Near-infrared photoluminescence enhancement in Ge/CdS and Ge/ZnS core/shell nanocrystals: Utilizing IV/II-VI semiconductor epitaxy

Ge nanocrystals have a large Bohr radius and a small, size-tunable band gap that may engender direct character via strain or doping. Colloidal Ge nanocrystals are particularly interesting in the development of near-infrared materials for applications in bioimaging, telecommunications and energy conversion. Epitaxial growth of a passivating shell is a common strategy employed in the synthesis of highly luminescent II-VI, III-V and IV-VI semiconductor quantum dots. Here, we use relatively unexplored IV/II-VI epitaxy as a way to enhance the photoluminescence and improve the optical stability of colloidal Ge nanocrystals. Selected on the basis of their relatively small lattice mismatch compared with crystalline Ge, we explore the growth of epitaxial CdS and ZnS shells using the successive ion layer adsorption and reaction method. Powder X-ray diffraction and electron microscopy techniques, including energy dispersive X-ray spectroscopy and selected area electron diffraction, clearly show the controllable growth of as many as 20 epitaxial monolayers of CdS atop Ge cores. In contrast, Ge etching and/or replacement by ZnS result in relatively small Ge/ZnS nanocrystals. The presence of an epitaxial II-VI shell greatly enhances the near-infrared photoluminescence and improves the photoluminescence stability of Ge. Ge/II-VI nanocrystals are reproducibly 1-3 orders of magnitude brighter than the brightest Ge cores. Ge/4.9CdS core/shells show the highest photoluminescence quantum yield and longest radiative recombination lifetime. Thiol ligand exchange easily results in near-infrared active, water-soluble Ge/II-VI nanocrystals. We expect this synthetic IV/II-VI epitaxial approach will lead to further studies into the optoelectronic behavior and practical applications of Si and Ge-based nanomaterials

Nonlinear fractional differential equations in nonreflexive Banach spaces and fractional calculus

The aim of this paper is to correct some ambiguities and inaccuracies in Agarwal et al. (Commun. Nonlinear Sci. Numer. Simul. 20(1): 59-73, 2015; Adv. Differ. Equ. 2013: 302, 2013, doi:10.1186/1687-1847-2013-302) and to present new ideas and approaches for fractional calculus and fractional differential equations in nonreflexive Banach spaces

Extraction of molecular electron momentum densities from electron density contour maps

Electron momentum densities and Compton profiles for some linear di- and tri-atomic heteronuclear molecules have been extracted from the exclusive knowledge of electron density in the coordinate space, &#961;(<SUB>r</SUB>). The procedure developed is based upon semi-classical considerations. The application of the present method to experimentally available electron dencontour maps is discussed

Use of energy constraint for refinement of electron momentum distributions

A procedure based on the calculus of variations to refine a given electron momentum density with the constraints of the given number of electrons and a prescribed &lt;p<SUP>2</SUP>&gt; expectation value has been developed. This procedure has been tested with near-Hartree-Fock (NHF) electron momentum density data employed as initial distributions for the atoms beryllium through neon. The constraints of the corresponding CI-theoretical and experimental energy values have been imposed. In all cases, the values of the refined electron momentum density at p=0 and the peak value of the Compton profile J(0) are lower than the corresponding NHF ones. This lowering of J(0) value is generally in conformity with the corresponding results from CI and MC-SCF calculations. The present procedure is seen to simulate well the electron momentum densities and &lt;p<SUP>-1</SUP>&gt; as well as &lt;p&gt; expectation values obtained from correlated wave functions without ever doing extra quantum mechanical calculations

Refinement of electron momentum densities of ionic solids using an experimental energy constraint

It is demonstrated how one can refine a given approximate momentum density distribution using a constraint of the experimental electronic energy. The technique developed is based on the calculus of variations. This technique has been applied to ionic solids such as LiF, LiCIl NaF, NACl, MgO, KF and KCl

Electron momentum distributions and atomic r<SUP>n</SUP> expectation values

The r<SUP>n</SUP> expectation values have been extracted from the known electron momentum distributions for hydrogen, helium, argon, and krypton atoms with the use of a semiclassical approach. These values compare fairly well with their Hartree-Fock counterparts. This procedure provides a link between the distribution of electrons in the momentum space and that in the coordinate space

Analysis Of Vedic Multiplier

Multipliers are extensively used in FIR filters, Microprocessors, DSP and communication applications. For higher order multiplications, a huge number of adders or compressors are to be used to perform the partial product addition. The need of low power and high speed Multiplier is increasing as the need of high speed processors are increasing. In this paper, a high performance, high throughput and area efficient architecture of a multiplier for the Field Programmable Gate Array (FPGAs) is proposed