LETTER pubs.acs.org/ac
X-ray Reflection Tomography: A New Tool for Surface Imaging Vallerie Ann Innis-Samson,† Mari Mizusawa,‡ and Kenji Sakurai*,†,‡ † ‡
University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8577 National Institute for Materials Science, 1-2-1, Sengen, Tsukuba, Ibaraki, 305-0047 Japan ABSTRACT: We report here a novel technique of surface imaging by X-ray reflection tomography utilizing an ordinary laboratory X-ray source. The technique utilizes the line projection, at different rotation angles, of the reflected beam from a highly reflecting patterned sample at grazing incidence. Filtered back-projection algorithm is applied to the line projection data to reconstruct an image of the pattern on the sample surface. Spatial resolution currently obtained is ∼1.6 mm. Nonetheless, we have achieved high correlation between the original image and the reconstructed image. This work is the first step in future efforts of nondestructive X-ray imaging for buried surfaces and interfaces.
X
-ray reflectivity (XRR) is a powerful nondestructive technique which gives structural information along the depth of thin films and layered materials with atomic-scale sensitivity. However, reflectivity lacks spatial resolution as it looks at a large surface area of the sample (mm2cm2) such that it only gives average information on the whole surface. Reflectivity cannot possibly obtain information on the location and distribution of heterogeneous structures on the surface. Although such information can be obtained by X-ray fluorescence imaging,1 X-ray diffraction imaging,2 and X-ray reflectivity with a scanning microbeam,3 these systems however require the high brilliance of a synchrotron radiation facility. An imaging technique using an ordinary laboratory X-ray source is introduced to image the pattern on a substrate by X-ray reflection at grazing incidence. In this work, we utilize the concept of standard computerized tomography (CT) imaging4 to allow X-ray reflectivity to image the heterogeneous structures on the surface of a sample. Reflection tomography is based on the measurement of line integrals of the object reflectivity function which has only been done with ultrasound and terahertz (THz) waves.57 For ultrasound and THz waves reflection tomography, instead of transmission geometry common in X-ray CT (absorption measurement), specular backreflections from forward-facing edges within the tomographic slice is being recorded by the transmitter/receiver.8 With X-ray reflection tomography, the forward specular reflection from the object is being recorded; thus, deconvolution with the incident beam profile is no longer required which can complicate the reconstruction computation. By rotating the sample in-plane, reflectivity line integral projections can be used to reconstruct the two-dimensional pattern or heterogeneous structures on the surface. We describe in this paper the instrumental setup and the very first results of image reconstruction from X-ray reflectivity projections. r 2011 American Chemical Society
’ EXPERIMENTAL SECTION Sample Preparation. Sputtering on precleaned Si substrate was done by an Emtech SC7620 sputter coater using gold as target. Si substrate (size: 2.5 cm 2.5 cm) was put inside the coater, and a mylar mask with the cut pattern was put on top of the Si. The cut pattern is the University of Tsukuba logo with a diameter of 9 mm to fit into the irradiated area of the X-ray beam, which is 9.5 mm at an incident angle of ∼5 mrad. Sputtering time was chosen at 2 min after several coating experiments to obtain the desired film thickness with sufficient reflectivity signal at the chosen incident angle. Instrumentation. Shown in Figure 1 is the experimental setup used for the X-ray reflection tomography measurements. The setup is mainly a RIGAKU Rint-ATX system used for reflection and diffraction measurements. Monochromatic Cu Kα line source (8.04 keV), from a rotating anode target, is collimated by a divergence slit with size 9.5 mm (V) 50 μm (H). This becomes the effective size of the beam as it exits the divergence slit. The size of the beam and the angle of incidence θ determines the irradiation area on the sample stage (SS) by simple geometrical consideration. To obtain an irradiation area of 9.5 mm in the horizontal direction, incident angle θ should be set at ∼0.30° (5.26 mrad). The sample stage is then fixed at this angle. To obtain different projections of the sample, the sample stage is rotated along the ϕ-axis or an in-plane rotation of the sample from 0° to 180° at 5° increments (37 projections). The reflected beam from the sample is recorded by an image plate (IP). An image plate is an area detector which utilizes a film-like radiation image sensor composed of specifically designed phosphors that trap and store X-rays by photostimulated luminescence. X-ray data on the IP is stored and stable until scanned with a laser beam Received: July 21, 2011 Accepted: September 14, 2011 Published: September 14, 2011 7600
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Analytical Chemistry during a read operation. Advantages of the use of an IP include: wide dynamic range (more than 5 orders of magnitude), high sensitivity (up to 60 keV), and high resolution (50 μm). The image plate is placed at a distance of 8.0 cm by a specialized holder. The distance from the sample to the IP is crucial as it determines the spatial resolution or the maximum size of the structures on the sample resolved by the technique. The beam has a vertical angular divergence of 20 mrad based on the calculation of the reflected beam height size at the IP position and the original pattern size over the SS to IP distance. Multiplying the vertical angular divergence with 8.0 cm (SS to IP distance) gives 1.6 mm spatial resolution. Further improvements are currently being done to lower this spatial resolution. For the measurements, X-ray source power is set at the lowest power 20 kV 10 mA as a compromise with the counting time so as to not saturate the image plate. For each ϕ angle, reflection is recorded for 30 s; then, the image plate is removed from the holder and put into an image plate reader for data reading. The
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image data is then processed by the image software tool ImagePro Plus.
