Unified form language: A domain-specific language for weak formulations of partial differential equations

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.

Choice of calibration equations in calibrating microwave test fixtures

The error theory of linear equation system has been applied to the calibration procedure of microwave network analyser in this article. A new explanation for the choice of the linear calibration equations is proposed and a general principle for choosing calibration equations is presented. The method can also be used to predict the occurrence of the problem of frequency limitation at some periodic frequencies. This principle is employed to the thru-short-delay (TSD) method and the solution using the chosen equations gives the most accurate results. A good agreement between the theory and the experiment has been obtained.

Mechanical and tribological properties of epitaxial cubic boron nitride thin films grown on diamond

电子邮箱nataliya.deyneka@uni-ulm.de

Structural, elastic, and electronic properties of cubic perovskite BaHfO3 obtained from first principles

We investigated the structural, elastic, and electronic properties of the cubic perovskite-type BaHfO3 using a first-principles method based on the plane-wave basis set. Analysis of the band structure shows that perovskite-type BaHfO3 is a wide gap indirect semiconductor. The band-gap is predicted to be 3.94 eV within the screened exchange local density approximation (sX-LDA). The calculated equilibrium lattice constant of this compound is in good agreement with the available experimental and theoretical data reported in the literatures. The independent elastic constants (C-11, C-12, and C-44), bulk modules B and its pressure derivatives B', compressibility beta, shear modulus G, Young's modulus Y, Poisson's ratio nu, and Lame constants (mu, lambda) are obtained and analyzed in comparison with the available theoretical and experimental data for both the singlecrystalline and polycrystalline BaHfO3. The bonding-charge density calculation make it clear that the covalent bonds exist between the Hf and 0 atoms and the ionic bonds exist between the Ba atoms and HfO3 ionic groups in BaHfO3. (C) 2009 Elsevier B.V. All rights reserved.

Determination of wurtzite InN/cubic In2O3 heterojunction band offset by x-ray photoelectron spectroscopy

In2O3 is a promising partner of InN to form InN/In2O3 heterosystems. The valence band offset (VBO) of wurtzite InN/cubic In2O3 heterojunction is determined by x-ray photoemission spectroscopy. The valence band of In2O3 is found to be 1.47 +/- 0.11 eV below that of InN, and a type-I heterojunction with a conduction band offset (CBO) of 0.49-0.99 eV is found. The accurate determination of the VBO and CBO is important for use of InN/In2O3 based electronic devices.

Growth-Parameter Spaces and Optical Properties of Cubic Boron Nitride Films on Si(001)

Cubic boron nitride (c-BN) films were deposited on Si(001) substrates in an ion beam assisted deposition (IBAD) system under various conditions, and the growth parameter spaces and optical properties of c-BN films have been investigated systematically. The results indicate that suitable ion bombardment is necessary for the growth of c-BN films, and a well defined parameter space can be established by using the P/a-parameter. The refractive index of BN films keeps a constant of 1.8 for the c-BN content lower than 50%, while for c-BN films with higher cubic phase the refractive index increases with the c-BN content from 1.8 at chi(c) = 50% to 2.1 at chi(c) = 90%. Furthermore, the relationship between n and rho for BN films can be described by the Anderson-Schreiber equation, and the overlap field parameter gamma is determined to be 2.05.

Comparison and combination of several stress relief methods for cubic boron nitride films deposited by ion beam assisted deposition

Cubic boron nitride (c-BN) films were prepared by ion beam assisted deposition (IBAD) technique, and the stresses were primary estimated by measuring the frequency shifts in the infrared-absorption peaks of c-BN samples. To test the possible effects of other factors, dependencies of the c-BN transversal optical mode position on film thickness and c-BN content were investigated. Several methods for reducing the stress of c-BN films including annealing, high temperature deposition, two-stage process, and the addition of a small amount of Si were studied, in which the c-BN films with similar thickness and cubic phase content were used to evaluate the effects of the various stress relief methods. It was shown that all the methods can reduce the stress in c-BN films to various extents. Especially, the incorporation of a small amount of Si (2.3 at.%) can result in a remarkable stress relief from 8.4 to similar to 3.6 GPa whereas the c-BN content is nearly unaffected, although a slight degradation of the c-BN crystallinity is observed. The stress can be further reduced down below I GPa by combination of the addition of Si with the two-stage deposition process. (c) 2008 Elsevier B.V. All rights reserved.

Effects of crystalline quality on the phase stability of cubic boron nitride thin films under medium-energy ion irradiation

To investigate the effect of radiation damage on the stability and the compressive stress of cubic boron nitride (c-BN) thin films, c-BN films with various crystalline qualities prepared by dual beam ion assisted deposition were irradiated at room temperature with 300 keV Ar+ ions over a large fluence range up to 2 x 10(16) cm(-2). Fourier transform infrared spectroscopy (FTIR) data were taken before and after each irradiation step. The results show that the c-BN films with high crystallinity are significantly more resistant against medium-energy bombardment than those of lower crystalline quality. However, even for pure c-BN films without any sp(2)-bonded BN, there is a mechanism present, which causes the transformation from pure c-BN to h-BN or to an amorphous BN phase. Additional high resolution transmission electron microscopy (HRTEM) results support the conclusion from the FTIR data. For c-BN films with thickness smaller than the projected range of the bombarding Ar ions, complete stress relaxation was found for ion fluences approaching 4 x 10(15) cm(-2). This relaxation is accompanied, however, by a significant increase of the width of c-BN FTIR TO-line. This observation points to a build-up of disorder and/or a decreasing average grain size due to the bombardment. (c) 2005 Elsevier B.V. All rights reserved.

