Fabrication of high-resolution zone plates with wideband
extreme-ultraviolet holography
Harun H. Solak,
a)
Christian David, and Jens Gobrecht
Laboratory for Micro and Nanotechnology, Paul Scherrer Institut, CH-5232 Villigen-PSI, Switzerland
(Received 11 May 2004; accepted 10 August 2004)
We report an achromatic holographic method to fabricate high-resolution x-ray optics using
coherent extreme-ultraviolet radiation from an undulator source. The interference pattern between
two spherical beams, which are created using Fresnel zone plates, is recorded to produce a
higher-resolution zone plate. Analytical and simulation results showing the formation of the zone
plate pattern was confirmed experimentally with the production and testing of a lens with 60-nm
outermost zone width. The combination of extreme-ultraviolet light, which exposes photoresists
with practically no proximity effect, and holography, which guarantees the accurate placement of
zones, addresses the main difficulties faced in the improvement of the resolution of x-ray lenses.
Holography with extreme-ultraviolet light has the potential to produce lenses with sub-10-nm
resolution. © 2004 American Institute of Physics. [DOI: 10.1063/1.1803937]
The use of x rays in imaging applications, such as mi-
croscopy or lithography, has long been pursued for its high-
resolution potential. Recent advances in the fabrication of
x-ray optics have led to unprecedented progress with the use
of reflective,
1
refractive,
2
or diffractive optics.
3
The highest
resolution in x-ray imaging is currently achieved with
electron-beam-written Fresnel zone plates (FZP). These
lenses are used in x-ray imaging applications that demand
high spatial resolution, such as the imaging of intracellular
structures
4
and magnetic domains.
5
New areas of use for
these optics have been emerging in recent years, such as
phase-contrast x-ray microscopy,
6
and advanced lithography
applications.
7,8
Driving the spatial resolution down to 10 nm
and below would make a qualitative difference in the perfor-
mance of x-ray imaging for all of these areas and would add
new applications to the list which have length scales that are
beyond the resolution capabilities of currently available
optics.
In its most common form, a FZP consists of absorbing or
phase shifting concentric circular rings positioned on a trans-
parent substrate. The resolution obtained with a FZP is de-
termined by the width of the smallest zones. Electron-beam
lithography (EBL) has been used to manufacture zone plates
with structures as small as 20 nm,
3
which provide optical
resolution performance in the same order.
9
The width of the
smallest zones that can be manufactured with EBL is mainly
limited by the proximity effect, due to the long range of
secondary electrons.
10
Another difficulty in this lithographic
method concerns the placement of zones with an accuracy
better than the zone width, which is required for achieving
diffraction limited optical performance. Interferometer con-
trolled stages are used to address this problem,
11
but residual
errors remain because a direct measurement of the beam po-
sition on the substrate is not provided.
FZP lenses have also been made with laser holography,
12
which is a powerful technique to produce diffractive optics
with excellent control of the phase.
13
Yun et al. proposed
using soft x rays to achieve higher resolution in holographic
fabrication.
14
They described a spatial-frequency multiplica-
tion scheme, where interference between two different dif-
fraction orders of a “parent” zone plate is used to create a
higher-resolution “daughter.” In this method, the illuminating
beam has to be spatially coherent and its spectral width given
by Dl/l (where Dl is the full width at half maximum of the
spectrum) has to be smaller than the inverse of the number of
zones of the parent zone plate in order to achieve the desired
interference. These conditions make the technique effectively
impractical, since the currently available soft x-ray sources
cannot provide the necessary photon flux satisfying both the
spatial coherence and the spectral-width requirements. We
have recently developed an achromatic interference method
using soft x rays to make nanometer scale linear periodic
patterns, where beams from a number of diffraction gratings
positioned on a transparent mask interfere to form a periodic
intensity pattern.
15
This spatial-frequency multiplication
technique can be used with wideband light if the diffraction
gratings on the mask have a single and constant period, en-
suring that all interfering beams reaching the image plane
travel the same optical path length. The illumination require-
ments of this scheme are satisfied by undulators in the soft x
ray and extreme-ultraviolet (EUV) region, which emit radia-
tion with good spatial coherence and a rather wide band-
width sDl/l<1%–5%d.
