Necessary conditions for normed convergence of critical multitype Bienaymé-Galton-Watson processes without variance

The condition on the offspring distribution in the critical multitype Bienaymé-Galton-Watson process without variance, which was previously shown to be sufficient for the existence of the analogue of the exponential limit law, is now shown also to be necessary. This completely extends previous one-type work of R. S. Slack.     

Neue Oxoferrate(III). Zur Kenntnis von Na14[Fe6O16]

New Oxoferrates(III). On the Knowledge of Na₁₄[Fe₆O₁₆] Na₁₄Fe₆O₁₆ crystallizes triclinic (P1 ) with a = 11.42₇, b = 8,27₁, c = 5.95₃ Å, α = 109.3, β = 87.7, γ = 111.4°, Z = 1, 2166 independent reflexions, R = 0.051. FeO₄ tetrahedra are connected by common cornes forming ?Zweier-Doppel-Ketten”? Effektive Coordination Numbers, ECoN, and the Madelung Part of Lattive Energy, MAPLE, are calculated and discussed.     

Organic p-i-n solar cells

We introduce a p-i-n-type heterojunction architecture for organic solar cells where the active region is sandwiched between two doped wide-gap layers. The term p-i-n means here a layer sequence in the form p-doped layer, intrinsic layer and n-doped layer. The doping is realized by controlled co-evaporation using organic dopants and leads to conductivities of 10^-4 to 10^-5 S/cm in the p- and n-doped wide-gap layers, respectively. The photoactive layer is formed by a mixture of phthalocyanine zinc (ZnPc) and the fullerene C₆₀ and shows mainly amorphous morphology. As a first step towards p-i-n structures, we show the advantage of using wide-gap layers in M-i-p-type diodes (metal layer–intrinsic layer–p-doped layer). The solar cells exhibit a maximum external quantum efficiency of 40% between 630-nm and 700-nm wavelength. With the help of an optical multilayer model, we optimize the optical properties of the solar cells by placing the active region at the maximum of the optical field distribution. The results of the model are largely confirmed by the experimental findings. For an optically optimized device, we find an internal quantum efficiency of around 82% under short-circuit conditions. Adding a layer of 10-nm thickness of the red material N,N-dimethylperylene-3,4:9,10-dicarboximide (Me-PTCDI) to the active region, a power-conversion efficiency of 1.9% for a single cell is obtained. Such optically thin cells with high internal quantum efficiency are an important step towards high-efficiency tandem cells. First tandem cells which are not yet optimized already show 2.4% power-conversion efficiency under simulated AM 1.5 illumination of 125 mW/cm² . PACS 73.61.Ph; 78.30.Jw; 89.30.Cc     

Andreev reflection in strong magnetic fields

We have studied the interplay of Andreev reflection and cyclotron motion of quasiparticles at a superconductor-normal-metal interface with a strong magnetic field applied parallel to the interface. Bound states are formed due to the confinement introduced by both the external magnetic field and the superconducting gap. These bound states are a coherent superposition of electron and hole edge excitations similar to those realized in finite quantum-Hall samples. We find the energy spectrum for these Andreev edge states and calculate transport properties.     

Inverse relation between photocurrent and absorption layer thickness in polymer solar cells

Organic solar cells based on polymer–fullerene bulk heterojunctions were optimised with respect to the short circuit photocurrent by means of optical modelling. Due to interference effects present in the thin film multilayer device, an inverse relation between active layer thickness and photocurrent was predicted and experimentally verified. Optimised photovoltaic devices yield power conversion efficiencies of 4%. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Correlation of charge transport with structural order in highly ordered melt‐crystallized poly(3‐hexylthiophene) thin films

A series of well‐defined poly(3‐hexylthiophene)s (P3HT) of different molecular weight (MW) and high regioregularity was investigated for charge transport properties in as‐cast and melt‐crystallized films. The semicrystalline structure of the P3HT was characterized by X‐ray scattering and Atomic force microscopy. Crystallization by cooling from the melt led to a substantial increase in crystallinity and a stronger alignment of the crystals in comparison to as‐cast films. The increase in crystallinity went along with an increase in hole mobility of up to an order of magnitude as measured by the space charge limited current method. Additionally, the hole mobility depended on the long period of P3HT lamellae and consequently on the MW. In compliance with the long period, the charge carrier mobility first increased with the MW before decreasing again at the onset of chain folding. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013 , 51, 943–951