Mixed finite-element methods for elliptic convection-dominated problems arising in semiconductor physics

In this work we develop and analyze an adaptive numerical scheme for simulating a class of macroscopic semiconductor models. At first the numerical modelling of semiconductors is reviewed in order to classify the Energy-Transport models for semiconductors that are later simulated in 2D. In this class of models the flow of charged particles, that are negatively charged electrons and so-called holes, which are quasi-particles of positive charge, as well as their energy distributions are described by a coupled system of nonlinear partial differential equations. A considerable difficulty in simulating these convection-dominated equations is posed by the nonlinear coupling as well as due to the fact that the local phenomena such as "hot electron effects" are only partially assessable through the given data. The primary variables that are used in the simulations are the particle density and the particle energy density. The user of these simulations is mostly interested in the current flow through parts of the domain boundary - the contacts. The numerical method considered here utilizes mixed finite-elements as trial functions for the discrete solution. The continuous discretization of the normal fluxes is the most important property of this discretization from the users perspective. It will be proven that under certain assumptions on the triangulation the particle density remains positive in the iterative solution algorithm. Connected to this result an a priori error estimate for the discrete solution of linear convection-diffusion equations is derived. The local charge transport phenomena will be resolved by an adaptive algorithm, which is based on a posteriori error estimators. At that stage a comparison of different estimations is performed. Additionally a method to effectively estimate the error in local quantities derived from the solution, so-called "functional outputs", is developed by transferring the dual weighted residual method to mixed finite elements. For a model problem we present how this method can deliver promising results even when standard error estimator fail completely to reduce the error in an iterative mesh refinement process.

Dynamical Casimir effect and the structure of vacuum in quantum field theory

Some of the most interesting phenomena that arise from the developments of the modern physics are surely vacuum fluctuations. They appear in different branches of physics, such as Quantum Field Theory, Cosmology, Condensed Matter Physics, Atomic and Molecular Physics, and also in Mathematical Physics. One of the most important of these vacuum fluctuations, sometimes called "zero-point energy", as well as one of the easiest quantum effect to detect, is the so-called Casimir effect. The purposes of this thesis are: - To propose a simple retarded approach for dynamical Casimir effect, thus a description of this vacuum effect when we have moving boundaries. - To describe the behaviour of the force acting on a boundary, due to its self-interaction with the vacuum.

A tool for the qualitative comparison of membrane-embedded and detergent-solubilized membrane protein structures in projection

The calculation of projection structures (PSs) from Protein Data Bank (PDB)-coordinate files of membrane proteins is not well-established. Reports on such attempts exist but are rare. In addition, the different procedures are barely described and thus difficult if not impossible to reproduce. Here we present a simple, fast and well-documented method for the calculation and visualization of PSs from PDB-coordinate files of membrane proteins: the projection structure visualization (PSV)-method. The PSV-method was successfully validated using the PS of aquaporin-1 (AQP1) from 2D crystals and cryo-transmission electron microscopy, and the PDB-coordinate file of AQP1 determined from 3D crystals and X-ray crystallography. Besides AQP1, which is a relatively rigid protein, we also studied a flexible membrane transport protein, i.e. the L-arginine/agmatine antiporter AdiC. Comparison of PSs calculated from the existing PDB-coordinate files of substrate-free and L-arginine-bound AdiC indicated that conformational changes are detected in projection. Importantly, structural differences were found between the PSV-method calculated PSs of the detergent-solubilized AdiC proteins and the PS from cryo-TEM of membrane-embedded AdiC. These differences are particularly exciting since they may reflect a different conformation of AdiC induced by the lateral pressure in the lipid bilayer.

Faulted Structures in Li Ion Exchanged NaMO2 (M=Ni(0.25)Mn(0.75))

A family of LiMO2 materials (M=Ni0.25Mn0.75) was prepared from Na1.2-xLixMO∂ precursors (0≤x≤0.6) via ion exchange. The resulting IE products were examined via XRD and compared to simulated XRD patterns produced using DIFFax to determine the defect structures resulting from the IE process. For the 0.1≤x≤0.6 materials, it is observed that there are 3 LiMO2 sub-phases with different Li contents present. As the amount of Li in the precursor increases, the amount of each phase changes resulting in a net shift to higher 2-theta; corresponding to an overall decrease in lattice parameter, approaching the theoretical values for LiMO2. Additionally, as x increases, the probability of O3-type shifting increases, most likely due to an increase in the amount O3-Li2MO3 minority phase which acts to weaken bonds in the TM layer, allowing the O3 shift to occur more easily. For the x=0 IE product, it was seen that the product had an ~O2-type structure, but with lattice parameters closer to those expected for a NaMO2 material.

Two-dimensional assembly and local redox-activity of molecular hybrid structures in an electrochemical environment

The self-assembly and redox-properties of two viologen derivatives, N-hexyl-N-(6-thiohexyl)-4,4-bipyridinium bromide (HS-6V6-H) and N,N-bis(6-thiohexyl)-4,4-bipyridinium bromide (HS-6V6-SH), immobilized on Au(111)-(1x1) macro-electrodes were investigated by cyclic voltammetry, surface enhanced infrared spectroscopy (SEIRAS) and in situ scanning tunneling microscopy (STM). Depending on the assembly conditions one could distinguish three different types of adlayers for both viologens: a low coverage disordered and an ordered striped phase of flat oriented molecules as well as a high coverage monolayer composed of tilted viologen moieties. Both molecules, HS-6V6-H and HS-6V6-SH, were successfully immobilized on Au(poly) nano-electrodes, which gave a well-defined redox-response in the lower pA–current range. An in situ STM configuration was employed to explore electron transport properties of single molecule junctions Au(T)|HS-6V6-SH(HS-6V6-H)|Au(S). The observed sigmoidal potential dependence, measured at variable substrate potential ES and at constant bias voltage (ET–ES), was attributed to electronic structure changes of the viologen moiety during the one-electron reduction/re-oxidation process V2+ V+. Tunneling experiments in asymmetric, STM-based junctions Au(T)-S-6V6-H|Au(S) revealed current (iT)–voltage (ET) curves with a maximum located at the equilibrium potential of the redox-process V2+ V+. The experimental iT–ET characteristics of the HS-6V6-H–modified tunneling junction were tentatively attributed to a sequential two-step electron transfer mechanism.