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Schematic illustration of grazing incidence in-plane X-ray diffraction measurement of GaN nanopillars. Inset (a) shows the cross section ofthe pillar with the presence of light evanescence into the pillar and inset (b) shows the top view of the pillar with the presence of diffracting planes.
SEM images of GaN tapered nanopillars (a) at top view and (b) at 80°.
(a) Normalized in-plane XRD spectra of a GaN epilayer grown on Si and GaN tapered pillars with different pillar heights. The pillar spectrum is fitted by two Gaussian curves. (b) Measured a-spacing and corresponding in-plane strain as function of pillar height. The relaxation is well fitted by an exponential curve (red) and the fitting parameters are shown in the figure.
Simulated strain distribution of (a) a fully relaxed GaN tapered pillar (∅top/∅bottom/height: 250/350/250 nm) and (b) a partially relaxed tapered pillar (∅top/∅bottom/height: 250/270/50 nm) on a bulk with initial in-plane stress of 780 MPa, and (c) the average simulated in-plane strain at the top of the pillar as function of pillar height with fitting curve (red) and fitting parameters presented.
Measured lattice spacing and calculated stress of GaN epilayers and pillars (diameter = 250 nm) on Si and sapphire, derived from in-plane and symmetric XRD measurements. σa and εa denote the in-plane stress and in-plane strain, respectively.
Relaxation depth (R) obtained from three different structure geometries. Three nanostructure models from left to right are two circular cylinders and an elliptic cylinder. Relaxation depth (R) is defined by the equation , where and are the initial strain of as-grown GaN epilayer and pillar height, respectively.
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