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

Abstract

The vertical variation of in-plane strain induced by an In0.1Ga0.9As single quantum well (SQW) embedded in a free-standing wire structure 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 (2̄20) and (2̄2̄0) 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 (Δa‖/a≈3.5×10−4) 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.

Evaluation of strain distribution in freestanding and buried lateral nanostructures

“…11 Combining the curve simulations in terms of the distorted wave Born approximation ͑DWBA͒ and finite-element calculations, we found a quantitative correlation between the residual in-plane strain and the PL-energy of GaAs /In x Ga 1Ϫx As/GaAs nanostructures. 14 Furthermore, we found a periodic strain modulation for the first time in an almost homogeneous Al x Ga 1Ϫx As layer overgrown onto a GaAs lateral wire structure. 15 This periodic strain distribution may suppress the strain relaxation within the SQW and has to be considered for device optimization.…”

“…As was found to be the case for Sample 2, the real spatial distribution of strains dominates in the formation of the diffraction pattern. Our previous attempts at modeling the displacement functions by polynomials 14 resulted in some discrepancies between theory and experiment. Fig.…”

“…9, 10, and 11, where the panels ͑a͒ and ͑b͒ correspond to the negative and positive order GTR's, respectively. According to recent studies, 14 the GTR fringe structure contains detailed information on the shape and symmetry of the wires as well as on the depth composition of the sample. The mismatch of the maxima positions in different GTR's occurs when the wires have a trapezoidal or triangular shape, whereas the mismatching of the ϩn and Ϫn GTR's points out the asymmetry of the wire cross-section.…”

“…The transverse scan across the 2 20 RLP shown in Fig. 8͑b͒ provides a unique possibility 5,14 to investigate the geometrical parameters of the quantum wires because of the insensitivity to the strain profile of the sample. The statistically averaged values for the dimensions of the wire segments were extracted from the fits of experimental data.…”

“…The phase shift induced by the SQW and the interference between surface scattered and SQW waves produce an anharmonic modulation of GTR's, typical for ͑200͒ reflection. 13,14 The oscillations of truncation rods dampen rapidly with increasing GTR order. The behavior of diffraction curves from this reflection is very sensitive to the vertical strain gradient within the undersurface region of the wires.…”