Logo PTB
symbolic picture: "magazines"

Algorithm for reconstructing 3D nanostructures

Characterizing surface structures by means of X-ray fluorescence measurements

PTBnews 3.2020
Especially interesting for

the semiconductor industry

dimensional nanometrology

Methods for the element-specific reconstruction of periodically nanostructured surfaces have been optimized at PTB. Such surfaces are used to manufacture ultra-modern integrated circuits. Measurements have shown that it is possible to characterize the spatial distribution of different atoms in nanostructures by analyzing X-ray fluorescence radiation.

Schematic representation of the fluorescence excitation of a nanostructureconsisting of atoms of different elements (A, B, C). When excitation iseffected with an X-ray beam (E0) characteristic fluorescence radiation (E1, E2) is emitted.

Within the scope of a cooperation project of PTB with the Dutch University of Twente and the Kurchatov Institute in Moscow, a new algorithm has been developed. This algorithm describes the X-ray fluorescence that is emitted when periodic 3D nanostructures are excited under grazing incidence by means of synchrotron radiation. It has the potential to become an efficient tool to develop and manufacture 3D nanostructures, which will, in turn, be used to set up integrated circuits. This algorithm exploits the periodic structure of nanogeometry and solves the Maxwell equations semi-analytically with an accuracy and a precision that are equivalent to conventional simulations based on the finite-element method (FEM). In this way, computations of the light/matter interactions in layer systems and of periodic nanostructures become less demanding – and thus faster by nearly two orders of magnitude than corresponding FEM simulations.

To characterize a 3D nanostructure, the electrons of the atoms forming the structure were excited at the Berlin electron storage ring BESSY II using monochromatic synchrotron radiation in the X-ray range, and their fluorescence radiation was detected with angular resolution while the atoms were returning to the ground state. From the X-ray fluorescence emitted, it was possible to reconstruct the spatial distribution of the atoms – and thus the geometry of the nanostructure – in three dimensions.

Moreover, by making the computations so much faster, it becomes possible to use statistical methods to determine the measurement uncertainties (e.g. Monte Carlo or Bayesian methods). This is therefore an important element of hybrid measurement technologies that are currently being developed. These technologies involve, for example, analyzing one and the same nanostructure by means of different measurement methods and combining them into one result in a statistically consistent way. Objects can thus be measured more accurately than would be possible using only one individual measurement method. This will extend and complement PTB's existing measuring capacities in the field of nanometrology, so that future developments of circuits made of 3D nanostructures can be metrologically supported.



Victor SoltwischDepartment 7.1 Radiometry with Synchrotron RadiationPhone: +49 30 3481-7129victor.soltwisch@ptb.de


Philipp Hönicke
Department 7.2 X-ray Metrology with Synchrotron Radiation
Phone: +49 30 3481-3228

Sebastian Heidenreich
Department 8.4 Mathematical Modelling and Data Analysis
Phone: +49 30 4381-7726

Scientific publication

K. V. Nikolaev, V. Soltwisch, P. Hönicke, F. Scholze, J. de la Rie, S. N. Yakunin, I. A. Makhotkin, R. W. E. van de Kruijs, F. Bijkerk: A semi-analytical approach for the characterization of ordered 3D nanostructures using grazing-incidence X-ray fluorescence. J. Synchrotron Rad. 27 (2020)