A New Near-Field Scanning Transmission X-Ray
Microscopy with 10-nm Resolution
R. E. Burge, X.-C. Yuan, J. N. Knauer
Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, UK
and
Physics Department, King’s College London, Strand, London WC2R 2LS, UK
Abstract. We show by computer modelling that scanning soft X-ray
microscopy using a 10 nm to 20 nm aperture in near field conditions
can provide a point to point resolution in transmission of 10 nm. Implementation of this new proposal will radically move forward the present
best resolution in scanned X-ray imaging of about 35 nm. The method
is realistic in terms of exposure time per point with third generation
synchrotron sources of soft X-rays.
1
Introduction
The development of soft X-ray transmission microscopes and their applications
in biology have been reviewed recently [1]. The concentration on biological applications has been due in large part to the design of the synchrotron sources of
soft X-rays currently in mature operation which are near optimum for studies in
the “water-window” at wavelengths between the C and O K-absorption edges.
The present study considers the imaging of “biological” material by scanning
X-ray microscopy in the near-field and in the water-window, but 10 nm resolution
is also expected to be of value in the solution of structural problems in material
science and in spectromicroscopy. The optical set-up assumes the collection of
all the photons transmitted by the specimen by a detector in the far-field. A
wavelength of 2.4 nm, within the water window (X-ray energy about 500 eV), is
selected for the calculations below and the material to be imaged is taken to be
the organic photoresist PMMA. Detailed specimen composition is not critical to
the computer modelling to be presented.
The point to point resolution so far achieved in scanning (and imaging) X-ray
microscopes is limited by the problems of fabricating nanodimensional Fresnel
zoneplates with high zone positional accuracy [2]–[4]. Current point to point
resolutions in practice in scanning X-ray microscopy [1] are at best about 35 nm,
even after deconvolution for the probe size [5]. Very considerable efforts are being
made to increase the zoneplate resolution, or to work with a zoneplate focus
higher than the first order, in pursuit of the goal of 10 nm resolution [6].
X-Ray Microscopy and Spectromicroscopy
Eds.: J. Thieme, G. Schmahl, D. Rudolph, E. Umbach
c Springer-Verlag Berlin Heidelberg 1998
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There has been recent intense activity in the study of scanning near-field optical systems(SNOM, e.g. [7], [8]) where the scanning optical probe is defined by
the light passing through a sub-wavelength diameter aperture or an optical fibre
forming a nanoscale dielectric tip. The best lateral resolution so far achieved
in SNOM is about 20 nm with a scanning aperture of the same size. However,
because the probe retains the width of the scanning aperture only as far downstream as about one-half the diameter of the aperture itself before very strong
divergence of the probe occurs, there is a strong limitation on the specimen
thickness for high-resolution transmission imaging.
We propose imaging in near field for the soft X-ray case also using a small
aperture to provide improved spatial resolution but for much thicker specimens
than are possible with SNOM. To improve on the resolution so far achieved by Xray microscopy, we consider a range of apertures with widths between 5 nm and
20 nm at the primary focus of a zoneplate in the schematic optical arrangement
of Fig. 1. The zone plate acts as a condenser and calculations have been made
for monochromatic X-rays consistent with its use in first order.
Incident
Beam
λ=2.4nm
Zone Plate
Order Sorting Aperture
Au
t=200nm
d
h=10nm
y
x
H
PMMA Specimen
z
Fig. 1. Schematic diagram of the proposed optical arrangement.
Near-Field Scanning Transmission X-Ray Microscopy
2
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Probe Modelling
Calculations of the X-ray flux transmitted through X-ray masks with sub-micron
feature sizes have been made [9]–[11]. We adopt here the full vector theory of
Maxwell’s equations as the aperture size is close to the wavelength dimension
and we require to establish the effects of polarisation.
Methods of calculating SNOM images [12], [13] are available and may be supplemented by the various accurate methods to calculate the near field diffraction
from a dielectric grating structure. We have chosen the coupled wave theory [14]
for the transmission of the X-ray probe through the aperture and specimen regions and Rayleigh-Sommerfeld theory to propagate the wave motions through
vacuum from the specimen towards the detector. The coupled wave method
requires a periodic structure in order to expand the electromagnetic fields in
Fig. 2. Probe propagation through vacuum: intensity distributions z = 0nm to
z = 400nm TE tangential component. Thickness of gold aperture defining probe
=200 nm, ngold = 1 − 0.4274 × 10−2 + i0.4295 × 10−2 for λ = 2.4nm.
