Evaluation of strain distribution in freestanding and buried lateral nanostructures

Abstract

A free-standing lateral nanostructure based on GaAs͓001͔ containing a Ga 0.97 In 0.03 As single quantum well and similar structures after the overgrowth with GaAs and AlAs, respectively, have been investigated by high-resolution x-ray grazing incidence diffraction ͑GID͒ and conventional x-ray diffraction ͑HRXRD͒. The wire shape of the freestanding structure and the lateral density variation in the overgrown samples, were determined by running scans with constant length of the scattering vector ͑transverse scans͒ across the grating truncation rods ͑GTR's͒ close to the (2 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 for depth resolution, the in-plane strain distribution was analyzed for different values of depth below the sample surface. The strain analysis was completed by HRXRD measurements close to the ͑004͒ reflection. The x-ray measurements were interpreted in terms of the distorted wave Born approximation applied for GID geometry. The strain distribution is determined by comparing the measured GTR intensities with the corresponding simulations containing the displacement fields obtained from finite-element calculations. At the freestanding wire structure we find laterally compressive strain of about ⌬a/a ʈ ϭϪ2ϫ10 Ϫ3 at the single quantum well ͑SQW͒ 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-plane strain is still compressive after GaAs overgrowth and of similar amount compared to the freestanding grating. The strain is increased by about 30% after overgrowth with AlAs. For both overgrown samples the strain gradient near the wire side walls is reduced, but reaches a maximum close to the SQW. Accompanied by the defect passivation, these findings explain the difference in the energy shift of the photoluminescence line between freestanding and overgrown lateral nanostructures. ͓S0163-1829͑99͒08047-9͔

Determination of strain fields and composition of self-organized quantum dots using x-ray diffraction

“…18,21 For example, the determination of the strain distribution within etched nanostructures using high resolution x-ray diffraction and grazing incidence diffraction is discussed in Refs. [9][10][11][12][13][14][15][16][17]. Similarly, the lattice distortions in self-organized nanostructures have been determined in Refs.…”

Strain in buried quantum wires: Analytical calculations and x-ray diffraction study

“…X-ray diffraction is proven to be a very sensitive technique to measure the strain in wires. [2][3][4][5][6][7][8][9][10][11][12][13] A mean strain in the wires can be obtained simply from positions of the corresponding diffraction peaks or their envelope functions. The strain distribution, however, cannot be directly obtained from the x-ray diffraction pattern, and requires a solution of the elastic equilibrium problem.…”

“…Up to now x-ray diffraction studies of wire arrays were either restricted with a qualitative analysis and plausible assumptions [2][3][4][5][6][7][8] or used laborious finite element calculations. [9][10][11][12][13] The problem of elastic equilibrium of a periodic array of domains misfitted with respect to the surrounding matrix allows an analytical solution by means of Fourier series expansion. The solutions were obtained for diverse physical applications.…”

Ripple structure of crystalline layers in ion-beam-induced Si wafers

“…[8][9][10][11] In particular, grazing incidence diffraction (GID) is sensitive to the in-plane crystalline structure [12][13][14][15][16] and can be used to map the in-plane structure as a function of depth. The purpose of the present work is to demonstrate how GID can be utilized to bring out the subsurface (amorphous-crystalline interface) ripple structure in addition to the top ripple structure observed by atomic force microscopy (AFM) of a keV ionbeam-modified Si(001) surface.…”