’ RESULTS AND DISCUSSION We demonstrate the imaging technique using a sputtered gold pattern of the University of Tsukuba logo. Gold was used because of its high reflectivity and its high reflectivity coefficient contrast with the Si substrate at the incidence angle of 5.3 mrad. Critical angle for Si is 3.9 mrad while Au is 9.9 mrad. Reflected beam image data was processed by Image-Pro Plus to output the line projection along the y-axis as shown in Figure 2 for different projection angles ϕ. Pixel intensities along the x-axis for 810 pixels for a particular y-axis position (or y pixel number) are summed up, and the summed intensity at each y-axis position is the line projection. Image plate resolution is 50 μm per pixel. Inset in Figure 2 shows the actual sample as it is rotated with ϕ. The image plate would be located on the right-hand side of the sample. Thus, we can clearly see how the line projection would vary with the change in rotation angle of the sample. The projections pθ(u), where u is a point on the projection axis, is related to the reflectivity edge map f(x,y) by the Radon transform: Z ∞Z ∞ f ðu cos θ s sin θ, u sin θ þ s cos θÞ ds pθ ðuÞ ¼ ∞ ∞
ð1Þ
Figure 1. X-ray reflection tomography setup using a Rigaku RINT-ATX system. An 8.04 keV Cu Kα monochromatic X-ray source passes through a divergence slit DS and hits the sample on the sample stage SS for a chosen incident angle θ. Inset shows the geometry for the sample stage. The sample is rotated along the ϕ-axis of SS to have different reflectivity projections which is recorded on an image plate IP (for each ϕ) placed 8.0 cm away from the sample. This system also consists of soller slit assembly, attenuator assembly AA, and the detector for normal X-ray reflectivity and diffraction measurements.
The line projection data for the 37 ϕ angles (0180° at 5° increment) is inputted into a Matlab program utilizing the Fourier-back projection (FBP) algorithm to reconstruct the 2D pattern on the sample surface. The FBP algorithm is based on the Fourier slice theorem, which relates the Fourier transform of an image projection to a slice in the two-dimensional Fourier transform of the image. The FBP algorithm inverts eq 1 to recover f(x,y) by first filtering the projection data with a filter kernel then backprojecting it across the image plane. The filter kernel removes the blurring in simple backprojection (due to summation of “tail” artifacts from the projections) and results in a mathematically exact reconstruction of the image. An image is reconstructed by summing all the resulting filtered backprojections. This algorithm for image reconstruction from projections is common in computer tomography (CT) as it is computationally efficient.4
Figure 2. Reflected beamline as imaged on the image plate and corresponding line projection (intensity integrated along the x-axis) for the sputtered gold pattern on Si at different projection angles ϕ (a) 0°, (b) 45°, and (c) 90°. 7601
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Analytical Chemistry
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This technique is indeed very promising for nondestructive analysis of heterogeneous structures on surfaces and buried interfaces, and more improvements are underway mainly in the instrumentation and the calculation aspect to strengthen the capabilities of this technique. Extension of this work with synchrotron radiation (SR) source is also envisioned as SR allows higher X-ray energies (or deeper penetration into materials) and different beam configurations (e.g., microbeam and line scanning).
