Convergence of an implicit Voronoi finite volume method for reaction–diffusion problems

We investigate the convergence of an implicit Voronoi finite volume method for reaction–diffusion problems including nonlinear diffusion in two space dimensions. The model allows to handle heterogeneous materials and uses the chemical activities of the involved species as primary variables. The numerical scheme works with boundary conforming Delaunay meshes and preserves positivity and the dissipative property of the continuous system. Starting from a result on the global stability of the scheme (uniform, mesh‐independent global upper, and lower bounds), we prove strong convergence of the chemical activities and their gradients to a weak solution of the continuous problem. To illustrate the preservation of qualitative properties by the numerical scheme, we present a long‐term simulation of the Michaelis–Menten–Henri system. Especially, we investigate the decay properties of the relative free energy over several magnitudes of time, and obtain experimental orders of convergence for this quantity. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 141–174, 2016     

Mechanisms of morphological evolution on faceted core–shell nanowire surfaces

Core-shell nanowires with radial heterostructures hold great promise in photonic and electronic applications and controlling the formation of these heterostructures in the core-shell configuration remains a challenge. Recently, GaAs nanowires have been used as substrates to create AlGaAs shells. The deposition of the AlGaAs layer leads to the spontaneous formation of Al-rich stripes along certain crystallographic directions and quantum dots/wires near the apexes of the shell. A general two-dimensional model has been developed for the motion of the faceted solid-vapor interfaces for pure materials that accounts for capillarity and deposition. With this model, the growth processes and morphological evolution of shells of nanowires around hexagonal cores (six small facets {112} in the corners of six equivalent facets {110}) are investigated in detail both analytically and numerically. It is found that deposition can yield facets that are not present on the Wulff shape. These small facets can have slowly time-varying sizes that can lead to stripe structures and quantum dots/wires depending on the balances between diffusion and deposition. The effects of deposition rates and polarity (or asymmetry) on planes {112} on the development of the configurations of nanowires are discussed. The numerical results are compared with experimental results giving almost quantitative agreement, despite the fact that only pure materials are treated herein whereas the experiments deal with alloys.     

GaN-based heterostructures: electric--static equilibrium and boundary conditions

In the GaN-based heterostructures, this paper reports that the strong electric fields induced by polarization effects at the structure boundaries complicate the electric--static equilibrium and the boundary conditions. The basic requirements of electric--static equilibrium for the heterostructure systems are discussed first, and it is deduced that in the application of the coupled Schr\"{o}dinger--Poisson model to the heterostructures of electric--static equilibrium state, zero external electric field guarantees the overall electric neutrality, and there is no need to introduce the charge balance equation. Then the relation between the screening of the polar charges in GaN-based heterostructures and the possible boundary conditions of the Poisson equation is analysed, it is shown that the various boundary conditions are equivalent to each other, and the surface charge, which can be used in studying the screening of the polar charges, can be precisely solved even if only the conduction band energy is correctly known at the surface. Finally, through the calculations on an AlGaN/GaN heterostructure with typical structure parameters by the coupled Schr\"{o}dinger--Poisson model under the various boundary conditions, the correctness of the above analyses are validated.     

Temperature dependence of Hall electron density of GaN-based heterostructures

The theoretic calculation and analysis of the temperature dependence of Hall electron density of a sample AlGaN/GaN heterostructure has been carried out in the temperature range from 77 to 300K. The densities of the two-dimensional electron gas and the bulk electrons are solved by self-consistent calculation of one-dimensional Schr?dinger and Poisson equations at different temperatures, which allow for the variation of energy gap and structure strain, and are used for evaluation of the temperature dependence of Hall electron density. The calculated Hall electron density agrees with the measured one quite well with the appropriate bulk mobility data. Analysis revealed that for the temperature range considered, even in the heterostructures with a small bulk conductance the factors that determine the Hall mobility and electron density could be of different sources, and not just the two-dimensional electron gas as generally supposed.     

WS2/MoS2 Heterostructures through Thermal Treatment of MoS2 Layers Electrostatically Functionalized with W3S4 Molecular Clusters

The preparation of 2D stacked layers combining flakes of different nature gives rise to countless numbers of heterostructures where new band alignments, defined at the interfaces, control the electronic properties of the system. Among the large family of 2D/2D heterostructures, the one formed by the combination of the most common semiconducting transition metal dichalcogenides, WS₂/MoS₂, has awakened great interest owing to its photovoltaic and photoelectrochemical properties. Solution as well as dry physical methods have been developed to optimize the synthesis of these heterostructures. Here, a suspension of negatively charged MoS₂ flakes is mixed with a methanolic solution of a cationic W₃S₄-core cluster, giving rise to a homogeneous distribution of the clusters over the layers. In a second step, a calcination of this molecular/2D heterostructure under N₂ leads to the formation of clean WS₂/MoS₂ heterostructures, where the photoluminescence of both counterparts is quenched, proving an efficient interlayer coupling. Thus, this chemical method combines the advantages of a solution approach (simple, scalable, and low-cost) with the good quality interfaces reached by using more complicated traditional physical methods.     