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terms of spatial harmonics matched at the boundary interface. A grating is chosen which locally approximates to a pinhole. For example a gold grating with
period 100 nm and slit width 10 nm represents a 10 nm pinhole. Calculations for
large period gratings require many spatial harmonic components in the coupled
wave expansion of the field. We use 131 spatial harmonics here. In the soft X-ray
region the refractive indices of materials are close to unity (see Figure legends
for Henke values of refractive indices for 2.4 nm wavelength X-rays).
For computation in a realistic time with available resources the probe defining
aperture has to be taken as two-dimensional i.e. a slit with given width along
the x dimension, and infinite in y; the probe propagates along z, (see Fig. 1).
Similarly the specimen structure is taken to be constant along the y dimension.
Thus TE polarisation is polarised parallel and TM polarised perpendicular to
the length of the slit. It needs to be made clear that the quantitative aspects
of the calculations for two-dimensional imaging will be modified in detail when
undertaken with a square or circular aperture rather than a long slit. However
there is good evidence from optical calculations [7], [8] that the general pattern of
image features seen in one dimension is repeated in two dimensions but obviously
with reduced fractional transmission. Calculations were made for both TE and
TM polarisation.
The material of the aperture was selected as gold 200 nm thick for the given
X-ray energy. It is instructive [10] to consider the aperture as a waveguide and,
according to the slit width, a series of guided TE and TM modes will be transmitted by the slit, with TE0 (and TM0 ) modes dominant for the narrow slits
to be considered here. However small the slit width the zero order modes never
reach cut off.
In Fig. 2 are shown the calculated probe shapes and normalised intensities
for the TE (radial) polarisation of the probe emerging from a slit of width 10 nm
into vacuum at different z distances downstream in the range from zero, at the
probe aperture, to 400 nm. The probe shows rapid divergence as z increases
beyond 200 nm, but the width is maintained close to the aperture dimension
for many times the slit width in contrast to the effect for visible light. These
results and corresponding ones for 5 nm, 15 nm, 20 nm wide slits are shown in
Fig. 3 as variations in the probe full width at half maximum height (FWHM)
with distance downstream. The curves in Figure 3 are closely similar despite
the four-fold range of aperture width and are consistent with the transmission
of the single TE0 and TM0 modes for such narrow slits. The FWHM for the
four slits increase smoothly from about 10 nm near the slit to about 20 nm at
z = 200nm. The efficiencies of photon transfer of the flux from the condenser
zoneplate intercepted by the slits are respectively 17%, 29%, 32% and 35% for
z = 10nm and the 5, 10, 15, 20 nm slits.
Considering TM polarisation, account must be taken of both the tangential
and the normal components of the electric field. Calculations show that the
radial TE and TM results are virtually identical for all the slit widths studied
and the normal TM field is negligible in comparison.
Near-Field Scanning Transmission X-Ray Microscopy
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Fig. 3. Probe propagation through vacuum: FWHM of intensity distributions on axial
propagation, for slit widths 5, 10, 15, 20 nm.
3
Image Calculations and Image Resolution
The calculations to be discussed, based on TE polarisation, refer to the highresolution potential of the new method. Because of the limited range in z over
which the probe retains the slit width then, as in the SNOM, the specimen
surface must be kept within a few nm from the slit aperture. Calculations are
shown in Fig. 4, for a wavelength of 2.4 nm, of the intensities in the images
of a hypothetical thin film support (400 nm thick PMMA) with a superposed
rectangular block of calcium, 50 nm wide (and hence near in dimension to the
present resolution of the zoneplate microscope) and 40 nm thick; in one image
the calcium block is on top of the thin film and it is underneath the film in the
second. In effect the block is imaged, as shown in Fig. 2, with probes that are
respectively 10 nm and 60 nm in width. The definition of the image with the
block on top of the film near the slit is greatly superior to that of the second
image. The dotted lines in Fig. 4 show for comparison the absorption images for
both object locations determined directly from the Henke data; at sufficiently
long distances from the edges of the specimen the Henke data become valid.
