ANALYSIS OF STRAIN RELAXATION IN FREE STANDING AND BURIED SQW--LATERAL- STRUCTURES
N. Darowski1, U. Pietsch1, K.H. Wang2, A. Forchel2, S. Kycia3 and Q. Shen3
1Department of Physics, University of
Potsdam, Germany
2Technical Physics, University of
Würzburg, Germany
3CHESS, Cornell University, Ithaca
N.Y., USA
Keywords: SQW, strain relaxation, x-ray diffraction
Lateral surface nanostructures defined on a MBE grown GaAs/GaInAs/GaAs single quantum well structure have been investigated before and after overgrowth with (Al)GaAs. The geometric parameters of the free standing grating were defined by electron beam exposure and a subsequent etching step. Two different shapes (triangular and rectangular) were realized by wet-chemical and ion beam etching, respectively. Some of the samples were overgrown partially or completely by a second MBE step.
The strain analysis was performed by two complementary x-ray diffraction methods, coplanar high resolution x-ray diffraction (HRXRD) and non--coplanar depth resolved x-ray grazing incidence diffraction (GID). Photoluminescence experiments provided additional information about the strain relaxation in the nanostructure and were compared to the x-ray diffraction results.
In case of HRXRD we determined the average out-of plane and in-plane strain acting in the nanostructure by running reciprocal space maps close to fundamental Bragg reflections of the substrate [1]. Whereas the in-plane strain appears tensile at the free standing wires we found compressive strain after overgrowth. The photoluminescence experiments confirmed the results as a shift of the signal was observed, for the free standing grating towards smaller energies and in case of the buried grating towards higher energies.
Since 1D surface structures were under investigation GID experiments enable us to determine the wire shape and their strain profile separately running either transverse or longitudinal scans across symmetry-equivalent in-plane Bragg reflections [2]. We resolved the variation of in-plane strain as a function of depth below the surface. For the overgrown samples we found a lateral structure of the same periodicity as the grating in the nominal homogeneous top layer appearing up to the complete smooth sample surface. This was interpreted as a lateral strain modulation induced by the buried nanostructure itself [3].
The strain acting in the quantum well and surrounding material depends on the wire shape and can be interpreted in terms of elasticity theory using finite-element calculations.