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

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012