The coalescence in dense arrays of spontaneously formed GaN nanowires proceeds by bundling: adjacent nanowires bend and merge at their top, thus reducing their surface energy at the expense of the elastic energy of bending. We give a theoretical description of the energetics of this bundling process. The bending energy is shown to be substantially reduced by the creation of dislocations at the coalescence joints. A comparison of experimental and calculated x-ray diffraction profiles from ensembles of bundled nanowires demonstrates that a large part of the bending energy is indeed relaxed by plastic deformation. The residual bending manifests itself by extended tails of the diffraction profiles.
Top-down fabricated GaN nanowires, 250 nm in diameter and with various heights, have been used to experimentally determine the evolution of strain along the vertical direction of 1-dimensional objects. X-ray diffraction and photoluminescence techniques have been used to obtain the strain profile inside the nanowires from their base to their top facet for both initial compressive and tensile strains. The relaxation behaviors derived from optical and structural characterizations perfectly match the numerical results of calculations based on a continuous media approach. By monitoring the elastic relaxation enabled by the lateral free-surfaces, the height from which the nanowires can be considered strain-free has been estimated. Based on this result, NWs sufficiently high to be strain-free have been coalesced to form a continuous GaN layer. X-ray diffraction, photoluminescence and cathodoluminescence clearly show that despite the initial strain-free nanowires template, the final GaN layer is strained.
We investigate the strain state of ensembles of thin and nearly coalescence-free self-assembled GaN nanowires prepared by plasma-assisted molecular beam epitaxy on Ti/Al$_{2}$O$_{3}(0001)$ substrates. The shifts of Bragg peaks in high-resolution X-ray diffraction profiles reveal the presence of a homogeneous tensile strain in the out-of-plane direction. This strain is inversely proportional to the average nanowire radius and results from the surface stress acting on the nanowire sidewalls. The superposition of strain from nanowires with different radii in the same ensemble results in a broadening of the Bragg peaks that mimics an inhomogeneous strain on a macroscopic scale. The nanowire ensembles show a small blueshift of the bound-exciton transitions in photoluminescence spectra, reflecting the existence of a compensating in-plane compressive strain, as further supported by grazing incidence x-ray diffraction measurements carried out at a synchrotron. By combining X-ray diffraction and photoluminescence spectroscopy, the surface stress components $f_{x}$ and $f_{z}$ of the air-exposed GaN${1bar100}$ planes that constitute the nanowire sidewalls are determined experimentally to be 2.25 and $-0.7$~N/m, respectively.
We depict the use of x-ray diffraction as a tool to directly probe the strain status in rolled-up semiconductor tubes. By employing continuum elasticity theory and a simple model we are able to simulate quantitatively the strain relaxation in perfect crystalline III-V semiconductor bi- and multilayers as well as in rolled-up layers with dislocations. The reduction in the local elastic energy is evaluated for each case. Limitations of the technique and theoretical model are discussed in detail.
We analyze the lineshape of x-ray diffraction profiles of GaN epitaxial layers with large densities of randomly distributed threading dislocations. The peaks are Gaussian only in the central, most intense part of the peak, while the tails obey a power law. The $q^{-3}$ decay typical for random dislocations is observed in double-crystal rocking curves. The entire profile is well fitted by a restricted random dislocation distribution. The densities of both edge and screw threading dislocations and the ranges of dislocation correlations are obtained.
Temperature dependent structural phase transitions of SrRuO3 thin films epitaxially grown on SrTiO3(001) single crystal substrates have been studied using high-resolution x-ray diffraction. In contrast to bulk SrRuO3, coherently strained epitaxial layers do not display cubic symmetry up to ~730 oC and remain tetragonal. Such behavior is believed to be induced by compressive strain between the SrRuO3 layer and SrTiO3 substrate due to lattice mismatch. The tetragonal symmetry during growth explains the single domain growth on miscut SrTiO3 substrates with step edges running along the [100] or [010] direction.
Vladimir M. Kaganer
,Bernd Jenichen
,Oliver Brandt
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(2016)
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"Elastic vs. plastic strain relaxation in coalesced GaN nanowires: an x-ray diffraction study"
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Vladimir Kaganer
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