Influence of processing conditions on morphology and performance of vacuum deposited organic solar cells

This thesis discusses vacuum deposited organic solar cells. It focuses on the investigation of new donor molecules blended with the standard electron acceptor C60. These donor-acceptor heterojunctions form the photoactive system of organic solar cells. In addition, the influence of the processing conditions on the morphology of the blend layers is investigated, as the morphology is crucial for an efficient generation of free charge carriers upon photon absorption. Bulk heterojunction solar cells with the donor DTDCTB are deposited at different substrate temperatures. We identify three substrate temperature regimes, discriminated by the behavior of the fill factor (FF ) as a function of the blend layer thickness. Devices deposited at RT have a maximum FF between 50 and 70 nm blend thickness, while devices deposited at 110 °C have a monotonically decreasing FF. At Tsub=85 °C, the devices have an S-kinked current-voltage curve. Grazing incidence wide angle X-ray scattering measurements show that this peculiar behavior of the FF is not correlated with a change in the crystallinity of the DTDCTB, which stays amorphous. Absorption measurements show that the average alignment of the molecules inside the blend also remains unchanged. Charge extraction measurements (OTRACE) reveal a mobility for the 110 °C device that is an order of magnitude higher than for the RT device. The difference in mobility can be explained by a higher trap density for the RT samples as measured by impedance spectroscopy. Despite slightly higher carrier lifetimes for the RT device obtained by transient photovoltage measurements, its mobility-lifetime product is still lower than for the 110 °C devices. Based on DTDCTB, three new donor materials are designed to have a higher thermal stability in order to achieve higher yields upon material purification using gradient sublimation. For PRTF, the thermal stability is increased demonstrated by a higher yield upon sublimation. However, all new materials have a reduced absorption as compared to DTDCTB, which limits the short current density, and the FF is more sensitive to an increase of the blend layer thickness. The highest power conversion efficiency is achieved for a PRTF:C60 solar cell with 3.8%. Interestingly, PRTF:C60 solar cells show exceptionally low nonradiative voltage losses of only 0.26 V. Another absorber molecule is the push-pull chromophore QM1. Scanning electron microscope (SEM) measurements show a growth of the molecule in nanowires on several substrates. The nanowires have lengths up to several micrometers and are several tens of nanometers wide. The formation of the nanowires is accompanied by a strong blue shift (650 meV) of the thin film absorption spectrum in comparison to the absorption in solution, which is attributed to H-aggregation of the molecules. Furthermore, the thin film absorption onset reaches up to 1100 nm, making the material a suitable candidate for a near infrared absorber in organic solar cells. For a solar cell in combination with C60, a power conversion efficiency of 1.9% was achieved with an external quantum efficiency of over 19% for the spectral range between 600 and 1000 nm. The method of “co-evaporant induced crystallization” as a means to increase the crystallinity of blend layers without increasing the substrate temperature during the deposition is investigated. Mass spectrometry (LDI-ToF-MS) measurements show that polydimethylsiloxane (PDMS), which is used as a co-evaporant, decomposes during the evaporation and only lighter oligomers evaporate. Quartz crystal microbalance (QCM) measurements prove that the detection of PDMS saturates at higher amounts of evaporated material. LDI-ToF-MS measurements show further that the determination of the volatilization temperature by QCM measurements is highly error prone. The method was applied to zinc phthalocyanine (ZnPc) :C60 solar cells, accepting the insertion of PDMS into the blend layer. Diffraction (GIXRD) measurements show a large increase in crystallinity. ZnPc:C60 solar cells produced by applying the method reveal a similar behavior as solar cells processed at a higher substrate temperature

Training Two-Layer ReLU Networks with Gradient Descent is Inconsistent

We prove that two-layer (Leaky)ReLU networks initialized by e.g. the widely used method proposed by He et al. (2015) and trained using gradient descent on a least-squares loss are not universally consistent. Specifically, we describe a large class of one-dimensional data-generating distributions for which, with high probability, gradient descent only finds a bad local minimum of the optimization landscape. It turns out that in these cases, the found network essentially performs linear regression even if the target function is non-linear. We further provide numerical evidence that this happens in practical situations, for some multi-dimensional distributions and that stochastic gradient descent exhibits similar behavior.Comment: Changes in v2: Single-column layout, NTK discussion, new experiment, updated introduction, improved explanations. 20 pages + 33 pages appendix. Code available at https://github.com/dholzmueller/nn_inconsistenc

Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimation

Sampling from Gibbs distributions $p(x) \propto \exp(-V(x)/\varepsilon)$ and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics. However, while efficient algorithms are known for convex potentials $V$, the situation is much more difficult in the non-convex case, where algorithms necessarily suffer from the curse of dimensionality in the worst case. For optimization, which can be seen as a low-temperature limit of sampling, it is known that smooth functions $V$ allow faster convergence rates. Specifically, for $m$-times differentiable functions in $d$ dimensions, the optimal rate for algorithms with $n$ function evaluations is known to be $O(n^{-m/d})$, where the constant can potentially depend on $m, d$ and the function to be optimized. Hence, the curse of dimensionality can be alleviated for smooth functions at least in terms of the convergence rate. Recently, it has been shown that similarly fast rates can also be achieved with polynomial runtime $O(n^{3.5})$, where the exponent $3.5$ is independent of $m$ or $d$. Hence, it is natural to ask whether similar rates for sampling and log-partition computation are possible, and whether they can be realized in polynomial time with an exponent independent of $m$ and $d$. We show that the optimal rates for sampling and log-partition computation are sometimes equal and sometimes faster than for optimization. We then analyze various polynomial-time sampling algorithms, including an extension of a recent promising optimization approach, and find that they sometimes exhibit interesting behavior but no near-optimal rates. Our results also give further insights on the relation between sampling, log-partition, and optimization problems.Comment: Changes in v2: Minor corrections and formatting changes. Plots can be reproduced using the code at https://github.com/dholzmueller/sampling_experiment

National differences in materialism - Using alternative research strategies to explore the construct

One of the core objectives in cross-national marketing research is to establish research results which are comparable across national entities. Nevertheless certain national idiosyncrasies (unique meaning of constructs, distinctive expressions) may hamper these cross-national research endeavors. Two different approaches have been introduced in the social sciences, in order to cope with this comparability-dilemma. The "emic" and the "etic" school of thought. These can be seen as two extremes on the continuum of cross-national research methodology. The paper tries to illustrate advantages and potential shortcomings of the etic (mostly quantitative) vs. the emic (mostly qualitative) research approach. A combination of alternative, qualitative and quantitative research strategies was used to explore national differences in materialism. A questionnaire was developed comprising both both qualitative and quantitative sections on materialism. The materialism scale, as operationalized by Richins and Dawson (1992) was used, for the quantitative section. The research findings call for the use of 'alternative research strategies' to overcome the emic - etic duality in cross-national research. Comparative text analysis and graphical representations of consumers statements can help to explore the reasons for conceptual differences

Risk Management in Banks : new challenges of the management of interest rate risk

Die Finanzkrise und deren Auswirkungen auf die Banken weltweit waren der Auslöser für einen steigenden Stellenwert des Risikomanagements innerhalb dieser Branche. Aus diesem Anlass befasst sich die vorliegende Masterarbeit mit dem Thema Risikomanagement und im Speziellen mit dem Zinsänderungsrisiko. Die gesetzlichen Vorgaben und das „Zinsrisikopapier“ des Basler Ausschusses für Bankenaufsicht werden dargelegt. Anhand von Berechnungsbeispielen werden die verschiedenen Modelle zur Messung des Zinsrisikos erläutert und die Entwicklung von einer statischen zu einer dynamischen Sicht-weise aufgezeigt

Ultra--cold gases and the detection of the Earth's rotation: Bogoliubov space and gravitomagnetism

The present work analyzes the consequences of the gravitomagnetic effect of the Earth upon a bosonic gas in which the corresponding atoms have a non--vanishing orbital angular momentum. Concerning the ground state of the Bogoliubov space of this system we deduce the consequences, on the pressure and on the speed of sound, of the gravitomagnetic effect. We prove that the effect on a single atom is very small, but we also show that for some thermodynamical properties the consequences scale as a non--trivial function of the number of particles.Comment: 4 page