The image edge spread functions derived from the block boundaries (calcium to PMMA boundaries) are consistent with a resolution of 10 nm, but fur-
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0.72
0.7
0.68
Intensity
0.66
0.64
0.62
0.6
0.58
-50
-40
-30
-20
-10
0
X (nm)
10
20
30
40
50
Fig. 4. Comparison of images of 50 nm wide, 40 nm thick particle of calcium on
400 nm thick PMMA support. Solid curve: particle on top of film near probe; Dashed
curve: particle on bottom of film further from probe; Dotted line: Henke Data.
nPMMA = 1 − 0.8731 × 10−3 + i0.1826 × 10−3 , nCa = 1 − 0.9396 × 10−3 + i0.6747 × 10−3
at λ = 2.4nm.
ther consideration was undertaken with similar materials (PMMA) at the edge,
and the results were again compared with the Henke data. Calculations of the
edge spread functions were made for a 50 nm PMMA film, with a perpendicular
edge partly covering a uniform PMMA film also 50 nm thick and for a similar
100 nm/100 nm film combination. These calculations are shown in Fig. 5.
A final computer experiment was conducted by deconvolving for the effects
of the slit (or probe) width on the edge spread functions. First deconvolution of
the edge spread functions was carried out using the correct probe as in Fig. 2
with noise-free data following a Fourier transform approach. Then deconvolution
of noisy data was carried out using the Wiener filter to simulate experimental
conditions after adding Poisson noise with the aid of a random number generator. Additive noise of 2% was assumed on the thinner PMMA specimen; the
corresponding additive noise for the same number of incident photons per unit
area of the thicker sample is 6.6%. The estimated resolution derived from the
edge spread functions before and after deblurring for the probe are given in Table 1. In accord with the different definitions for resolution in common use, we
Near-Field Scanning Transmission X-Ray Microscopy
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Normalised Absorption
0.2
0.18
200nm
0.16
Normalised Intensity
0.14
0.12
0.1
100nm
0.08
0.06
50nm
0.04
0.02
0
0
10
20
30
40
50
Specimen Co-ordinate (nm)
60
70
80
Fig. 5. Normalised absorption at density steps from 50 nm to 400 nm. Solid curves:
full vector calculation; Dashed curves: Henke Data. λ = 2.4nm.
Table 1. Image Resolution Estimated from Edge Spread Function
20% − 80% criteria
10% − 90% criteria
50 nm step 100 nm step 50 nm step 100 nm step
Original Noise Free Image
9 nm
10 nm
11 nm
13 nm
Noise Free Deconvolution
6 nm
6 nm
9 nm
9 nm
Deconvolution of Noisy Data
6 nm
6 nm
9 nm
9 nm
show figures for resolution based on both the “20% to 80%” and the “10% to
90%” edge criteria.
These calculated results, following deconvolution for the probe, show that
image resolution at a level better than 10 nm is predicted for specimens with
thickness up to about 200 nm, which is consistent with our motivation.
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Experimental Arrangements
By analogy with SNOM, and among several possibilities, the control of the
height of the probe relative to the moving specimen might be accomplished
by combining the near-field scanning X-ray microscope with an atomic force
microscope (AFM, e.g. [15]). We note the use [15] of a combined AFM and
optical transmission scanning tip (in the given example of 20 nm diameter) and
the successful work to pull micropipettes [16] also to an outer diameter of about
20 nm. For a circular 20 nm aperture a conservative value for the transfer of Xray energy through a 100 nm thick specimen from the focus of the zoneplate to
the detector is about 5%. Synchrotron sources of high brightness are appearing
which are ideally suited for near field X-ray microscope operation. The third
generation ELETTRA storage ring at Trieste, Italy, produces 2 × 109 photons/s
[1] at 600 eV energy into the 0.2µm diameter focus of a zoneplate which in the
given example, for good counting statistics, corresponds to the satisfactory pixel
dwell time of order 1ms.
