In-plane strain distribution in free-standing GaAs/InGaAs/GaAs single quantum well surface nanostructures on GaAs(001)

The vertical variaton of in-plane strain induced by an In01Ga0.9As single quantum well (SQW) embedded in a free-standing wire stucture on GaAs(001) has been investigated by depth resolved x-ray grazing incidence diffraction. If the wires are oriented along the (110) direction both the shape and strain influence on the x-ray intensity distribution can be separated by running transverse or longitudinal scans across the grating truncation rods (GTRs) close to the (220) and (220) in-plane Bragg reflection, respectively. The GTRs themselves are modulated due to the vertical layering of the wires. The vertical strain variation in the vicinity of SQW is particularly inspected at the weak (200) Bragg reflection which is most sensitive to the scattering density difference between the SQW and GaAs. The theoretical analysis is based on the distorted wave Born approximation for grazing incidence geometry. The structural parameters of the surface nanostructure were determined with high accuracy by fitting of the complete set of experimental GTRs simultaneously. In agreement with finite-element calculations we find a maximum in-plane lattice displacement within the SQW of (Formel) with respect to the substrate. It induces dilative in-plane strain in the GaAs confinement layers decreasing towards the upper free surface and the bulk, respectively. The evaluated in-plane strain within the SQW is used for estimating the strain induced redshift of the photoluminescence wavelength of the respective optical device.