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.

Electronic transport in the heavy fermion superconductors UPd 2 Al 3 and UNi 2 Al 3

This work addresses the electronical properties of the superconductors UPd2Al3 and UNi2Al3 on the basis of thin film experiments. These isotructural compounds are ideal candiates to study the interplay of magnetism and superconductivity due to the differences of their magnetically ordered states, as well as the experimental evidence for a magnetic pairing mechanism in UPd2Al3. Epitaxial thin film samples of UPd2Al3 and UNi2Al3 were prepared using UHV Molecular Beam Epitaxy (MBE). For UPd2Al3, the change of the growth direction from the intrinsic (001) to epitaxial (100) was predicted and sucessfully demonstrated using LaAlO3 substrates cut in (110) direction. With optimized deposition process parameters for UPd2Al3 (100) on LaAlO3 (110) superconducting samples with critical temperatures up to Tc = 1.75K were obtained. UPd2Al3-AlOx-Ag mesa junctions with superconducting base electrode were prepared and shown to be in the tunneling regime. However, no signatures of a superconducting density of states were observed in the tunneling spectra. The resistive superconducting transition was probed for a possible dependence on the current direction. In contrast to UNi2Al3, the existence of such feature was excluded in UPd2Al3 (100) thin films. The second focus of this work is the dependence of the resisitive transition in UNi2Al3 (100) thin films on the current direction. The experimental fact that the resisitive transition occurs at slightly higher temperatures for I║a than for I║c can be explained within a model of two weakly coupled superconducting bands. Evidence is presented for the key assumption of the two-band model, namely that transport in and out of the ab-plane is generated on different, weakly coupled parts of the Fermi surface. Main indications are the angle dependence of the superconducting transition and the dependence of the upper critical field Bc2 on current and field orientation. Additionally, several possible alternative explanations for the directional splitting of the transition are excluded in this work. An origin due to scattering on crystal defects or impurities is ruled out, likewise a relation to ohmic heating or vortex dynamics. The shift of the transition temperature as function of the current density was found to behave as predicted by the Ginzburg-Landau theory for critical current depairing, which plays a significant role in the two-band model. In conclusion, the directional splitting of the resisitive transition has to be regarded an intrinsic and unique property of UNi2Al3 up to now. Therefore, UNi2Al3 is proposed as a role model for weakly coupled multiband superconductivity. Magnetoresistance in the normalconducting state was measured for UPd2Al3 and UNi2Al3. For UNi2Al3, a negative contribution was observed close to the antiferromagnetic ordering temperature TN only for I║a, which can be associated to reduced spin-disorder scattering. In agreement with previous results it is concluded that the magnetic moments have to be attributed to the same part of the Fermi surface which generates transport in the ab-plane.

