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We investigate the strain state of ensembles of thin and nearlycoalescence-free self-assembled GaN nanowires prepared by plasma-assistedmolecular beam epitaxy on Ti/Al$_{2}$O$_{3}(0001)$ substrates. The shifts ofBragg peaks in high-resolution X-ray diffraction profiles reveal the presenceof a homogeneous tensile strain in the out-of-plane direction. This strain isinversely proportional to the average nanowire radius and results from thesurface stress acting on the nanowire sidewalls. The superposition of strainfrom nanowires with different radii in the same ensemble results in abroadening of the Bragg peaks that mimics an inhomogeneous strain on amacroscopic scale. The nanowire ensembles show a small blueshift of thebound-exciton transitions in photoluminescence spectra, reflecting theexistence of a compensating in-plane compressive strain, as further supportedby grazing incidence x-ray diffraction measurements carried out at asynchrotron. By combining X-ray diffraction and photoluminescence spectroscopy,the surface stress components $f_{x}$ and $f_{z}$ of the air-exposedGaN$\{1\bar100\}$ planes that constitute the nanowire sidewalls are determinedexperimentally to be 2.25 and $-0.7$~N/m, respectively.

Radius-Dependent Homogeneous Strain in Uncoalesced GaN Nanowires