Evaluation of strain distribution in freestanding and buried lateral nanostructures

A free-standing lateral nanostructure based on GaAs[001] containing a Ga0.9 7In0.03As single quantum well and similar structures after the overgrowth w ith GaAs and AlAs, respectively, have been investigated by high-resolution x-ray grazing incidence diffraction (GID) and conventional x-ray diffractio n (HRXRD). The wire shape of the freestanding structure and the lateral den sity variation in the overgrown samples, were determined by running scans w ith constant length of the scattering vector (transverse scans) across the grating truncation rods (GTR's) close to the ((2) over bar 20) reflection. The in-plane strain distribution became available crossing the (220) GTR's by a scan in the longitudinal direction. Exploiting the capability of GID f or depth resolution, the in-plane strain distribution was analyzed for diff erent values of depth below the sample surface. The strain analysis was com pleted by HRXRD measurements close to the (001) reflection. The x-ray measu rements were interpreted in terms of the distorted wave Born approximation applied for GID geometry. The strain distribution is determined by comparin g the measured GTR intensities with the corresponding simulations containin g the displacement fields obtained from finite-element calculations. At the freestanding wire structure we End laterally compressive strain of about D elta a/a(parallel to) = -2 X 10(-3) at the single quantum well (SQW) with a steep strain gradient close to the wire side walls. Both overgrown samples show pronounced lateral strain variation within the overgrown layer, which still appears up to the completely planar surface. Within the SQW the in-p lane strain is still compressive after GaAs overgrowth and of similar amoun t compared to the freestanding grating. The strain is increased by about 30 % after overgrowth with AlAs. For both overgrown samples the strain gradien t near the wire side walls is reduced, but reaches a maximum close to the S QW. Accompanied by the defect passivation, these findings explain the diffe rence in the energy shift of the photoluminescence line between freestandin g and overgrown lateral nanostructures. [S0163-1829(99)08047-9].