Figure 3. (a) Image of University of Tsukuba logo cut pattern on the Si surface in grayscale. Grayscale image was used for image correlation analysis. (b) Intensity (arb. units) profile associated with image (a) along the white line. (c) Output reconstructed image from 37 projections of the UT logo pattern. (d) Intensity (arb. units) profile along the white line shown in image (c).
Using the FBP procedure, the reconstructed image for 37 projections is shown in Figure 3b along with the cut pattern sample of the UT logo in grayscale (Figure 3a). As can be observed, the reconstructed image captures most of the details of the outside edges. On the right-hand side of each image is the intensity profile along the white line shown which shows the similarity of both images. Quantitatively, we calculated the correlation of the two images by the overlap coefficient R defined as:
∑
s1i s2i i R ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðs1i Þ2 ðs2i Þ2
∑i
ð2Þ
The value s1 is the signal intensity from image 1 while s2 is the signal intensity from image 2 at each image pixel i. R value ranges from 0 to 1 where 0 signifies no overlap and 1 represents complete image overlap. R value for the two images was calculated to be 0.915. This correlation coefficient can be improved further by increasing the number of projections used in the reconstruction in which case more details can be resolved by the reconstruction. Also, an improvement in the resolution of the imaging technique can be done by decreasing the sample to image plate distance or using a high resolution CCD detector placed very near the sample. We have tried using a CCD detector, but the major drawback is that the CCD detector can easily saturate with the high reflectivity coming from the sample at very low glancing angles. The CCD detector can be of major use when the incidence angle is increased; therefore, lower intensities are recorded, and accumulation time will just be increased. By varying the incident angle, a three-dimensional view of the buried interface (within 100 nm or around the penetration depth of the X-ray source used) is possible, albeit nondestructively with 1 Å precision. However, some improvements in the X-ray optics must be done to obtain a full 3-D view as the viewing area of X-rays changes with the incident angle.
’ CONCLUSION We have succeeded in imaging a gold pattern (9 mm in diameter) on a Si surface by X-ray reflection tomography which cannot be done by ordinary X-ray reflectivity measurements. Incident angle was set at 5.3 mrad to obtain high reflectivity contrast between the gold and Si on the sample as well as to obtain an X-ray viewing area of ∼9.5 mm horizontally (9.5 mm vertical). By putting an image plate (with 50 μm resolution) at a distance of 80 mm near the sample, a spatial resolution of ∼1.6 mm is obtained. 37 reflectivity projections were obtained by rotating the sample in-plane from 0180° at 5° increments. Line projection data of the 37 projections along the y-axis position was used to reconstruct the image by the Fourier-back projection algorithm. A good correlation between the original image and the reconstructed image was successfully obtained. This is the first step toward the development of X-ray reflection tomography as a tool in nondestructive three-dimensional imaging. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT One of the authors (V.A.I.-S.) is supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) Japanese Government Scholarship. ’ REFERENCES (1) Sakurai, K; Eba, H Anal. Chem. 2003, 75, 355. (2) Sakurai, K.; Mizusawa, M. Anal. Chem. 2010, 82, 3519. (3) Sakurai, K.; Mizusawa, M.; Ishii, M.; Kobayashi, S.; Imai, Y. J. Phys.: Conf. Ser. 2007, 83, 012001. (4) Herman, G.T. Image Reconstruction from Projections: The Fundamentals of Computerized Tomography; Academic Press: New York, London, 1980; Chapters 12. (5) Dines, K. A.; Gross, S. A. IEEE Trans. Ultrason. Ferroelectr. Freq. Control UFFC-34 1987, 309. (6) Mittleman, D. M.; Hunsche, S.; Bovin, L.; Nuss, M. C. Opt. Lett. 1997, 22, 904. (7) Pearce, J.; Choi, H.; Mittleman, D.; White, J.; Zimdars, D. Opt. Lett. 2005, 30, 1653. (8) Kak, A.C.; Slaney, M. Principles of Computerized Tomographic Imaging; IEEE Press: New York, 1988; Chapter 8.
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