1. 6 – 9 June 2011, Dortmund, Germany
Geometrical Optics Modelling of Grazing Incidence X-ray Fluorescence of Nanoscaled Objects S. H. Nowak1, F. Reinhardt2, H. Bresch3, Y. Kayser1, J. Osán4, A.E. Pap5   1University of Fribourg, Ch. du Musée 3, CH-1700 Fribourg, Switzerland 2Physikalisch-Technische Bundesanstalt, Abbestr. 2-12, D Berlin, Germany 3Bundesanstalt für Materialforschung und -prüfung, Unter den Eichen 44-46, D Berlin, Germany 4Hungarian Academy of Sciences, KFKI Atomic Energy Research Institute, P.O. Box 49, H-1525 Budapest, Hungary 5Hungarian Academy of Sciences, Research Institute for Technical Physics and Materials Science, P.O. Box 49, H-1525 Budapest, Hungary
Motivation
Artificial structures on wafer surfaces are becoming more and more sophisticated. The increasing ability to produce such patterned wafer surfaces calls for more evolved methods to further match the high standard in quality and reproducibility of the products. The characterisation of both nanoscaled structures and nanoparticles deposited on semiconductor surfaces requires reliable measurement procedures, quantification process analysis on schemes and related validation.
One of the methods having the potential to effectively contribute to the characterisation of nanostructures deposited on flat surfaces is the Grazing Incidence X-ray Fluorescence (GIXRF) analysis [1]. The GIXRF method is based on the Total Reflection X-ray Fluorescence (TXRF) geometry which offers a high sensitivity to the near surface area and low levels of detection in the pg to fg range.
Grazing incidence X-ray fluorescence analysis (GIXRF)Topmost layer of a flat surface (e.g. Si-wafer) or a minute amount of material deposited on top of that surface is probed. Below the critical angle, the exciting X-ray beam is totally reflected at the substrate surface:
low scattering background due
to small penetration-depth
- large solid angle of detection
absolute detection limits in pg
or fg range
Numerical method
In the model the field amplitudes are summed over multiple rays for each excited point. To decrease the number of considered incident x-ray directions, structures are approximated by rectangular prisms placed in the parallel direction to the excitation direction.
Problem
A very elegant and widely used way of interpreting the GIXRF measurements of nanoparticles on surfaces involves calculations of the X-ray Standing Wave (XSW) field resulting from the total reflection of an exciting x-ray beam [2]. The change of the incident angle modifies the XSW field, i.e., the radiation intensity exciting the particles,ew ye
particles, yielding changes in the x-ray fluorescence signal. However, the XSW based based theory treats the particles as a small perturbation, which is only valid if absorption and interference effects can be neglected [3]. This requires small particle dimensions and large distances between them. For wide or densely distributed structures the XSW approximation is likely to fail.
M. K. Tiwari, et al., Investigation of metal nanoparticles on a Si surface using an x-ray standing wave field, J. Appl. Phys. 103 (2008)
Results
Pads:
Solution
Providing the wavelength of the exciting radiation is much smaller than the size of the structures, Geometrical Optics (GO) can be used. The ray tracing explicitly follows on-surface structures respecting the absorption effects. The interferences can be ___________introduced by summing the field amplitudes over multiple rays. In the ___________geometrical optics approach the XSW method can be seen as a limiting _____________________case of very thin (no absorption) and sparsely distributed ___________________________________________(interference only of the direct and ___________________________________________singly reflected wave) particles.
NaCl nanoparticles:
The mean particle size is 45 nm.
The XSW linear combination corresponds to the weighted sum of the XSW curves for individual particles according to the distribution given in the inset.
The geometrical optics calculations were performed using the morphology data from the SEM images.
Samples
The numerical calculations employing geometrical optics are compared to experimental GIXRF profiles for:
Conclusions
The resulting geometrical optics curves follow better the experimental data than the XSW simulations. In particular the effect of the beam absorption in the pads is well reproduced.
The extinction of the interference fringes could be achieved by introducing the roughness of the pad top surfaces.
For NaCl nanoparticles significant discrepancies are observed between the GO and XSW simulations and the measurements. However, the maximum intensity position for GO is closer to the measured one.
The differences with the measured data could be due to the difficulties encountered at small angles with the intensity normalization or to the support surface roughness that was not taken into consideration.
Structures of artificial permalloy and Cr pads with lateral dimensions of 2.7 μm and heights in the range of 10 to 100 nm. The width of the pads was large enough to absorb the incident x-rays.
NaCl nanoparticles, with diameter of ~45 nm deposited on Si surfaces by means of electrostatic aerosol sampling. The influence of the dense distribution of particles on the incident x-ray radiation is large.
Bibliography
[1] A. von Bohlen, Total reflection X-ray fluorescence and grazing incidence X-ray spectrometry-
Tools for micro- and surface analysis. A review. Spectrochimica Acta B 64 (2009), 821.
[2] D.L. Windt, IMD-Software for modelling the optical properties of multilayer films. Computers in
Physics 4 (1998), 360.
[3] A. von Bohlen, M. Krämer, C. Sternemann, and M. Paulus, The influence of X-ray coherence length
on TXRF and XSW and the characterization of nanoparticles observed under grazing incidence of
X-rays,. J. Anal. At. Spectrom. 24 (2009) 792.
[4] J. Osán, F. Reinhardt, B. Beckhoff, A. E. Pap, and S. Torok, Probing patterned wafer structures by
means of grazing incidence x-ray fluorescence analysis. ECS Transactions 25 (2009) 441.
14th International Conference on Total Reflection X-ray Fluorescence and Related Methods
6 – 9 June 2011, Dortmund, Germany