Structural investigations of silicon nanostructures grown by self-organized island formation for photovoltaic applications

The self-organized growth of crystalline silicon nanodots and their structural characteristics are investigated. For the nanodot synthesis, thin amorphous silicon (a-Si) layers with different thicknesses have been deposited onto the ultrathin (2 nm) oxidized (111) surface of Si wafers by electron beam evaporation under ultrahigh vacuum conditions. The solid phase crystallization of the initial layer is induced by a subsequent in situ annealing step at 700 °C, which leads to the dewetting of the initial a-Si layer. This process results in the self-organized formation of highly crystalline Si nanodot islands. Scanning electron microscopy confirms that size, shape, and planar distribution of the nanodots depend on the thickness of the initial a-Si layer. Cross-sectional investigations reveal a single-crystalline structure of the nanodots. This characteristic is observed as long as the thickness of the initial a-Si layer remains under a certain threshold triggering coalescence. The underlying ultra-thin oxide is not structurally affected by the dewetting process. Furthermore, a method for the fabrication of close-packed stacks of nanodots is presented, in which each nanodot is covered by a 2 nm thick SiO₂ shell. The chemical composition of these ensembles exhibits an abrupt Si/SiO₂ interface with a low amount of suboxides. A minority charge carrier lifetime of 18 µs inside of the nanodots is determined.     

Structure Investigations on 4‐Halo‐1,2,3,5‐dithiadiazolyl Radicals XCNSSN• (X = F,Cl, Br): The Shortest Intradimer S···S Distance in Dithiadiazolyl Dimers

Crystals of the 4‐halo‐1,2,3,5‐dithiadiazolyl radicals (X = F, Cl, Br) were obtained by sublimation at 80 °C and 10^?2 Torr, and the structures were determined by X‐ray diffraction. The fluoro derivative crystallizes as a cisoid dimer in the space group P2₁/n, whereas the chloro and bromo derivatives crystallize isomorphous as twisted dimers in the space group C2/c. The chloro and bromo derivatives show the shortest intradimer S···S contacts of all known 1,2,3,5‐dithiadiazolyl dimers. In addition the obtained structure of ClCN₂S₂^? represents the fifth polymorph of ClCN₂S₂^? characterized by X‐ray crystallography. The structures and the packing including secondary interactions are discussed.     

Replacing suffix trees with enhanced suffix arrays

The suffix tree is one of the most important data structures in string processing and comparative genomics. However, the space consumption of the suffix tree is a bottleneck in large scale applications such as genome analysis. In this article, we will overcome this obstacle. We will show how every algorithm that uses a suffix tree as data structure can systematically be replaced with an algorithm that uses an enhanced suffix array and solves the same problem in the same time complexity. The generic name enhanced suffix array stands for data structures consisting of the suffix array and additional tables. Our new algorithms are not only more space efficient than previous ones, but they are also faster and easier to implement.     

NSF3 und NSF2NMe2 als Liganden in der metallorganischen Chemie

Thiazyltrifluoride NSF₃ and Thiazyldifluoridedimethylamide NSF₂NMe₂: Ligands in Organometallic Chemistry From the reaction of [Re(CO)₅SO₂]⁺AsF₆^? ( 1 ) and [CpFe(CO)₂SO₂]⁺AsF₆^? ( 6 ) with NSF₃ ( 2 ) and NSF₂NMe₂ ( 4 ) the complexes [Re(CO)₅NSF₃]⁺AsF₆^? ( 3 ), [Re(CO)₅NSF₂NMe₂]⁺AsF₆^? ( 5 ), [CpFe(CO)₂NSF₃]⁺AsF₆^? ( 7 ), and [CpFe(CO)₂NSF₂NMe₂]⁺AsF₆^? ( 8 ) were obtained. The compounds have been characterised by X-ray crystallography, the ligand properties of 2 and 4 are discussed.     

Syntheses and structures of Me3Sb+CH2COO−·H2O,the monohydrate of the antimony analogue of betaine,and related compounds

The syntheses of the antimony analogue of betaine, Me₃Sb⁺CH₂COO^? (1), of the precursor [Me₃SbCH₂COOH][Br] (2) and of [Me₃SbCH₂COOCH₂CH₃][Br] (3) are reported. A new method for the synthesis of solvent‐free Me₃Sb is described. The structures of 1·H₂O and 3 were determined by single crystal X‐ray diffractometry. Copyright © 2002 John Wiley & Sons, Ltd.     

Uniqueness of non-linear ground states for fractional Laplacians in {\mathbb{R}}

We prove uniqueness of ground state solutions Q = Q(|x|) ≥ 0 of the non-linear equation $$(-\Delta)^s Q+Q-Q^{\alpha+1}= 0 \quad {\rm in} \, \mathbb{R},$$ ( ? Δ ) s Q + Q ? Q α + 1 = 0 i n R , where 0 < s < 1 and 0 < α < 4s/(1?2s) for ${s<\frac{1}{2}}$ s < 1 2 and 0 < α < ∞ for ${s\geq \frac{1}{2}}$ s ≥ 1 2 . Here (?Δ) ^s denotes the fractional Laplacian in one dimension. In particular, we answer affirmatively an open question recently raised by Kenig–Martel–Robbiano and we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for ${s=\frac{1}{2}}$ s = 1 2 and α = 1 in [5] for the Benjamin–Ono equation. As a technical key result in this paper, we show that the associated linearized operator L ₊ = (?Δ) ^s +1?(α+1)Q ^α is non-degenerate; i.e., its kernel satisfies ker L ₊ = span{Q′}. This result about L ₊ proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for non-linear dispersive PDEs with fractional Laplacians, such as the generalized Benjamin–Ono (BO) and Benjamin–Bona–Mahony (BBM) water wave equations.     

On the Continuum Limit for Discrete NLS with Long-Range Lattice Interactions

We consider a general class of discrete nonlinear Schrödinger equations (DNLS) on the lattice ${h\mathbb{Z}}$ with mesh size h > 0. In the continuum limit when h → 0, we prove that the limiting dynamics are given by a nonlinear Schrödinger equation (NLS) on ${\mathbb{R}}$ with the fractional Laplacian (?Δ) ^α as dispersive symbol. In particular, we obtain that fractional powers ${\frac{1}{2} < \alpha < 1}$ arise from long-range lattice interactions when passing to the continuum limit, whereas the NLS with the usual Laplacian ?Δ describes the dispersion in the continuum limit for short-range or quick-decaying interactions (e. g., nearest-neighbor interactions). Our results rigorously justify certain NLS model equations with fractional Laplacians proposed in the physics literature. Moreover, the arguments given in our paper can be also applied to discuss the continuum limit for other lattice systems with long-range interactions.     

Computational Statistical Methods for Social Network Models

We review the broad range of recent statistical work in social network models, with emphasis on computational aspects of these methods. Particular focus is applied to exponential-family random graph models (ERGM) and latent variable models for data on complete networks observed at a single time point, though we also briefly review many methods for incompletely observed networks and networks observed at multiple time points. Although we mention far more modeling techniques than we can possibly cover in depth, we provide numerous citations to current literature. We illustrate several of the methods on a small, well-known network dataset, Sampson's monks, providing code where possible so that these analyses may be duplicated.