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

I. A. Makhotkin,P. Hönicke,J. de la Rie,R. W. E. van de Kruijs,V. Soltwisch,K. V. Nikolaev,F. Scholze,F. Bijkerk,S. N. Yakunin

doi:10.1107/s1600577519016345

Abstract

Following the recent demonstration of grazing-incidence X-ray fluorescence (GIXRF)-based characterization of the 3D atomic distribution of different elements and dimensional parameters of periodic nanoscale structures, this work presents a new computational scheme for the simulation of the angular-dependent fluorescence intensities from such periodic 2D and 3D nanoscale structures. The computational scheme is based on the dynamical diffraction theory in many-beam approximation, which allows a semi-analytical solution to the Sherman equation to be derived in a linear-algebraic form. The computational scheme has been used to analyze recently published GIXRF data measured on 2D Si3N4 lamellar gratings, as well as on periodically structured 3D Cr nanopillars. Both the dimensional and structural parameters of these nanostructures have been reconstructed by fitting numerical simulations to the experimental GIXRF data. Obtained results show good agreement with nominal parameters used in the manufacturing of the structures, as well as with reconstructed parameters based on the previously published finite-element-method simulations, in the case of the Si3N4 grating.

Highlights

Achievements in the field of science and technology related to the manufacturing of nanoscale devices are usually associated with the systematic decrease of the characteristic sizes of the structures within such devices
A new computational scheme based on the dynamical diffraction theory has been developed and applied for the analysis of grazing-incidence X-ray fluorescence (GIXRF) experiments on 2D and 3D periodic nanostructures
The computational scheme has been validated with a Maxwell solver based on the finite-element method and benchmarked on GIXRF experimental data obtained from Si3N4 2D lamellar gratings and Cr 3D nanocolumns

Summary

Introduction

Achievements in the field of science and technology related to the manufacturing of nanoscale devices are usually associated with the systematic decrease of the characteristic sizes of the structures within such devices. Understanding and improving the performance of such devices requires the use of nanometrology techniques which, at best, are capable of reconstructing the geometry of the structure and the threedimensional (3D) atomic concentration distributions of different elements Such element-selective analysis can be performed using grazing-incidence X-ray fluorescence (GIXRF) (Soltwisch et al, 2018; Andrle et al, 2019). In recent works (Soltwisch et al, 2018; Dialameh et al, 2018), 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 carried out under different grazing-incidence and azimuthal-orientation angles. The semi-analytical nature of the derived equations allowed us to strongly reduce the computational effort, and to perform analysis of GIXRF from a 3D nanostructured surface for the first time using the experimental data previously published by Dialameh et al (2018)

Theory

Many-beam dynamical diffraction theory

Characteristic equation

Boundary conditions

Numerical stability

X-ray fluorescence intensity

Numerical simulations

Discussion

Findings

Conclusions

Funding information