Application of kinoform lens for X-ray reflectivity analysis

X-ray reflectivity (XRR) is a non-destructive technique widely used for thin layered materials characterization. The brilliance achieved by third generation synchrotron sources, such as Diamond, has opened new opportunities for the study of materials at the micro and nanoscales and has driven the development of new X-ray micro-focussing optical devices, such as kinoform lenses. We have demonstrated the first practical application of kinoform lenses for the X-ray reflectivity characterization of thin layered materials. The focused X-ray beam generated from a kinoform lens, a line of nominal size ~50 micron x 2 micron, provides a unique possibility to measure the X-ray reflectivities of thin layered materials in sample scanning mode. Moreover, the small footprint of the X-ray beam, generated on the sample surface at grazing incidence angles, enables one to measure the absolute X-ray reflectivities. This approach has been tested by analyzing a few thin multilayer structures.

Various advantages of kinoform lenses, such as a line-shaped focused X-ray beam, high X-ray transmission efficiency and low scattered background, make them ideal for XRR applications, especially at higher incident X-ray energies. Moreover, the small footprint of the X-ray beam at grazing incidence angle also offers another possibility of performing XRR analysis in sample scanning mode. Such measurements are very useful in investigating the degree of homogeneity of thin layered materials, for example X-ray multilayer structures or planar thin film X-ray waveguide structures coated on plane or curved-shaped substrates.

X-ray reflectivity is a widely used technique for surface–interface characterization of thin films and X-ray multilayer structures, deposited on substrate surfaces. In XRR, the requirement of glancing incidence angle for the incoming X-ray beam, on the sample surface, imposes a constraint for the maximum allowable vertical size of the incoming X-ray beam. Usually, a line-shaped X-ray beam with a vertical size of ~20–50 μm and a horizontal size of ~2–10 mm is used for the XRR measurements. Such a micrometre-size beam is generated by slitting down the primary beam, which however reduces the incident flux. The XRR technique has a limitation: it cannot be applied for sample scanning analysis mode because of the large footprint of the X-ray beam generated on the sample surface at grazing incidence angles.

The applicability of microfocused synchrotron X-ray beams seems to be very useful especially for investigating the structural properties of heterogeneous thin film structures [1][2]. Focusing, of course, increases the beam divergence, which can be a drawback for some techniques. In the case of the XRR technique, however, it has already been shown [3] that the primary beam divergence effect can easily be taken into account in the model calculation while fitting the experimental XRR data.

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 Figure 1: (a) Schematic view of the focusing of X-rays from a planar kinoform single-element lens. The step length L is given by the ratio of the incident wavelength to the refractive index decrement of the lens material (L = λ/δ). The width W depends on the aperture of the lens. The kinoform lens generates a line-focus X-ray beam of nominal size ~ 50 μm × 2 μm.
(b) Schematic of the XRR arrangement using a focused X-ray beam generated from a kinoform lens structure. The inset shows a scanning electron micrograph of the Si kinoform lens structure.

A kinoform lens is a one-dimensional X-ray focusing optics that generates a line-focused X-ray beam of vertical size typically ~0.5–3 μm [4][5][6]. The kinoform lenses are based on refraction and work in a similar way to compound refractive lenses (CRLs) [7]. The absorption losses in a kinoform lens are significantly lower compared with CRLs. We have used Si kinoform lenses fabricated at Diamond Light Source [6] for the XRR characterization of Nb/C/Nb and Mo/Si multilayer structures performed on the B16 Test Beamline [8].

For the measurement reported here, we used unfocused monochromatic X-rays in the energy range 10–20 keV, selected by a Si(111) double-crystal monochromator (DCM). The XRR measurements were performed on the five-axis Huber diffractometer in q–2q geometry, for incidence angles ranging from 0 to 3° and with an angular resolution of both q and 2q motions better than 0.5 mdeg.

Fig. 1a shows a schematic view of the focusing of X-rays using a kinoform lens, while Fig. 1b shows experimental arrangement for the XRR measurements, and a scanning electron micrograph image of the kinoform lens is shown in the inset. Fig. 2 shows photographs of the experimental set-up. By properly selecting the primary beam aperture a line-shaped X-ray beam of size ~ 50 μm (h) × 2 μm was generated.

