Probing Surface Morphology using X-ray Grating Interferometry

X-ray reflectometry (XRR), a surface-sensitive technique widely used for characterizing surfaces, buried interfaces, thin films, and multilayers, enables determination of the electron density distribution perpendicular to a well-defined surface specularly reflecting X-rays. However, the electron density distribution parallel to the surface cannot be determined from an X-ray reflectivity curve. The electron density correlation in the lateral direction is usually probed by measuring the grazing-incidence small-angle X-ray scattering (GISAXS). GISAXS measurement, however, typically requires using a collimated X-ray point beam to distinguish the GISAXS from the specularly reflected X-rays, and so the sample must be scanned in the lateral direction with the point beam to investigate variations in the surface and interface morphology for a region larger than the size of the beam. In this paper, we report a new approach based on X-ray grating interferometry: an X-ray sheet beam is used instead of an X-ray point beam. A method using this approach can simultaneously provide one-dimensional real-space images of X-ray reflectivity, surface curvature, and ‘dark-field’ contrast with a field-of-view of more than a few millimetres. As a demonstration, a sample having a 400 nm line and space SiO2 pattern with a depth of 10 nm on its surface was used, and the dark-field contrast due to the unresolved line and space structure, creating GISAXS in the lateral direction, was successfully observed. Quantitative analysis of these contrasts provided the real-space distribution of the structural parameters for a simple model of the grating structure. Our study paves the way to a new approach to structure analysis, providing a quantitative way to investigate real-space variations in surface and interface morphology through wavefront analysis.


Results of numerical calculations for normalised visibility
Here, we show the dependences of normalised visibility on the structural parameters of the sample shown in Fig. 5 (a) and the width of the point spread function (PSF) of the image detector. Figures S1, S2, S3, S4, and S5 plot the glancing-angle dependences of for psd1 = 400 nm. Figure S1 shows the glancing-angle dependence of on Ds for ds = 800 nm, as = 0.5, ws = 0, and σD = 6 μm, where σD ≡ WD/(2√2ln2). The glancing-angle dependence of sensitively changes the fringe period of . These fringes are similar to the Kiessig fringes in X-ray reflectivity curves but have a different origin: is determined by the autocorrelation in the lateral direction. Figure S2 shows the glancing-angle dependence of on as for ds = 800 nm, Ds = 12 nm, ws = 0, and σD = 6 μm, and Fig. S3 shows it on ws for ds = 800 nm, Ds = 12 nm, as = 0.5, and σD = 6 μm. A deviation of as from 0.5 reduced the amplitude of the fringes of normalised visibility while a change in ws caused a shift in the dip position of the normalised-visibility fringes.

Figure S2.
Glancing-angle dependence of on as for ds = 800 nm, Ds = 12 nm, ws = 0, and σD = 6 μm. Figure S4 shows the glancing-angle dependence of on σD for ds =800 nm, Ds = 12 nm, as = 0.5, and ws = 0. The minimum value of the normalised visibility changed while the effect of the blur due to a finite value of σD decreased as the glancing angle increased.   was not sensitive to ds. As shown below, the psd1 dependence on ds at a fixed glancing angle is much more sensitive than the glancing angle dependence.

Results of other experimental techniques
Here, we show the results of atomic force microscopy (AFM), transmission electron microscopy (TEM), and three-dimensional optical profilometry for the sample obtained after the experiment of X-ray grating interferometry. Figure S11 shows an image of the sample surface obtained by AFM (nanocute, Hitachi

AFM
High-Technologies Corporation) in the tapping-mode operation with a resonant frequency of 400 kHz. A cantilever with a spring constant of 40 N/m was used.
Although AFM can provide only local structural information, the structural parameters ds, Ds, and as (defined in Fig. 5 (a)) obtained from the AFM image were consistent with those obtained from our technique and TEM shown below. The slop width 2dsws was on the order of a few tens of nm, which was one order of magnitude larger than those obtained from our technique and TEM. The discrepancy of ws should be attributed to the effect of the shape of the AFM tip used. Figure S11. Image of sample surface obtained by atomic force microscopy. Figure S12 shows a sectional image of the sample obtained by TEM (JEM-2100F, JEOL Ltd.) operated with an acceleration voltage of 200 kV.

TEM
Although TEM requires sample destruction and provides only local structural information, the structural parameters ds, Ds, as, and ws (defined in Fig. 5 (a)) obtained from the TEM image were consistent with those obtained from our technique.

Three-dimensional optical profilometry
The    Figure S14 shows ℐ obtained from Fig. 3 (a). The red crosses in the figure are ℐ in the region with the line and space pattern averaged over 100 pixel in the lateral direction, while blue filled circles are those in the region without the line and space pattern. The black solid curve was calculated from the Fresnel equation for a flat surface of SiO2 (2.3 g/cm 3 ). Note that the behavior of ℐ below the critical angle was explained with an effective width of the PSF for the 100-pixel area and the Fresnel diffraction by the sample taken into account.

X-ray reflectivity
It can be seen that the difference between the two experimental curves is negligible and they agree well with the calculated curve for a flat SiO2 surface. In addition, no clear Kiessig fringes can be seen in the X-ray reflectivity curve for the region with the line and space pattern. ℐ in the region without the line and space pattern, black solid curve: calculated X-ray reflectivity from the Fresnel equation for a flat SiO2 surface.