Small-angle X-ray scattering from GaN nanowires on Si(111): facet truncation rods, facet roughness and Porod's law

Small-angle X-ray scattering from GaN nanowires grown on Si(111) is measured in the grazing-incidence geometry and modelled by means of a Monte Carlo simulation that takes into account the orientational distribution of the faceted nanowires and the roughness of their side facets. It is found that the scattering intensity at large wavevectors does not follow Porod's law I(q) ∝ q −4. The intensity depends on the orientation of the side facets with respect to the incident X-ray beam. It is maximum when the scattering vector is directed along a facet normal, reminiscent of surface truncation rod scattering. At large wavevectors q, the scattering intensity is reduced by surface roughness. A root-mean-square roughness of 0.9 nm, which is the height of just 3–4 atomic steps per micrometre-long facet, already gives rise to a strong intensity reduction.

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Small angle X-Ray Scattering in Grazing Incidence Geometry

Encyclopedia of Nanotechnology ◽

10.1007/978-90-481-9751-4_100769 ◽

2012 ◽

pp. 2435-2435

Author(s):

Yimei Zhu ◽

Hiromi Inada ◽

Achim Hartschuh ◽

Li Shi ◽

Ada Della Pia ◽

...

Keyword(s):

Small Angle ◽

Grazing Incidence ◽

Incidence Geometry ◽

X Ray ◽

X Ray Scattering ◽

Grazing Incidence Geometry ◽

Ray Scattering

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Small Angle X-Ray Scattering in Grazing Incidence Geometry

Encyclopedia of Nanotechnology ◽

10.1007/978-94-017-9780-1_101033 ◽

2016 ◽

pp. 3719-3719

Keyword(s):

Small Angle ◽

Grazing Incidence ◽

Incidence Geometry ◽

X Ray ◽

X Ray Scattering ◽

Grazing Incidence Geometry ◽

Ray Scattering

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IsGISAXS: a program for grazing-incidence small-angle X-ray scattering analysis of supported islands

Journal of Applied Crystallography ◽

10.1107/s0021889802006088 ◽

2002 ◽

Vol 35 (4) ◽

pp. 406-421 ◽

Cited By ~ 313

Author(s):

Rémi Lazzari

Keyword(s):

Form Factor ◽

Small Angle ◽

Disordered Systems ◽

Pair Correlation ◽

Grazing Incidence ◽

Incidence Geometry ◽

Full Account ◽

X Ray ◽

X Ray Scattering ◽

Ray Scattering

This paper describes a Fortran program,IsGISAXS, for the simulation and analysis of grazing-incidence small-angle X-ray scattering (GISAXS) of islands supported on a substrate. As is usual in small-angle scattering of particles, the scattering cross section is expressed in terms of an island form factor and interference function. However, the emphasis is placed on the specificity of the grazing-incidence geometry, in particular in the evaluation of the island form factor in the distorted-wave Born approximation. A library of simple geometrical shapes is available. A full account of size and possible shape distributions is given in the decoupling approximation, where sizes and positions are not correlated, and in the local monodisperse approximation. Two types of island repartitions on the substrate are considered: disordered systems characterized by their particle–particle pair correlation functions, and bidimensional crystalline or paracrystalline systems of particles.

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Grazing Incidence Small Angle X-Ray Scattering Study on Low Dielectric Thin Films

MRS Proceedings ◽

10.1557/proc-612-d5.23.1 ◽

2000 ◽

Vol 612 ◽

Cited By ~ 5

Author(s):

C.-H. Hsu ◽

Hsin-Yi Lee ◽

K.S. Liang ◽

U-Ser Jeng ◽

D. Windover ◽

...

Keyword(s):

Thin Films ◽

Small Angle ◽

Grazing Incidence ◽

Dielectric Materials ◽

Incidence Geometry ◽

Silica Xerogel ◽

Saxs Data ◽

X Ray ◽

X Ray Scattering ◽

Ray Scattering

AbstractHighly porous silica films with pore size in the nanometer scale are being extensively studied as potential candidates for interlevel dielectrics. Because these dielectric materials appear in the form of thin films with a thickness of only several thousand Angstroms, conventional techniques are difficult to be readily applied to study their structure and porosity. We employed small angle scattering in the grazing incidence geometry in this study. Using high resolution xray beamline with synchrotron radiation source, we demonstrate that the small angle x-ray scatteirng (SAXS) data of the porous films can be obtained. The structure of sol-gel derived silica - xerogel films on silicon substrate studied by specular reflectivity and grazing incidence small angle x-ray scattering (GISAXS) will be presented.

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Grazing-incidence small-angle X-ray scattering in a twofold rough-interface medium: a new theoretical approach using theq-eigenwave formalism

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273315016666 ◽

2015 ◽

Vol 71 (6) ◽

pp. 612-627 ◽

Cited By ~ 1

Author(s):

F. N. Chukhovskii ◽

B. S. Roshchin

Keyword(s):

Surface Finish ◽

Small Angle ◽

Grazing Incidence ◽

Root Mean Square Roughness ◽

Surface Model ◽

X Rays ◽

Acta Cryst ◽

X Ray ◽

X Ray Scattering ◽

Ray Scattering

Based on the rigorous Green function formalism to describe the grazing-incidence small-angle X-ray scattering (GISAXS) problem, a system of two linked integral equations is derived with respect to amplitudes of the reflected and transmitted planeq-eigenwaves (eigenstatefunctions) propagating through two homogeneous media separated from each other by a rough surface interface. To build up the coupled solutions of these basic equations beyond the perturbation theory constraint 2kσθ0< 1, a simple iteration procedure is proposed as opposed to the self-consistent wave approach [Chukhovskii (2011).Acta Cryst.A67, 200–209; Chukhovski (2012).Acta Cryst.A68, 505–512]. Using the first-order iteration, analytical expressions for the averaged specular and non-specular scattering intensity distributions have been obtained. These expressions are further analysed in terms of the GISAXS parameters {k, θ, θ0} and surface finish ones \{ \sigma, \ell, h\}, where θ and θ0are the scattering and incidence angles of the X-rays, respectively, σ is the root-mean-square roughness, \ell is the correlation length,his the fractal surface model index,k= 2π/λ, and λ is the X-ray wavelength. A direct way to determine the surface finish parameters from the experimental specular and diffuse scattering indicatrix scan data is discussed for an example of GISAXS measurements from rough surfaces of α-quartz and CdTe samples.

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