A Study on Parasitic Slit-Scatteringsin SAXS Equipment

Tuo HuangGrinnell College, IA, USA

PI/Mentor: Dr. Youli LiMaterials Research Laboratory, University of California, Santa Barbara, CA, USA

August 2007, University of California, Santa Barbara

I. Introduction

The X-Ray Diffraction (XRD) Facility is one of the most frequently used user-

facilities lab at MRL, UCSB. By using X-ray diffractometers, researchers who work

with nanosystems, such as organic/inorganic/hybrid crystals, biomacromolecules,

semiconductor devices, polymers, microfibers, etc, are able to obtain information

about the nanoscale structures of their materials. Among the many XRD techniques,

Small Angle X-ray Scattering (SAXS) is best suited for examining nanostructures on

the scale of 101 to 102 Å. In SAXS instruments, incident X-ray beam must be well

collimated and have a clear edge, so that user can clearly distinguish the scattering

signals from the transmitted direct beam. To obtain such a beam profile, multiple

apertures formed by pairs of horizontal and vertical slits made of heavy metals such as

tantalum or tungsten, which are strong x-ray attenuators, are used to define the

geometrical shape and size of the beam.1 However, slits made from such

polycrystalline metals, no matter how finely machined and polished, will generate

undesirable "parasitic scattering", where slits themselves scatter X-ray photons in a

wide angle and produce strong background noise in the beam profile.

In this research, we conducted a series of experiments to characterize the slit

scattering from different materials under various conditions in order to find possible

ways to enhance the performance of SAXS instruments.

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II. Experiment Approaches

We first studied the scattering profile of traditional tungsten blades from actual

x-ray slits widely used in x-ray diffractometers (Figure 1). One of such slits was

placed at the sample-holder of the SAXS instrument and moved across the x-ray beam

to produce slit-scattering images (the incident beam is normal to the edge of the slit).

Before the image was taken, an X-ray pin-diode was placed right behind the slit to

measure the X-ray beam intensity when the slit was moved to a certain position.

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Scattered Beam(To detector)

Incident Beam

Slit moves into the beam

Figure 2 shows that as the slit cuts across the beam (the slit moves in negative x

direction), the X-ray intensity drops because a larger part of the beam is blocked. The

plot above also shows that, on the interval where the intensity is between 5000 and

20000 (counts per second), intensity drops linearly, which means that the slit is

cutting into the central part of the beam. This interval is chosen for data-taking so that

scattering at different cutting-depth happen on the same length-interval on the edge of

the slit.

After taking the intensity-depth plot, the pin-diode is removed, and the slit is

driven to selected points of cutting-depths by high-precision stepping-motors

(accuracy within 10 microns) and a two-dimensional scattering image was taken at

each point with a multiwire x-ray area detector (Bruker HISTAR).

The aforementioned steps were then repeated, only replacing the tungsten slit

with a piece of silicon wafer, with its 1 0 0 crystal plane facing the beam and 0 0 1

plane on the edge (so slit scattering, if any, should occur on the 0 0 1 plane).

Fig. 3: Experiment with Silicon wafer

The scattering profile of silicon wafer shows reduced slit-scattering, but the

scattering from the wafer’s edge still fits into a Lorentzian function. Attempts were

made to polish the (0 0 1) plane for greater flatness but that did not yield much

improvement. However, we noticed that the (1 0 0) plane was very well polished

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(1 0 0) Plane(0 0 1) Plane

Incident X-ray Beam

when the wafer was produced; therefore, if we could make (1 0 0) plane instead of (0

0 1) plane on the edge, scattering may be significantly reduced.

This resulted in making a tungsten slit with a tiny strip of silicon wafer mounted

on the edge (Figure 4). This hybrid slit was again tested using the same method as

above.

III. Results and Analysis

1. Tungsten Slit & Single-Crystal Silicon Slit

To explain the analysis of scattering profile, let us take the image of tungsten slit

at position x=-6.17 and intensity I=12827 Counts/sec as an example. All the other

images taken are processed in the same manner.

The image is first displayed from the raw data file (Figure 5). After finding the

pixel position of the beam center (597.2536, 538.6029), a rectangular area is defined

along the X direction i.e. the direction of the scattering “tail.”

Fig. 5: Analyzing the Scattering Tail

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Tungsten Slit

Silicon Wafer

1-0-0 Plane

Incident X-ray Beam

Fig. 4: Hybrid

Slit

Then numerical integral is computed along the X axis of the image to reflect the

average intensity of the points in the rectangular at each x position. The resulting plot

is shown in Figure 6. In the plot, x axis is the 2-theta scattering angle that each point

corresponds to (label on x axis is in reverse order, and the peak corresponds to the

scattering “tail” in the image):

1 J. S. Pedersen in Modern Aspects of Small-Angle Scattering edited by H. Brumberger (Kluwer Academic Publishers, Dordrecht/Boston/London, 1995), 57-91

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Figure 6: Result of Numerical Integration along the x-axis

The result is then exported to a two-column chiplot file that can be read by

analysis software such as MS Excel™ or Origin™. The data was further assorted and

the data points that are on the scattering “tail” were extracted to be studied alone for

curve fitting.

