Qian Zhang
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MATHEMATICS COLLOQUIUM
Speaker: Qian Zhang Abstract. GaAs-AlGaAs core-shell nanowires with heterostructures have attracted much attention because of their significant advantages and great potentials for creating high performance nanophotonics and nanoelectronics. The spontaneous formation of Al-rich stripes along certain crystallographic directions and quantum dots near the apexes of the shell observed in AlGaAs shells. Controlling the formation of these heterostructures in the core-shell structure remains a challenge. A two-dimensional model valid on the wire cross section, that accounts for capillarity in the faceted surface limit and deposition has been developed for the evolution of the shell morphology and concentration in AlGaAs alloys. The model concerns a completely faceted shell-vapor interface. The objective is to understand the mechanisms of the formation of the radial heterostructures (Al-rich stripes and Al-poor quantum dots) in the nanowire shell. There are two issues that need to be understood. One is the mechanism responsible for the morphological evolution of the shells. Analysis and simulation results suggest that deposition introduces facets not present on the equilibrium Wulff shapes. Balance between diffusion and deposition yields the small facets with slowly time-varying sizes, which are stripe structures, whereas deposition dominant growth can lead to quantum dots structures observed in experiments. There is no self-limiting facet size in this case. The other issue is the mechanism responsible for the segregation of Al atoms in the shells. It is found that the mobility difference of the atoms on the {112} and {110} facets together determine the non-uniform concentration of the atoms in the shell. In particular, even though themobility of Al on {110} facets is smaller than that of Ga, Al rich stripes are predicted to form along the {112} facets when the difference of the mobilities of Al and Ga atoms is large enough on {112} facets. As the size of the shell increases, deposition becomes more important. The Al-poor dots are obtained at the apices of {112} facets, if the attachment rate of Al atoms is smaller there. |