Recent advances in synthesis and properties of cubic boron nitride films

Cubic boron nitride (c-BN) attracts widespread interest as a promising material for many potential applications because of its unique physical and chemical properties. Since the 1980's the research in c-BN thin films has been carried out, which reached its summit in the mid of 1990's, then turned into a downward period. In the past few years, however, important progress was achieved in synthesis and properties of cubic boron nitride films, such as obtaining > 1 mu m thick c-BN films, epitaxial growth of single crystalline c-BN films, and advances in mechanics properties and microstructures of the interlayer of c-BN films. The present article reviews the current status of the synthesis and properties of c-BN thin films.

Dynamics of quantum dissipation systems interacting with fermion and boson grand canonical bath ensembles: Hierarchical equations of motion approach

A hierarchical equations of motion formalism for a quantum dissipation system in a grand canonical bath ensemble surrounding is constructed on the basis of the calculus-on-path-integral algorithm, together with the parametrization of arbitrary non-Markovian bath that satisfies fluctuation-dissipation theorem. The influence functionals for both the fermion or boson bath interaction are found to be of the same path integral expression as the canonical bath, assuming they all satisfy the Gaussian statistics. However, the equation of motion formalism is different due to the fluctuation-dissipation theories that are distinct and used explicitly. The implications of the present work to quantum transport through molecular wires and electron transfer in complex molecular systems are discussed. (c) 2007 American Institute of Physics.

Raman scattering detection of stacking faults in free-standing cubic-SiC epilayer

We report on stacking fault (SF) detection in free-standing cubic-SiC epilayer by the Raman measurements. The epilayer with enhanced SFs is heteroepitaxially grown by low pressure chemical vapour deposition on a Si(100) substrate and is released in KOH solution by micromechanical manufacture, on which the Raman measurements are performed in a back scattering geometry. The TO line of the Raman spectra is considerably broadened and distorted. We discuss the influence of SFs on the intensity profiles of TO mode by comparing our experimental data with the simulated results based on the Raman bond polarizability (BP) model in the framework of linear-chain concept. Good agreement with respect to the linewidth and disorder-induced peak shift is found by assuming the mean distance of the SFs to be 11 angstrom in the BP model.

A 16-term error model based on linear equations of voltage and current variables

Formulation of a 16-term error model, based on the four-port ABCD-matrix and voltage and current variables, is outlined. Matrices A, B, C, and D are each 2 x 2 submatrices of the complete 4 x 4 error matrix. The corresponding equations are linear in terms of the error parameters, which simplifies the calibration process. The parallelism with the network analyzer calibration procedures and the requirement of five two-port calibration measurements are stressed. Principles for robust choice of equations are presented. While the formulation is suitable for any network analyzer measurement, it is expected to be a useful alternative for the nonlinear y-parameter approach used in intrinsic semiconductor electrical and noise parameter measurements and parasitics' deembedding.

Design of high brightness cubic-GaN LEDs grown on GaAs substrate

The Principle of optical thin film was used to calculate the feasibility of improving the light extraction efficiency of GaN/GaAs optical devices by wafer-bonding technique. The calculated results show that the light extraction efficiency of bonded samples can be improved by 2.66 times than the as-grown GaN/GaAs samples when a thin Ni layer was used as adhesive layer and Ag layer as reflective layer. Full reflectance spectrum comparison shows that reflectivity for the incident light of 459.2 nm of the bonded samples was improved by 2.4 times than the as-grown samples, which is consistent with the calculated results.

Method for measurement of lattice parameter of cubic GaN layers on GaAs (001)

An extended technique derived from triple-axis diffraction setup was proposed to measure lattice parameters of cubic GaN(c-GaN) films. The fully relaxed lattice parameters of c-GaN are determined to be 4.5036+0.0004 Angstrom, which is closer to the values of a hypothetical perfect crystal. The speculated zero setting correction (Deltatheta) is very slight and within the range of the accuracy of measurement. Additionally, we applied this method to analyze strain of four different kinds of c-GaN samples. It is found that in-plane strain caused by large lattice mismatch and thermal expansion coefficients mismatch directly influence the epilayer growth at high temperatures, indicating that the relaxation of tensile strain after thermal annealing helps to improve the crystalline quality of c-GaN films and optical properties. (C) 2003 Elsevier Science B.V. All rights reserved.

Optical constants of cubic GaN/GaAs(001): Experiment and modeling

The optical constants epsilon(E)=epsilon(1)(E)+iepsilon(2)(E) of unintentionally doped cubic GaN grown on GaAs(001) have been measured at 300 K using spectral ellipsometry in the range of 1.5-5.0 eV. The epsilon(E) spectra display a structure, associated with the critical point at E-0 (direct gap) and some contribution mainly coming from the E-1 critical point. The experimental data over the entire measured spectral range (after oxide removal) has been fit using the Holden-Munoz model dielectric function [M. Munoz et al., J. Appl. Phys. 92, 5878 (2002)]. This model is based on the electronic energy-band structure near critical points plus excitonic and band-to-band Coulomb-enhancement effects at E-0, E-0 + Delta(0) and the E-1, E-1 + Delta(1), doublet. In addition to evaluating the energy of the E-0 critical point, the binding energy (R-1) of the two-dimensional exciton related to the E-1 critical point was estimated using the effective mass/k.p theory. The line, shape of the imaginary part of the cubic-GaN dielectric function shows excitonic effects at room temperature not withstanding that the exciton was not resolved. (C) 2003 American Institute of Physics.