well as from photophysicists, particularly in view of the search for synthetic model analogies to photoelectric materials to fabricate organic light-emitting diodes (OLEDs), and even more advanced areas of research such as light-harvesting system, energy transfer and non-host device. Geometrically, dendrimers are unique systems that consist of a core, one or more dendrons, and surface groups. The different parts of the macromolecule can be selected to give the desired optoelectronic and processing properties. Compared to small molecular or polymeric light-emitting materials, these dendritic materials can combine the benefits of both previous classes. The high molecular weights of these dendritic macromolecules, as well as the surface groups often attached to the distal ends of the dendrons, can improve the solution processability, and thus can be deposited from solution by simple processes such as spin-coating and ink-jet printing. Moreover, even better than the traditional polymeric light-emitting materials, the well-defined monodisperse distributed dendrimers possess a high purity comparable to that of small molecules, and as such can be fabricated into high performance OLEDs. Most importantly, the emissive chromophores can be located at the core of the dendrimer, within the dendrons, and/or at the surface of the dendrimers because of their unique dendritic architectures. The different parts of the macromolecule can be selected to give the desired optoelectronic and processing properties. Therefore, the main goals of this thesis are the design and synthesis, characterization of novel functional dendrimers, e.g. polytriphenylene dendrimers for blue fluorescent, as well as iridium(III) complex cored polyphenylene dendrimers for green and red phosphorescent light emitting diodes. In additional to the above mentioned advantages of dendrimer based OLEDs, the modular molecular architecture and various functionalized units at different locations in polyphenylene dendrimers open up a tremendous scope for tuning a wide range of properties in addition to color, such as intermolecular interactions, charge mobility, quantum yield, and exciton diffusion. In conclusion, research into dendrimer containing OLEDs combines fundamental aspects of organic semiconductor physics, novel and highly sophisticated organic synthetic chemistry and elaborate device technology.rn

Packing a trunk : a physically based approach with full motional freedom

Geometric packing problems may be formulated mathematically as constrained optimization problems. But finding a good solution is a challenging task. The more complicated the geometry of the container or the objects to be packed, the more complex the non-penetration constraints become. In this work we propose the use of a physics engine that simulates a system of colliding rigid bodies. It is a tool to resolve interpenetration conflicts and to optimize configurations locally. We develop an efficient and easy-to-implement physics engine that is specialized for collision detection and contact handling. In succession of the development of this engine a number of novel algorithms for distance calculation and intersection volume were designed and imple- mented, which are presented in this work. They are highly specialized to pro- vide fast responses for cuboids and triangles as input geometry whereas the concepts they are based on can easily be extended to other convex shapes. Especially noteworthy in this context is our ε-distance algorithm - a novel application that is not only very robust and fast but also compact in its im- plementation. Several state-of-the-art third party implementations are being presented and we show that our implementations beat them in runtime and robustness. The packing algorithm that lies on top of the physics engine is a Monte Carlo based approach implemented for packing cuboids into a container described by a triangle soup. We give an implementation for the SAE J1100 variant of the trunk packing problem. We compare this implementation to several established approaches and we show that it gives better results in faster time than these existing implementations.