Selective coherent x-ray diffractive imaging of displacement fields in (Ga,Mn)As/GaAs periodic wires

Minkevich, A. A.; Fohtung, Edwin; Slobodskyy, T.; Riotte, M.; Grigoriev, D.; Schmidbauer, M.; Irvine, A. C.; Novák, V.; Holý, V.; Baumbach, Tilo

doi:10.1103/physrevb.84.054113

Cited by 28 publications

(37 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In contrast to that, the signal to noise ratio of the experimental scattering data used by Minkevich et al in [24,25] had signal to noise ratio of approximately 100 (in the diffuse cloud, excluding the central Bragg peak). As a consequence, most data points in reciprocal space are corrupted by noise and additional diffuse scattering, e.g., by optical elements, Be windows of vacuum flight tubes, etc.…”

Section: Artifacts In Reciprocal Spacementioning

confidence: 74%

“…The shape Ω can be accessed by complementary techniques like GISAXS [8], AFM [9][10][11][12] or SEM [13]. By this approach, several inhomogeneously strained nano-sized objects like quantum dots and quantum wires have already been inspected at synchrotron facilities by CXDI [2,5,6,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. In most cases, a combination of the hybrid input output algorithm (HIO-algorithm) and error reduction (ER-algorithm) has been employed [29][30][31] to solve the non-linear non-local system of equations underlying the reconstruction of the displacement field.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Retrieving the displacement of strained nanoobjects: the impact of bounds for the scattering magnitude in direct space

Köhl¹,

Schroth²,

Minkevich³

et al. 2013

Opt. Express

Self Cite

View full text Add to dashboard Cite

Coherent X-ray diffraction imaging (CXDI) of the displacement field and strain distribution of nanostructures in kinematic far-field conditions requires solving a set of non-linear and non-local equations. One approach to solving these equations, which utilizes only the object's geometry and the intensity distribution in the vicinity of a Bragg peak as a priori knowledge, is the HIO+ER-algorithm. Despite its success for a number of applications, reconstruction in the case of highly strained nanostructures is likely to fail. To overcome the algorithm's current limitations, we propose the HIO M O R +ER M -algorithm which allows taking advantage of additional a priori knowledge of the local scattering magnitude and remedies HIO+ER's stagnation by incorporation of randomized overrelaxation at the same time. This approach achieves significant improvements in CXDI data analysis at high strains and greatly reduces sensitivity to the reconstruction's initial guess. These benefits are demonstrated in a systematic numerical study for a periodic array of strained silicon nanowires. Finally, appropriate treatment of reciprocal space points below noise level is investigated.

show abstract

Section: Artifacts In Reciprocal Spacementioning

confidence: 74%

mentioning

confidence: 99%

Retrieving the displacement of strained nanoobjects: the impact of bounds for the scattering magnitude in direct space

Köhl¹,

Schroth²,

Minkevich³

et al. 2013

Opt. Express

Self Cite

View full text Add to dashboard Cite

show abstract

“…This is particularly important for strained nanostructures where the calculation often uses a fast Fourier transform approximation, even though the displacements from the ideal structure are large. This could also be useful for coherent diffraction imaging in Bragg condition for strained nanostructures (Minkevich et al, 2007;Robinson & Harder, 2009;Minkevich et al, 2009;Favre-Nicolin et al, 2010;Diaz et al, 2010), especially in order to extend this method to severely distorted lattices (e.g. near an epitaxial interface with dislocations, a grain boundary,...).…”

Section: Resultsmentioning

confidence: 99%

Fast computation of scattering maps of nanostructures using graphical processing units

et al. 2011

View full text Add to dashboard Cite

Scattering maps from strained or disordered nano-structures around a Bragg reflection can either be computed quickly using approximations and a (Fast) Fourier transform, or using individual atomic positions. In this article we show that it is possible to compute up to 4.10 10 re f lections · atoms · s −1 using a single graphics card, and we evaluate how this speed depends on number of atoms and points in reciprocal space. An open-source software library (PyNX) allowing easy scattering computations (including grazing incidence conditions) in the Python language is described, with examples of scattering from non-ideal nanostructures.