The scattering profiles of both tungsten and Silicon Wafer slits fit into a

Lorentzian function in the form of where A and Γ are

variables positively correlated to the height and width of the peak, respectively.

Fitting results are shown in Table 1 & 2.2

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Table 1: Curve-fitting Results for the Scattering Profile of Tungsten Slits

Relative Slit

Position (mm)

y0 x0 ΓError for

Γ(±)A

Error for A (±)

Goodness of Fit

Reduced χ-square

R-square

0.1 0.37544 -0.10555 0.08392 0.00062 2.55588 0.02912 0.0212 0.997610.3 0.14054 -0.10711 0.08135 0.00051 6.57875 0.06011 0.1095 0.998280.5 0 -0.10576 0.07709 0.00046 14.48919 0.13391 0.60831 0.998080.7 0 -0.1055 0.07277 0.00046 19.62139 0.19278 1.28709 0.99790.9 0 -0.1057 0.07012 0.00047 18.51033 0.19293 1.36157 0.997621.1 0 -0.10615 0.06815 0.00051 11.93119 0.13408 0.71214 0.99715

Table 2: Curve-fitting Results for the Scattering Profile of Silicon-

Wafer Slits

Relative Slit

Position (mm)

y0 x0 ΓError for

Γ(±)A

Error for A (±)

Goodness of Fit

Reduced χ-square

R-square

0.1 0.44246 -0.07578 0.06998 0.00239 1.59566 0.11902 0.0071 0.992590.3 0.3661 -0.06647 0.06178 0.00413 3.28324 0.33896 0.01076 0.995170.5 0.24839 -0.07342 0.06174 0.00171 4.58296 0.2264 0.01238 0.998050.7 0.11366 -0.07905 0.05567 0.00113 5.71605 0.22145 0.0195 0.998490.9 0.01246 -0.08087 0.04189 0.00171 6.36557 0.4097 0.03271 0.997721.1 0 -0.08774 0.03415 0.00081 4.61314 0.17914 0.01491 0.99871

2. Hybrid Slit

Numerical integration was also done for the images from the hybrid slit and

compared with the background (Figure 7). The negative half on the horizontal axis

corresponds to the scattering tail on the image. The profile of the hybrid slits (blue

curves) are basically superposed on the background (dark-red curve) i.e. having

almost the same intensity with the background at each point, but only lower because

2 In curve-fitting, y0 is forced to be zero if the automated fit returns a negative y0 value, because the background offset cannot possibly be negative in this case.

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the overall intensity decreases as the slit moves from x= -6.2 to x= -6.6, blocking a

greater part of the beam. The profile from the hybrid slit is insignificant compared to

scattering from tungsten slits (gold curve).3 Hence, we concluded that the hybrid slit

has no obvious slit-scattering.

IV. Discussion

We are not sure about what has caused the Lorentzian pattern in the scattering

tail, which can also be modeled by a -2 power function. S.K. Sinha et al.4 suggest that

it may be due to the exponentially distributed roughness of the surface and, in the case

of tungsten, also the randomly oriented polycrystalline micro-domains.

3 Data from tungsten slit is not extracted from the ones analyzed above, but was retaken in the same set-up as the hybrid slit right after the hybrid slit’s data was taken in order to show more valid comparison.4 S. K. Sinha, E. B. Sirota, and S. Garoff. Phys. Rev. B 38, 2297 - 2311 (1988)

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The absence of slit-scattering for hybrid slit is both exciting and well within

expectation. Because the (1 0 0) plane is well polished and has no roughness, when

this plane is on the edge of the slit, the lowest detectable x-ray diffraction angle is the

one at 69.13 degrees for the (4 0 0) plane (which is parallel to the (1 0 0) plane).5 Yet

in SAXS, the X-ray beam is collimated to a divergence angle of less than 0.05 degrees

and the detection range of scattered angle is less than 2 degrees, both of which

characteristics make it impossible for any X-ray photons scattered at a 69.13-degree

angle to be picked up by the detector.

V. Conclusion

After studies on tungsten and silicon wafer slits, we can make a tentative

conclusion that roughness of the surface on the edge of the slit seems to be the

primary cause of slit-scattering. Meanwhile, scatterings from polycrystalline micro-

domains also contributed to the overall slit-scattering and can be reduced by using

single-crystal material for slits. When both factors are taken care of, as in the case of a

hybrid slit, slit-scattering is reduced to undetectable level.

If further experiments continue to show satisfactory results, these newly

designed hybrid slits can lead to dramatic improvement to optical configuration of the

SAXS instrumentation. In the traditional three-slit setup, besides the two set of slits

that collimate the X-ray beam, additional slits are needed to cut off slit-scattering

from those previous slits. In contrast, hybrid slits do not generate slit-scattering and

thus can significantly simplify the design of SAXS equipment and boost the

5 Natl. Bur. Stand. (U.S.) Monogr. 25, 13, 35, (1976)

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efficiency and performance of the equipment.

VI. Acknowledgements

It is a pleasure to acknowledge the superb technical assistance from Joanna

Deek, Nicholas Judy and Eric Welsh, and the help and guidance from the program’s

coordinator, Dr. Patricia Halpin and supermentor Brett Brotherton.

This work was supported by the MRSEC Program of the National Science

Foundation under Award No.DMR05-20415.

Notes and Citations

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