Figure 2: Photographs of the experimental set-up showing the arrangement of the XRR measurement using a Si kinoform lens. The kinoform lens structures were mounted on an attocube tower having five degrees of motion. The beam-defining slits were mounted upstream of the kinoform lens optics.

The structural parameters of the Mo/Si multilayer structure such as thickness, roughness of high- and low-Z layers, and Γ ratio (the thickness ratio of high-Z layer to multilayer period) were determined using XRR measurements, carried out with a kinoform-focused X-ray beam.

The best-fit XRR results (Fig. 3) yield a thickness value of 2.47 ± 0.03 nm for the Mo layers and 4.05 ± 0.03 nm for the Si layers. The roughness of the Mo (Si) layers was found to be 0.3 nm (0.8 nm). The detailed fitting also indicated that an oxide layer of thickness 2.0 nm and roughness 0.8 nm is present on the top Si layer of the Mo/Si multilayer structure.

Figure 3: Fitted XRR profile of the Mo/Si multilayer structure at an incident X-ray energy of 19 keV. From this figure it can be seen that fitted and measured XRR profiles match quite well at lower incidence angles as well as at higher incidence angles.

In another application, we have performed XRR characterization of an Nb/C/Nb trilayer structure deposited on a Si substrate. Such trilayer structures w e-designed kinoform lens structure was employed. To measure the XRR profile of the trilayer structure in sample scanning mode, sample movement with a step of 2 mm was employed. The obtained values of thicknesses of the individual layers of the Nb/C/Nb structure are more or less similar for the various locations on the sample surface, as are the determined r.m.s. roughness values of the three layers. This shows that the Nb/C/Nb layer structure is quite homogeneous. We did not observe any spatial variation in the microstructural properties of the Nb/C/Nb layer structure.

The above measurements on the multilayer and the trilayer structures show that by using line-focused X-ray beams generated from a kinoform lens the XRR characterization of thin layered materials is readily possible with equal ease compared with the more conventional XRR measurement procedures of using unfocused X-ray beams and employing a knife-edge to restrict the beam footprint on the sample surface.

Various advantages of kinoform lenses, such as a line-shaped focused X-ray beam, high X-ray transmission efficiency and low scattered background, make them ideal for XRR applications, especially at higher incident X-ray energies. Moreover, the small footprint of the X-ray beam at grazing incidence angle also offers another possibility of performing XRR analysis in sample scanning mode.

The small physical dimension of a kinoform structure makes it possible to fabricate several lenses for different X-ray energies and/or different focal lengths on a single Si chip. Thus, it is easy to change the photon energy by just a lateral translation of the lens chip, without changing the focal distance. Apart from the above advantages, the focused beam from a kinoform is divergent in nature; therefore one needs to take into account the beam divergence effect during XRR calculation/fitting of experimental data.

The effective aperture of a kinoform lens decreases with increasing X-ray energy [6], therefore the observed beam divergence of the kinoform lens also decreases at higher X-ray energies. Thus, kinoform lenses are especially useful in performing XRR measurements of thin layered materials at higher incident X-ray energies.
 

References
[1] M. Wolkenhauer et al., Appl. Phys. Lett. 89, 054101, (2006).
[2] J. Matsui et al., Nucl. Instrum. Methods Phys. Res. B, 261, 634–638 (2007).
[3] M.K. Tiwari et al., Anal. Sci. 21, 757–762 (2005).
[4] K. Evans-Lutterodt et al., Opt. Express, 11, 919–926 (2003).
[5] A. Stein et al., J. Vac. Sci. Technol. B, 26, 122–127 (2008).
[6] L. Alianelli et al., J. Synchrotron Rad. 16, 325–329 (2009)
[7] A. Snigirev et al., Nature, 384, 49–51 (1996)
[8] K.J.S. Sawhney et al., AIP Conference Proceedings - Tenth International Conference on Synchrotron Radiation Instrumentation, 1234, 627-630 (2010)

Principal Publications and Authors
M. K .Tiwari, L. Alianelli, I. P. Dolbnya, and K. J. S. Sawhney, Application of Kinoform lens for X-ray reflectivity, J. Synchrotron Rad. 17, 237–242 (2010).

Funding Acknowledgement
Science and Technology Facilities Council in the UK - facility development grant STFC/F001665/1.