Download Attainment of 60nm Resolution in Phase-Contrast X

3. Methods and Novel Approaches
Proc. 8th Int. Conf. X-ray Microscopy
IPAP Conf. Series 7 pp.343-345
Attainment of <60nm Resolution in Phase-Contrast X-ray Microscopy using an
add-on to an SEM
S.C. Mayo, P.R. Miller, J.Sheffield-Parker*, Tim Gureyev and S. W. Wilkins
CSIRO, Manufacturing and Infrastructure Technology, Private Bag 33, Clayton South, VIC 3169, Australia;
* XRT Ltd, A3.0, 63 Turner Street, Port Melbourne, VIC 3207, Australia
Laboratory-based phase-contrast microscopy is a practical and versatile technique for X-ray imaging and tomography of a
wide variety of samples. Using phase-retrieval techniques we can obtain quantitative information about the sample as well as making images easier to interpret. We have demonstrated resolution of <60nm in XuM imaging by coupling phase-retrieval with deconvolution methods for reducing the effect of the X-ray source size and shape in the image.
KEYWORDS: X-ray microscopy, Phase-contrast, Phase-retrieval
for a wider range of applications. Development work in
this area is continuing.
1. Introduction
The X-ray ultra-Microscope (XuM) developed at
CSIRO, and commercialized by XRT Ltd, is based around
a Scanning Electron Microscope (SEM). The SEM electron beam is focused on a target to produce a microfocus
x-ray source for point-projection imaging, a technique pioneered by Cosslett & Nixon1,2). The sample is placed between the source and an X-ray detector such that X-rays
pass through the sample and form an image on the detector. A sketch of the geometry is shown in Fig. 1.
R1
X-ray
source
2. Limits on Resolution
At high magnifications, when resolution is not detector
limited, two factors affect the resolution of in-line phasecontrast images from the XuM. These are:
1) Phase-contrast, or diffraction - this limits image resolution to the width of the near-field diffraction fringe. This
in turn depends on the imaging conditions including the
R1 distance and the energy range of the X-rays.
2) Source-size - the image can be considered to be the
convolution of a "perfect" image (as from a point source)
with the source distribution. Where the width of the Fresnel diffraction fringe in the image plane is smaller than the
magnified source size, the source size effect will limit
resolution.
R2
Object
contact image Phase-contrast image
z = R2
z=0
Fig 1 Sketch of XuM imaging geometry showing R1, the
source-sample distance, and R2, the sample-detector distance. In the XuM typically R1<<R2 and hence magnification M >>1.
This point-projection geometry benefits from natural
magnification, where for a given source to sample spacing,
R1, and a sample to detector spacing, R2, the magnification, M, is given by M=(R1+R2)/R1. The small source-size
enables large magnifications to be used without problems
arising from penumbral blurring.
The significant spacing between the sample and detector,
coupled with the small source-size, also gives rise to inline phase-contrast in the image. This is due to near-field
Fresnel diffraction and results in enhanced visibility of
edges and boundaries within a sample, and also enables
imaging of weakly- or non-absorbing features.
Phase-retrieval algorithms can be used to extract quantitative data from XuM phase-contrast images, and to improve image quality and interpretability.
The XuM has proven to be a useful and versatile instrument that we increasingly use for tomography as well as
imaging. Imaging resolution of better than 0.25µm is routinely achieved, however, a major focus of our activities is
pushing the limits of resolution to make the system useful
Fig. 2 - XuM image of an ink-jet print head showing the
polymer based ink nozzle – enlarged inset shows
black/white phase-contrast fringes which reveal the nonabsorbing features (image acquired by Leo Sudnik).
2.1 Phase-contrast resolution limit
In-line phase-contrast emerges from Fresnel diffraction
of X-rays by the object. This includes diffraction arising
from both absorption and phase-shift of the X-rays by the
object. In the near-field imaging regime that is characteristic of typical XuM imaging this manifests itself as narrow
bright and dark fringes around edges and boundaries
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Proc. 8th Int. Conf. X-ray Microscopy
within the object which in general enhance the visibility of
fine features. Fig. 2 shows an example of such an image
For lower magnifications the resolution of an in-line
phase-contrast image is limited by the width of the diffraction fringes. This characteristic width is in turn determined
by the imaging conditions, in particular R'
(R'=R1.R2/(R1+R2)§R1), and O the wavelength of the radiation (for polychromatic radiation an effective Ocan be
used instead). Thus the smallest resolvable feature size, s,
is given by
s = x.¥(O.R'),
where x § 1-2 with small variations depending on the
Gand Evalues of the sample (i.e. the real and imaginary
parts of the refractive index respectively), and the particular definition of resolution used.
For a given wavelength, and a fixed source to detector
distance the fringe width decreases with decreasing R', and
hence R1. This implies that for high resolution it is necessary to work at high magnification. However since contrast
(e.g. phase contrast) tends to reduce with increasing magnification, there is no benefit in increasing magnification
further once the desired resolution is reached (this will also
reduce the field of view).
2.2 Source size resolution limit
For an incoherent x-ray source such as that used in the
XuM, the actual image observed on the detector (provided
the detector is not limiting resolution) can be considered to
be the convolution of a "perfect" image (as from a point
source) with the X-ray source distribution. Thus the improvement of resolution by reducing R1 as described
above, can only progress so far before the source size effect begin to dominate – e.g. when the magnified source
size in the image plane is approximately equal to that of
the Fresnel fringe width.
Strictly speaking, for an image magnification M the
source size magnification in the image plane is M-1, however at high magnifications (M>>1) they are virtually the
same. Thus, the smallest resolvable object in the sample
will be limited to approximately the X-ray source size,
where it is not further limited by diffraction fringe width or
detector resolution.
