N. Darowski

Lateral arrangement of self-assembled quantum dots in an SiGe/Si superlattice

Lateral ordering of self-organized quantum dots in a SiGe/Si (001) multilayer has been investigated by grazing incidence x-ray diffraction and Monte Carlo growth simulation. It has been demonstrated that the lateral ordering stems from the elastic anisotropy of the crystal. From the reciprocal space map of the scattered intensity it follows that the dots create a disordered square grid with the axes along [100] and [010]. Both the orientation of the array axes and the mean dot distance have been obtained from the growth simulation.

Strain relaxation in periodic arrays of Si/SiGe quantum wires determined by coplanar high-resolution x-ray diffraction and grazing incidence diffraction

Elastic relaxation in dry-etched periodic wires fabricated from molecular beam epitaxy grown Si/SiGe multilayers was studied by coplanar and grazing incidence (GID) high-resolution x-ray diffraction. The inhomogeneous strain distribution in the wires was calculated by the finite element method, which provided the input data for simulations of the scattered intensities using kinematical diffraction theory used for comparison with measured reciprocal space maps. A fabrication-induced layer covering the wire surfaces, modifies the strain distribution. Using GID, the geometrical shape of the wires and their in-plane strain can be determined independently of each other.

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

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 (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...

X-RAY STUDY OF LATERAL STRAIN AND COMPOSITION MODULATION IN AN ALGAAS OVERLAYER INDUCED BY A GAAS LATERAL SURFACE GRATING

A lateral surface grating has been prepared by holographic photolithography followed by wet chemical etching on a slightly misaligned GaAs [001] substrate. The structural parameters were investigated before and after thermal annealing by triple-axis high resolution x-ray diffraction (HRXRD) and scanning electron microscopy (SEM). In particular HRXRD was used to collect reciprocal space maps providing periodicity and shape of the grating. After overgrowth of the free standing nanostructure with AlxGa1−xAs the HRXRD technique fails. Only first order grating truncation rods remain in the (004) HRXRD map. They disappear completely running asymmetric reflections. On the other hand SEM at the cleavage plane reveals the perfection of the overgrowth process and the smoothness of the sample surface. Thus nondestructive analysis of the buried lateral nanostructure was performed by triple-axis x-ray grazing incidence diffraction using synchrotron radiation. This method is exclusively sensitive to the lateral strain ...

Analysis of the strain distribution in lateral nanostructures for interpreting photoluminescence data

Abstract The strain distribution of free-standing and buried lateral wire structures based on GaAs [0 0 1] containing a In0.14Ga0.86 As single quantum well were measured by depth-resolved high-resolution grazing-incidence diffraction in order to interprete photoluminescence (PL) results obtained from these and similar samples. The spatial strain distribution was analyzed by running strain-sensitive in-plane scans for different penetration depths below the surface and recording the respective out-of-plane intensity curves, i.e. truncation rods. The 3D displacement distribution within the wires was derived from the X-ray scattering data using a simulation on basis of the distorted wave Born approximation taking into account the adapted parameters of a model structure generated by a finite-element calculation. Applying the deformation potential approach the corresponding strain distribution within the quantum well was translated into a local variation of the energy gap. Considering the twofold quantization and the exciton binding energy in addition the variation of the minimum gap energy of the model structures reproduces qualitatively the measured functional dependence of the PL-shift on the wire width.

Grazing-incidence diffraction strain analysis of a laterally-modulated multiquantum well system produced by focused-ion-beam implantation

Focused Ga+ ion beam implantation was used to define a laterally periodic modulation of the electronic band gap in a GaAs/Ga0.97In0.03As/Al0.2Ga0.8As/GaAs [001] multiquantum well structure. The samples were investigated as-implanted and after a rapid thermal annealing (60 s at 650 and 800 °C) by means of x-ray grazing-incidence diffraction. The method provides a separate inspection of the induced strain and the damage profiles as a function of depth below the sample surface. For samples with an ion dose of 5×1013 cm−2, we found a nearly uniform lateral strain amplitude of about 2×10−3 up to the maximum information depth of about 500 nm. It was accompanied by the appearance of structural defects. Rapid thermal annealing at 650 °C has reduced the strain amplitude by a factor of five as well as the density of volume defects. The maximum strain amplitude were found in a depth of about 100 nm. After rapid thermal annealing at 800 °C, the strain has disappeared.