Stress – structure correlations in grafted polymer films

In der vorliegenden Arbeit wurden experimentelle Untersuchungen zu gepfropften Polymerfilmen durchgeführt. Dabei wurden endgepfropfte poly-methyl-methacrylate (PMMA) Bürsten hergestellt durch „grafting from“ Methoden und polystyrol (PS)/ poly-vinyl-methyl-ether (PVME) Polymerfilme gepfropft auf UV sensitiven Oberflächen untersucht. Zur Strukturuntersuchung wurden die hergestellten Systeme wurden mit Rasterkraftmikroskopie (engl.: Surface Probe Microscopy, SPM), Röntgen - und Neutronenreflektivitätsmessungen, sowie mit Röntgenstreuung unter streifenden Einfall (engl.: Grazing Incidence Small Angle X-Ray Scattering, GISAXS) untersucht. rnEs wurde gezeigt, dass ein aus der Transmissionsstreuung bekanntes Model auch für auch für die GISAXS Analyse polydisperser Polymerdomänen und Kolloidsysteme verwendet werden kann. Der maximale Fehler durch die gemachten Näherungen wurde auf < 20% abgeschätzt.rnErgebnisse aus der Strukturanalyse wurden mit mechanischen Filmeigenschaften verknüpft. Dazu wurden mechanische Spannungsexperimente durchgeführt. Hierzu wurden die zu untersuchenden Filme selektiv auf einzelne Mikro-Federbalken-Sensoren (engl.: Micro Cantilever Sensor, MCS) der MCS Arrays aufgebracht. Dies wurde durch Maskierungstechniken und Mikro-Kontaktdrucken bewerkstelligt. rnPhasenübergansexperimente der gepfropften PS/PVME Filme haben gezeigt, dass die Möglichkeit einer Polymer/Polymer Phasenseparation stark von Propfpunktdichte der gebundenen Polymerketten mit der Oberfläche abhängt. PS/PVME Filmsysteme mit hohen Pfropfpunktdichten zeigten keinen Phasenübergang. Bei niedrig gepfropften Filmsystemen waren hingegen Polymer/Polymer Phasenseparationen zu beobachten. Es wurde geschlussfolgert, dass die gepfropften Polymersysteme einen hinreichenden Grad an entropischen Freiheitsgraden benötigen um eine Phasenseparation zu zeigen. Mechanische Spannungsexperimente haben dabei das Verstehen der Phasenseparationsmechanismen möglich gemacht.rnAus Quellexperimenten dichtgepfropfter PMMA Bürsten, wurden Lösungsmittel-Polymer Wechselwirkungsparameter (-Parameter) bestimmt. Dabei wurde festgestellt, dass sich die erhaltenen Parameter aufgrund von Filmbenetzung und entropischen Effekten maßgeblich von den errechneten Bulkwerten unterscheiden. Weiterhin wurden nicht reversible Kettenverschlaufungseffekt beobachtet.

Resonance properties of different neuronal populations in the immature mouse neocortex

Subthreshold resonance is a characteristic membrane property of different neuronal classes, is critically involved in the generation of network oscillations, and tunes the integration of synaptic inputs to particular frequency ranges. In order to investigate whether resonance properties of distinct neuronal populations in the immature neocortex contribute to these network oscillations, I performed whole-cell patch-clamp recordings from visually identified neurons in tangential and coronal neocortical slices from postnatal day (P) P0-P7 C57Bl/6 and P6-P13 GAD67-GFP knock-in mice. Subthreshold resonance was analyzed by sinusoidal current injection of varying frequency. All Cajal-Retzius cells showed subthreshold resonance with an average frequency of 2.6 ± 0.1 Hz (n=60), which was massively reduced by ZD7288, a blocker of hyperpolarization-activated cation currents. About 65.6% (n=61) of the supragranular pyramidal neurons showed subthreshold resonance with an average frequency of 1.4 ± 0.1 Hz (n=40). Application of 1 mM Ni2+ suppressed subthreshold resonance, suggesting that low-threshold Ca2+ currents contribute to resonance in these neurons. About 63.6% (n=77) of the layer V pyramidal neurons showed subthreshold resonance with an average frequency of 1.4 ± 0.2 Hz (n=49), which was abolished by ZD7288. Only 44.1% (n=59) of the subplate neurons showed subthreshold resonance with an average frequency of 1.3 ± 0.2 Hz (n=26) and a small resonance strength. Finally, 50% of the investigated GABAergic interneurons showed subthreshold resonance with an average frequency of 2.0 ± 0.2 Hz (n=42). Membrane hyperpolarization to –86 mV attenuated the frequency and strength of subthreshold resonance. Subthreshold resonance was virtually abolished in the presence of 1 mM Ni2+, suggesting that t-type Ca2+ currents are critically involved in the generation of resonance, while ZD7288 had no effect. Application of 0.4 µM TTX suppressed subthreshold resonance at depolarized, but not hyperpolarized membrane potential, suggesting that persistent Na+ current contribute to the amplification of membrane resonance. rnIn summary, these results demonstrate that all investigated neuronal subpopulations reveal resonance behavior, with either hyperpolarization-activated cation or low-threshold Ca2+ currents contributing to the subthreshold resonance. GABAergic interneurons also express subthreshold resonance at low frequencies, with t-type Ca2+ and persistent Na+ currents underlying the generation of membrane resonance. The membrane resonance of immature neurons may contribute to the generation of slow oscillatory activity pattern in the immature neocortex and enhance the temporal precision of synaptic integration in developing cortical neurons.rn