show abstract

“…A more detailed description of this approach can be found in our earlier work. [13,15] We transform this band-limited frequency domain constraint into a direct space constraint of limited lattice displacement gradient. By utilizing the uniformity of the electron density (and its threshold) constraints [15] along with the standard support constraints, we reconstruct the 3D distribution of NW electron density (shape) and corresponding phases (related to the projection of displacement field) from the (004) and (111) Bragg peaks, shown in Figs.…”

mentioning

confidence: 99%

“…[7,8] To test this assumption, we utilized the Bragg peak broadening in the vicinity of (111) and (004) to obtain a measure of the maximum displacement gradient along those crystallographic directions. [13,15] In order to confirm the reproducibility and uniqueness of the obtained solutions, we performed a series of phase retrieval procedures with different input random set of phases for the measured scattered radiation. We defined a cost function in the form of an error metric as E is the experimental intensity of point i in the reciprocal space map.…”

mentioning

confidence: 99%

Probing the three-dimensional strain inhomogeneity and equilibrium elastic properties of single crystal Ni nanowires

Fohtung

Kim

Chan

et al. 2012

Applied Physics Letters

Self Cite

View full text Add to dashboard Cite

We employ three dimensional x -ray coherent diffraction imaging to map the lattice strain distribution, and to probe the elastic properties of a single crystalline Ni (001) nanowire grown vertically on an amorphous Si02 Si substrate. The reconstructed density maps show that with increasing wire width, the equilibrium compressive stress in the core region decreases sharply while the surface tensile strain increases, and gradually trends to a nonzero constant. We use the retrieved projection of lattice distortion to predict the Young's Modulus of the wire based on the elasticity theory.Due to their high surface-to-volume ratio, transition metal nanostructures such as nanowires (NWs) could potentially be used in a broad range of applications in catalysis, sensors, batteries, fuel cells, and magnetic devices. [1-4] Most of these devices require NWs with welldefined size, shape, and spatial ordering. In addition, economical routes to mass production of NWs are desirable for practical applications. However, structural morphology of the NWs is strongly affected by the complex interplay between several growth parameters, such as temperature of the substrate, vertical and lateral material transfer, growth rate, in-plane mobility of ad-atoms, etc. In order to understand resulting morphology of NWs it is therefore vital to develop characterization tools that can nondestructively probe the three dimensional (3D) structural and mechanical properties of these NWs with nanoscale resolution.In this letter we study the structure, shape, 3D lattice distortion, and the electron density distribution in single crystal Ni NWs with the aid of synchrotron-based coherent x-ray diffraction (CXD) imaging [5,6]. The NWs were grown using thermal chemical vapor deposition (CVD) on a Si substrate that has been oxidized resulting in a 500-nm SiO 2 amorphous coating layer. CVD at 650 o C yields densely populated coverage of verticallyoriented single-crystal NWs depicted in Fig. 1(b) with well-defined orthogonal and smooth facets. [7,8] The NWs are grown in the [001] crystallographic orientation with widths ranging from 50 nm to about 300 nm and lengths of up to 5 µm and average coverage density of between 0.1 and 0.3 NW/µm 2 . CXD in the Bragg geometry has been shown to be a powerful characterization technique for imaging of local nanoscale lattice distortions, commonly described by deformation fields, u(r) within a small crystal. [5,6] CXD allows us to image not only the overall shape of the nanostructure in 3D, but also the projection of the crystal lattice displacement field on to the Q vector of the measured Bragg spot. The lattice distortion represents the * efohtung@physics.ucsd.edu imaginary component of object density and manifests itself as local asymmetry of the measured Bragg diffraction pattern. Upon an inversion of coherent x-ray diffraction pattern, the resulting real-space image of the object will be complex valued ρ (r) = ρ G hkl (r) exp [−iG hkl · u (r)], where the amplitude ρ G hkl represents the density of the object and the...

show abstract

Selective coherent x-ray diffractive imaging of displacement fields in (Ga,Mn)As/GaAs periodic wires

Cited by 28 publications

References 30 publications

Retrieving the displacement of strained nanoobjects: the impact of bounds for the scattering magnitude in direct space

Retrieving the displacement of strained nanoobjects: the impact of bounds for the scattering magnitude in direct space

Fast computation of scattering maps of nanostructures using graphical processing units

Probing the three-dimensional strain inhomogeneity and equilibrium elastic properties of single crystal Ni nanowires

Contact Info

Product

Resources

About