27.10.2017
Modelling X-ray scattering intensities based on the finite element method: the lower figure compares the model of a lattice profile reconstructed from GISAXS measurements with cross section images from a scanning electron microscope.
As demonstrated by initial studies carried out at PTB, indirect measurement methods such as small-angle X-ray scattering can be used for the dimensional reconstruction of nanostructured surfaces. Uncertainties of less than 1 nm can be achieved by measuring the angle-resolved intensity distributions in the X-ray scattering process.
The progress in miniaturization constantly presents metrology with new challenges. In the field of photolithography, current developments have already brought about structures with dimensions from 10 nm to 20 nm. The metrological characterization of these generally lattice-like nanostructured surfaces represents a huge challenge for the measurement methods that have been available to date. With the emerging change to EUV lithography, this development will further intensify. Solutions and alternatives are therefore being investigated everywhere in the world.
In the case of X-ray scattering, the interaction between the incident X-ray photons and the nanostructured surface are being investigated. Due to the very short wavelength and the grazing incidence of the X-rays, this method exhibits high surface sensitivity. Thanks to the very short measuring time, this method is an ideal candidate for process control in the industrial field. However, since this method is not a direct imaging procedure, it is not possible to directly derive the shape of the scattering object from the scattered photons. This requires elaborate modelling and optimization procedures. To date, rigorous so-called Maxwell solvers based on the finite element method (FEM) have not been included when working with X-rays. The very short wavelength requires an equally small size of the individual elements, which exceeds the present storage capacities of computers.
This limitation can, however, be bypassed by adapting the measuring geometry. In the presence of a grazing incidence angle of X-rays and a conical orientation of the lattice, the size of the finite elements can be increased by one order of magnitude, which, in turn, significantly reduces the memory requirements and the computing time. This makes it possible to use statistical validation procedures such as Markov chain Monte Carlo (MCMC) for the reconstruction. The lattice structures with dimensions from 50 nm to 65 nm, which have recently been investigated, show that a reconstruction of the surface structure with an uncertainty in the sub-nanometer range is possible.
Contact:
A. Fernández Herrero, 7.12, E-Mail: 
Analia.Fernandez.Herrero(at)ptb.de
V. Soltwisch, 7.12, E-Mail: Victor.Soltwisch(at)ptb.de
V. Soltwisch, A. Fernández Herrero, M. Pflüger, A. Haase, J. Probst, C. Laubis, M. Krumrey, F. Scholze,
Reconstructing detailed line profiles of lamellar gratings from GISAXS patterns with a Maxwell solver, J. Appl. Cryst. 50, 1524-1532 (2017)