3. Source Size Deconvolution & Phase Retrieval
To achieve and measure the maximum possible resolution the image is processed in two stages. The first stage is
deconvolution to reduce the effect of the source distribution, and the second is phase retrieval which converts the
resulting "clean" phase-contrast image into a more conventional density map which is more easily interpreted and
from which resolution may be measured.
The X-ray source distribution is simulated using Monte
Carlo methods. This takes account of the energy and focus
of the electron beam, the shape, orientation and composition of the target, absorption within the target, sample and
detector, and detector efficiency, to simulate the source
distribution as viewed from the detector. The x-ray generation calculation includes characteristic rays and an anisotropic model of bremsstrahlung.
IPAP Conf. Series 7
The X-ray source is often asymmetric which results in an
asymmetric appearance of otherwise symmetric features in
the image. Deconvolution of the image with the simulated
source distribution results in a cleaner image in which features such as phase-contrast fringes are symmetric.
Fig. 3a shows a raw image which has distinct asymmetry
in the fringes around the dark squares due to an asymmetric X-ray source distribution. This is corrected by source
deconvolution (Fig. 3b), making the phase-contrast fringes
around the squares more visible and symmetric.
a
c
b
d
Fig. 3 – Image processing steps for an image of a semiconductor test sample: a. Raw data, b. Deconvolution of
source-distribution, c. TIE phase-retrieval, d. Refinement
by Gerchberg-Saxton phase-retrieval
The next step in image processing is phase-retrieval.
This takes a phase contrast image with diffraction features
and extracts from it a density map of the object which is
easier to interpret and from which resolution measurements can be taken.
Phase-retrieval depends on understanding the mechanism of image formation and inverting it to restore a representation of the object3). It acts, in effect, as a software lens
bringing the defocused image into focus. It has two steps;
1) Transport of intensity equation (TIE) phase retrieval.
2) Gerchberg-Saxton refinement.
The effects of these two steps are illustrated in Fig. 3c
and Fig. 3d respectively.
IPAP Conf. Series 7
Proc. 8th Int. Conf. X-ray Microscopy
4. Resolution Measurements on Images of Semiconductor Sample
To produce an image with high resolution a thin-foil target was used in the XuM. This limits the source size in the
vertical direction to the thickness of the foil
The sample was a semi-conductor test device, backthinned to around 50 µm to permit penetration by the relatively soft X-rays used (~8keV). Magnification was increased to optimize resolution and raw images acquired.
The raw data was processed as described above to correct
for source distribution and produce a density map using
phase-retrieval.
The profile of an edge-feature within the final image was
measured and fitted to a curve. The resolution was defined
as the distance over which the intensity increased from
10% to 90% of the intensity difference on either side of the
edge.
Fig 4 shows the relevant image being measured and the
resolution calculated in a software application developed
for the purpose.
The mean horizontal and vertical resolutions measured
in this were both 53nm. The fact that they were both the
same shows the effectiveness of the effective source deconvolution in removing asymmetry arising from the Xray source distribution.
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5. Resolution in Tomography
Samples mounted in the XuM make use of the SEM
sample stage. This has a vertical rotation axis enabling the
acquisition of tomographic datasets. Phase retrieval is used
to preserve the visibility of fine features whilst putting the
data into a form suitable for reconstruction algorithms resulting in high quality 3D datasets.
Tomographic resolution is not limited by image resolution but by stage stability which is around 2µm. Current
work is focused on improving reconstruction resolution by
compensating for instabilities in the sample position arising from the sample stage.
100µm
200µm
Wood sample: Pinus Radiata
European Wasp Foot
Fig. 5 Examples of XuM tomographic reconstructions
6. Conclusions
Fig.4 Measuring resolution
in a processed image of a
semiconductor test device.
HORIZONTAL (nm) VERTICAL
1
53
1
2
58
2
3
54
3
4
58
4
5
54
5
6
49
6
7
55
7
8
57
8
9
42
9
10
49
10
s.d
Mean
5
53
s.d
Mean
(nm)
54
55
53
52
48
50
52
48
57
55
3
53
Although high resolution can be achieved as demonstrated here, the suitability for a particular application depends on a number of additional factors. Achieving high
resolution depends on using thin-foil targets which produce a lower X-ray flux and hence increases the acquisition time for an image of given signal-to-noise level. Another factor is the inherent visibility of small features
which depends on the size and phase-shift and absorption
of the object and will always be reduced for smaller objects, even with phase-contrast. Thus a deeper consideration of these and other imaging conditions is required to
optimize the imaging system for particular applications.
Such a discussion may be found in Nesterets et al 4).
Image resolution of <60nm can be achieved in the XuM
as demonstrated above. Detailed optimization of imaging
for particular applications, however, requires a consideration of more imaging parameters than resolution alone.
Our current and future focus is on improving the resolution of tomographic reconstruction which will involve addressing a new set of challenges.
1) V.E. Cosslett & W.C. Nixon (1960) X-ray Microscopy, Cambridge
University Press, London
2) S.C. Mayo, P.R. Miller, S.W. Wilkins, T.J. Davis, D. Gao, T.E.
Gureyev, D. Paganin, D.J. Parry, A. Pogany & A.W. Stevenson, (2002) J.
Microscopy, 207, Pt 2 Aug. 2002, 79-96.
3) D. Paganin, S.C. Mayo, T.E. Gureyev, P.R. Miller and Wilkins, S.W.
(2002). J.Microscopy. 206, 33-40
4) Ya. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany and A. W.
Stevenson (2005) Rev. Sci. Instr. in press