X-ray diffraction and reflectivity analysis of GaAs/InGaAs free-standing trapezoidal quantum wires

Combined x-ray diffraction and reflectivity experiments have been performed on free-standing trapezoidal GaAs/InGaAs quantum wires using a conventional x-ray tube. Interpreting the intensity distribution around (004) by curve simulation of the extracted coherent grating truncation rods on the basis of a semikinematical diffraction theory (DWBA) the shape and geometric parameters as well as the strain within the wires could be determined taking the results of a finite element calculation of the atomic displacements into account. The map of the coplanar x-ray reflectivity around (000), as well as the intensity profiles of the coherent grating truncation rods, located equidistantly around the specularly reflected beam, have been recorded in order to estimate the roughness properties of the sample interfaces as well as the wire shape and layer set-up without the influence of strain. All small-angle as well as wide-angle scattering experimental results went in to the mutually consistent estimate of the sample properties. The experiments performed for a conventional x-ray tube supply a parameter set comparable in completeness and precision to that obtained from similar samples by interpreting synchrotron experiments.

X-ray grazing incidence study of inhomogeneous strain relaxation in Si/SiGe wires

The elastic strain relaxation in a series of dry-etched periodic multilayer Si/SiGe wire samples with different etching depths was investigated systematically by means of grazing incidence diffraction (GID). The samples were patterned by holographic lithography and reactive ion etching from a Si/SiGe superlattice grown by molecular beam epitaxy. Scanning electron microscopy and atomic force microscopy were employed to obtain information on the shape of the wires. The inhomogeneous strain distribution in the etched wires and in the non-etched part of the multilayers was derived by means of finite element calculations which were used as an input for simulations of the scattered X-ray intensities in depth dependent GID. The theoretical calculations for the scattered intensities are based on distorted-wave Born approximation. The unperturbed scattering potential was chosen with a reduced optical density corresponding to the ratio of wire width and wire period, in order to reflect the main interaction between the incident X-rays and the patterned samples. The calculations are in good agreement with the experimental data demonstrating the variation of strain relaxation with depth.

In-plane strain and strain relaxation in laterally patterned periodic arrays of Si/SiGe quantum wires and dot arrays

The depth dependent strain relaxation in photolithographically defined and reactive ion etched Si/SiGe quantum wire and dot arrays is determined by high resolution grazing incidence x-ray diffraction. The laterally periodic structures were aligned along two orthogonal [110] and [110] directions on the (001) surface. By recording reciprocal space maps around the (220) and (220) reciprocal lattice points, the shape and in-plane strain could be determined independently of each other. Using triple axis diffractometry and changing the effective penetration depth of the x-ray radiation between 5 and 300 nm the strain relaxation in the wires and dots could be determined depth resolved.

In-plane strain and shape analysis of Si/SiGe nanostructures by grazing incidence diffraction

Abstract Surface-sensitive X-ray grazing incidence diffraction (GID) was used to investigate the elastic strain relaxation in laterally periodic Si/SiGe wires, oriented along the [ 1 1 0] direction, fabricated by holographic lithography and reactive ion etching from a 10-period multilayer. Using transverse and longitudinal scans, i.e. with the diffraction vector parallel and perpendicular to the wire direction information on the shape and the strain status were obtained from measurements at different incidence and exit angles. For the simulation a modified effective refractive index profile, i.e. a different average electron density for the etched and the non-etched wire pattern was taken into account. Using data from finite element calculations of the strain fields, a simulation based on DWBA is in good agreement with the experimental data.