Element sensitive reconstruction of nanostructured surfaces with finite elements and grazing incidence soft X-ray fluorescence

Abstract

The geometry of a Si3N4 lamellar grating was investigated experimentally with reference-free grazing-incidence X-ray fluorescence analysis. While simple layered systems are usually treated with the matrix formalism to determine the X-ray standing-wave field, this approach fails for laterally structured surfaces. Maxwell solvers based on finite elements are often used to model electrical field strengths for any 2D or 3D structures in the optical spectral range. We show that this approach can also be applied in the field of X-rays. The electrical field distribution obtained with the Maxwell solver can subsequently be used to calculate the fluorescence intensities in full analogy to the X-ray standing-wave field obtained by the matrix formalism. Only the effective 1D integration for the layer system has to be replaced by a 2D integration of the finite elements, taking into account the local excitation conditions. We will show that this approach is capable of reconstructing the geometric line shape of a structured surface with high elemental sensitivity. This combination of GIXRF and finite-element simulations paves the way for a versatile characterization of nanoscale-structured surfaces.

Reconstruction of evolving nanostructures in ultrathin films with X-ray waveguide fluorescence holography

“…In the former configuration, a detector of a very large solid angle is desired in order to collect as much fluorescence as possible for a better signal-noise ratio. The hologram is constructed by scanning the incidence angle of a well collimated monochromatic X-ray beam as is done in the conventional inverse XFH and the similar scenario of GIXRF (grazing-incidence X-ray fluorescence) [31][32][33][34] . When the incident angle is below the critical angle for the total-external reflection of the topmost surface or any buried interface, the evanescence wave is created, and a standing wave is also generated above the interface.…”

Grazing Emission X‐Ray Fluorescence: Novel Concepts and Applications for Nano‐Analytics

“…This 2D information on the dependence of the XRF intensity on both angles is useful for investigations of structured surfaces in two or three dimensions, such as line gratings or periodic patterns of identical nanostructures, as already been shown by means of GIXRF. [ 94,95 ]…”

“…In the case of well‐ordered periodic distributions of particles or structures with lateral and vertical dimensions in the range of few tens to hundreds of nanometers and periodicities in the same range, such as line gratings or periodically repeating identical surface structures, GIXRF measurements showed a sensitivity of the angular intensity profile to the azimuthal orientation of the periodical arrays, [ 94,148 ] as is exemplarily shown in Figure 10 . This class of samples has until recently not been considered for GIXRF and GEXRF investigations such that novel modeling, computationally demanding approaches are required which take into consideration the surface distribution pattern in terms of height, width, and periodicity in particular.…”

A semi-analytical approach for the characterization of ordered 3D nanostructures using grazing-incidence X-ray fluorescence

“…In recent works 3,13 , the sensitivity of GIXRF to the lateral distribution of atomic concentration in 2D and 3D structures of periodically arranged gratings and nanocolumns has been experimentally demonstrated. To achieve such sensitivity, a new experimental scheme has been employed, where measurements are done under different grazing incidence and azimuthal orientation angles.…”