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A pilot study for the thickness measurement of HfO2 films was performed by the Surface Analysis Working Group (SAWG) of the Consultative Committee for Amount of Substance (CCQM). The aim of this pilot study was to ensure the equivalency in the measurement capability of national metrology institutes for the thickness measurement of HfO2 films. In this pilot study, the thicknesses of six HfO2 films with nominal thickness from 1 nm to 4 nm were measured by X-ray Photoelectron Spectroscopy (XPS), X-ray Reflectometry(XRR), X-ray Fluorescence Analysis (XRF), Transmission Electron Spectroscopy (TEM), Spectroscopic Ellipsometry (SE) and Rutherford Backscattering Spectrometry (RBS). The reference thicknesses were determined by mutual calibration of a zero-offset method (Medium Energy Ion Scattering Spectroscopy (MEIS) of KRISS) and a method traceable to the length unit (the average thicknesses of three XRR data except the thinnest film). These reference thicknesses are traceable to the length unit because they are based on the traceability of XRR. For the thickness measurement by XPS, the effective attenuation length of Hf 4f electrons was determined. In the cases of XRR and TEM, the offset values were determined from a linear fitting between the reference thicknesses and the individual data by XRR and TEM. The amount of substance of HfO2, expressed as thickness of HfO2 films (in both linear and areal density units), was found to be a good subject for a CCQM key comparison.
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The final report has been peer-reviewed and approved for publication by the CCQM.
A versatile software package in the form of a Python extension, named CDEF (computing Debye’s scattering formula for extraordinary form factors), is proposed to calculate approximate scattering profiles of arbitrarily shaped nanoparticles for small-angle X-ray scattering (SAXS). CDEF generates a quasi-randomly distributed point cloud in the desired particle shape and then applies the open-source software DEBYER for efficient evaluation of Debye’s scattering formula to calculate the SAXS pattern (https://github.com/j-from-b/CDEF). If self-correlation of the scattering signal is not omitted, the quasi-random distribution provides faster convergence compared with a true-random distribution of the scatterers, especially at higher momentum transfer. The usage of the software is demonstrated for the evaluation of scattering data of Au nanocubes with rounded edges, which were measured at the four-crystal monochromator beamline of PTB at the synchrotron radiation facility BESSY II in Berlin. The implementation is fast enough to run on a single desktop computer and perform model fits within minutes. The accuracy of the method was analyzed by comparison with analytically known form factors and verified with another implementation, the SPONGE, based on a similar principle with fewer approximations. Additionally, the SPONGE coupled to McSAS3 allows one to retrieve information on the uncertainty of the size distribution using a Monte Carlo uncertainty estimation algorithm.