Grazing incidence small angle x-ray scattering from free-standing nanostructures

Abstract

We develop the theory for grazing incidence small-angle x-ray scattering (GISAXS) from nanometer-sized naked islands on a flat substrate in the framework of the distorted-wave Born approximation (DWBA). The scattered wave amplitude is composed of four terms, including all combinations of scattering from the islands and reflection from the substrate. We apply this theory to x-ray measurements on Ge islands grown on Si(111), and show that we can determine the full triangular symmetry of these islands. The results also show that the DWBA must be used for smooth substrates near the angle of total external reflection. We finally discuss the advantages of GISAXS as compared to transmission small angle x-ray scattering for determining the symmetry of nanostructures.

GISAXS study of the alignment of oriented carbon nanotubes grown on plain SiO2/Si(100) substrates by a catalytically enhanced CVD process

“…The GISAXS experiments [15,18,19] were performed on a dedicated experimental set up built on the ID1 beamline at ESRF (European Synchrotron Radiation Facility, Grenoble, France). Scattering patterns were collected on a 2D X-ray CCD detector (pixel size 54 µm) placed at a distance L equal to 4.3 m from the sample, and perpendicular to the incident beam at an X-ray beam wavelength λ of 0.1 nm, corresponding to beam energy of 12.3821 KeV.…”

Self-assembly of iron oxide nanoparticles studied by time-resolved grazing-incidence small-angle x-ray scattering

“…[20][21][22] Briefly, a semi-infinite substrate represents an undisturbed system and freestanding particles on it introduce a disturbance. The observed GISAXS intensity corresponds to the diffuse part of the total differential scattering cross section calculated for the disturbed system, which results in a product of a single particle form factor related to the nanoparticle shape and an interference function related to the nanoparticle arrangement.…”

Global scattering functions: a tool for grazing incidence small angle X-ray scattering (GISAXS) data analysis of low correlated lateral structures

“…However, for a rigorous data analysis of GISAXS one should use the DWBA. Theories for the most important film systems containing rough surfaces [8][9][10], buried particles [11] and supported islands [12] were previously derived. To compute and simulate GISAXS data, Lazzari developed the simulation and fitting software IsGISAXS 1 [13,14].…”