Localization of excitons in weakly disordered semiconductor structures: A model study

Localization of the center‐of‐mass (com) motion of an exciton in a disordered semiconductor structure is studied theoretically by focusing on nonlinear optical spectroscopy. A one‐dimensional tight‐binding model with diagonal disorder is applied and the Coulomb interaction is treated consistently. In the ordered situation the center‐of‐mass momentum (K) selection rule leads to only the lowest transition for K = 0. The break down of the com‐K‐selection rule produces the well known asymmetric excitonic lines of disordered semiconductors. The coupling between the lowest dominant transition to this modified com‐continuum yields Fano‐like features in the nonlinear spectra.     

以CuC2O4微球为模板可控合成一维CuC2O4/ZnO异质结构

以CuC2O4纳米微球为模板,通过水热法在120 ℃、1 h时成功合成了一维CuC2O4/ZnO异质结构。 采用热重分析（TGA）、场发射扫描电子显微镜（FE-SEM）、能量散射Ｘ射线谱（EDX）、透射电子显微镜(TEM)和Ｘ射线粉末衍射(XRD)等测试技术对产物的结构和形貌进行了表征。 结果表明,所得产物为一维CuC2O4/ZnO纳米棒束,长约1 μｍ,直径约500 nm。 每个棒束由许多纳米棒沿同一方向组装而成。 TEM照片和EDX光谱表明,CuC2O4和ZnO形成了均匀的异质结构。     

Structural and local electrical properties of AlInN/AlN/GaN heterostructures

GaN layers and Al_1−xIn_xN/AlN/GaN heterostructures have been studied by scanning probe microscopy methods. Threading dislocations (TDs), originating from the GaN (0 0 0 1) layer grown on sapphire, have been investigated. Using Current-Atomic Force Microscopy (C-AFM) TDs have been found to be highly conductive in both GaN and AlInN, while using semi-contact AFM (phase-imaging mode) indium segregation has been traced at TDs in AlInN/AlN/GaN heterostructures. It has been assessed that In segregation is responsible for high conductivity at dislocations in the examined heterostructures.     

Determination of the series resistance under the Schottky contacts of AlGaN/AlN/GaN Schottky barrier diodes

Rectangular AlGaN/AlN/GaN heterostructure field-effect transistors (HFETs) were fabricated,and the gate and the source of the HFETs consisted of AlGaN/AlN/GaN Schottky barrier diodes (SBDs).Based on the measured forward current-voltage and the capacitance-voltage characteristics of the AlGaN/AlN/GaN SBDs,the series resistance under the Schottky contacts (RS) was calculated using the method of power consumption,which has been proved to be valid.Finally,the method of power consumption for calculating R S was successfully used to study the two-dimensional electron gas electron mobility for a series of circular AlGaN/AlN/GaN SBDs.It is shown that the series resistance under the Schottky contacts cannot be neglected and is important for analysing and characterizing the AlGaN/AlN/GaN SBDs and the AlGaN/AlN/GaN HFETs.     

Synthesis of ultrathin and compact Au@MnO2 nanoparticles for shell‐isolated nanoparticle‐enhanced Raman spectroscopy (SHINERS)

Shell‐isolated nanoparticle‐enhanced Raman spectroscopy (SHINERS) based on Au@SiO₂ or Au@Al₂O₃ nanoparticles (NPs) shows great potential to break the long‐standing limitations of substrate and surface generality of surface‐enhanced Raman scattering (SERS). However, the shell of SiO₂ or Al₂O₃ can easily be dissolved in alkaline media, which limits the applications of SHINERS in alkaline systems. Besides that, the synthesis of Au@SiO₂ NPs can be further simplified and Au@Al₂O₃ NPs be replaced by other NPs that are more amenable for mass production. In an attempt to make SHINERS NPs available in any systems practically, we report the synthesis of ultrathin and compact Au@MnO₂ NPs. The shell thickness of MnO₂ can be controlled down to about 1.2 nm without any pinhole. SHINERS based on such Au@MnO₂ NPs exhibits much higher Raman enhancement effect than Au@SiO₂ NPs and can be applied in alkaline systems in which Au@SiO₂ or Au@Al₂O₃ NPs cannot be applied. Copyright © 2011 John Wiley & Sons, Ltd.