Deconvolution for the known probe shape, shown experimentally, and consistent with Table 1, to improve resolution in scanning X-ray microscopy by a
third [5], will improve the resolution for thin specimens below 10 nm and extend
the thickness range for 10 nm resolution to a thickness of at least 200 nm. For
much thicker specimens a larger probe size and poorer resolution is consistent
with the averaging of specimen structure through the depth.
5
Discussion
We are moving towards experimental implementation of our proposal, which
implies the possibility of macromolecular resolution with soft X-rays, subject to
the reduction of radiation damage possibly by cryo-specimen techniques. Further
consideration will be made of the experimental requirements of the near-field
approach, particularly for higher energy X-rays than the range of the water
window. As to the apparent limitation of a 200 nm specimen thickness for high
resolution imaging, we note that many studies in zone plate X-ray microscopy
and spectromicroscopy are routinely carried out in the 100 nm to 200 nm range
of specimen thickness. Unlike for visible light, the TE and TM plane polarised
components for soft X-rays behave in similar ways relative to image formation.
Acknowledgements
This work was supported by the Leverhulme Trust and the Royal Society and
has benefitted over a number of years from discussions with Dr Michael Browne
and Dr Pambos Charalambos.
Near-Field Scanning Transmission X-Ray Microscopy
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References
1. J. Kirz, C. Jacobsen, and M. Howells, Quat. Rev. Biophys. 28, 33 (1995).
2. E. Anderson and D. Kern, in Springer Series in Optical Sciences, Berlin, SpringerVerlag, 67, 75 (1992).
3. T. Matthies, C. David and J. Thieme, J. Vac. Sci. Technol. B 11, 1873 (1993).
4. P. Charalambous, P. Anastasi, R.E. Burge, and K. Popova, Procs SPIE 1995 Symposium on Optical Science, Engineering and Instrumentation, San Diego, 2516, 2
(1995).
5. C. Jacobsen, S. Williams, E. Anderson, M.T. Browne, C.J. Buckley, D. Kern,
J. Kirz, and X. Zhang, Opt. Comm. 86, 351 (1991).
6. R.E. Burge, Royal Institution Proceedings, 64, 137 (1992).
7. L. Novotny, D.W. Pohl, and P. Regli, J. Opt. Soc. Am. A 11, 1768 (1994).
8. J.L. Kahn, T.D. Milster, F.F. Froehlich. R.W. Ziolkowski, and J.B. Judkins, J. Opt.
Soc. Am. A 12, 1677 (1995).
9. S.D. Hector, H.I. Smith, and M.L. Schattenburg, J. Vac. Sci. Technol. B 11, 2981
(1993).
10. R.K. Kupka, Y. Chen, F. Rousseaux, A.M. Haghiri-Gosnet and H. Launois, J. Vac.
Sci. Technol. B 11, 667 (1993).
11. R.E.Burge and X.Yuan, Procs SPIE 1995 Symposium on Optical Science, Engineering and Instrumentation, San Diego, 2516, 108 (1995).
12. D. Van Labeke and P. Barchiesi, in Near field optics, Eds. D.W. Pohl and
D. Courjon, Kluwer Academic Publishers, Netherlands, NATO ASI series, Series
E: Applied Sciences, 242, 157 (1993).
13. Ch. Girard, A. Dereux, D. Andre, A. Castiaux and J.P. Vigneron, Phys. Low-Dim.
Struct., 4/5, 53 (1995).
14. M.G. Moharam and T.K. Gaylord, J. Opt. Soc. Am. 71, 818 (1981).
15. F. Baida, D. Courjon and G. Trebillon, in Near field optics, Eds. D.W. Pohl and
D. Courjon, Kluwer Academic Publishers, Netherlands, NATO ASI Series, Series
E: Applied Sciences, 242, 71 (1993).
16. E. Betzig, J.K. Trautman, T.D. Harris, J.S. Weiner and R.L. Kostelak, Science,
251, 1468 (1991).
17. B.L. Henke, J.C. Davis, E.M. Gullikson, and R.C.C. Perera, A Preliminary Report
on the X-ray Photoabsorption Coefficient and Scattering Factors for 92 elements
in the 10–10,000 eV Region. (University of California, Berkeley, Calif., 1988), Rep.
LBL-26259.
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