16
The achromatic spatial-frequency multiplication method
discussed above is not directly applicable to the production
of zone plates, because of the dependence of the zone period
on the radius in a FZP. In the following, we will show that
this limitation can be overcome with the holographic scheme
illustrated in Fig. 1, where beams interfering at a certain
image plane travel equal optical paths. Assuming that the
mask in Fig. 1 is illuminated with a unity amplitude plane
wave at normal incidence, we can write the amplitudes of the
two interfering spherical beams in the Fresnel approximation
as
U
n
=
A
n
expsikzdf
n
ilsf
n
+ zd
exp
S
− i
kr
2
2
1
f
n
+ z
D
, n = 1,2, s1d
where k is the wave number, A
n
is the diffraction efficiency,
and f
n
is the focal length of the n
th
zone plate.
14
The intensity
of the total field is found to be
a)
Electronic mail: harun.solak@psi.ch
APPLIED PHYSICS LETTERS VOLUME 85, NUMBER 14 4 OCTOBER 2004
0003-6951/2004/85(14)/2700/3/$22.00 © 2004 American Institute of Physics2700
I =
S
A
1
f
1
lsf
1
+ zd
D
2
+
S
A
2
f
2
lsf
2
− zd
D
2
+
2A
1
A
2
f
1
f
2
l
2
sf
1
+ zdsf
2
− zd
cos
F
kr
2
2
S
1
f
1
+ z
+
1
f
2
− z
D
G
. s2d
At the image plane, z=s, this equation simplifies to give
I =
S
A
1
f
1
lD
D
2
+
S
A
2
f
2
lD
D
2
+
2A
1
A
2
f
1
f
2
l
2
D
2
cos
S
kr
2
D
D
, s3d
where s =sf
2
− f
1
d/2, and D=sf
1
+ f
2
d/2. The cosine term in
the above expression is periodic in r
2
, and has the correct
form for a zone plate with a focal length of f = D / 2. After
some straightforward manipulation and using D / 4 as a typi-
cal value for the distance s between the mask and the image
plane, we can show that the interference pattern formed by
the two beams is invariant with respect to the wavelength
within the spectral region given by
Dl
l
0
!
4
Î
N
, s4d
where N is the maximum zone number of the daughter zone
plate. This shows the significant improvement in the band-
width of usable radiation, since without the achromatic ar-
rangement the allowed bandwidth is of the order of 1 / N.
Using similar arguments we can show that the depth of fo-
cus, where the image is formed, is given by
Dz !
l
c
NA
2
, s5d
where NA is the numerical aperture of the holographic set up
and l
c
=l
0
2
/Dl is the longitudinal coherence length of the
light.
Numerical simulations based on the method of stationary
phases
14
confirmed the formation of fringes with strong
modulation in the image plane with wideband illumination
(Fig. 2). When the illumination is perfectly monochromatic,
the fringes formed by the two interfering beams have good
visibility everywhere, whereas in the wideband case they re-
main visible only in a certain range around the image plane
as predicted by Eq. (5).
We confirmed the applicability of the proposed method
experimentally by making condenser lenses for phase-
contrast x-ray microscopy which requires large-diameter,
ring-shaped zone plates with high-resolution structures.
17
The holographic masks were written with EBL on thin
silicon-nitride membranes coated with a thin film of chro-
mium. The patterns, written in an electron-beam resist, were
later transferred into the underlying Cr and Si
3
N
4
layers with
reactive ion etching.
18
The inner and outer zone plates on the
mask had the smallest zone widths of about 120 nm and
focal lengths of 9.216 and 15.365 mm at 13.4-nm wave-
length, respectively. The annular ranges of these two zone
plates were chosen to create a daughter zone plate in the
annular range of 0.580– 0.690 mm.
The masks made with EBL were used in holographic
exposures at the x-ray interference lithography (XIL) beam-
line of the Swiss Light Source. The beamline, built as a
branch on a high-resolution spectroscopy beamline,
19
pro-
vides spatially filtered coherent illumination in the EUV re-
gion. By using either the diffracted or the reflected beam
from the beamline monochromator grating, it is possible to
obtain either a highly monochromatic or a wideband beam,
respectively. For the holographic exposures, the undulator
source was set to a central wavelength of 13.4 nm and a
spectral width of Dl/ l = 0.04. Test exposures confirmed the
large depth of focus of more than 100
m
m predicted by the
results of our analytical derivations and simulations. The
substrates and the pattern transfer scheme for the holographi-
cally exposed zone plates were the same as those used for the
EBL-made masks. Scanning electron microscopy (SEM) ex-
amination of the resulting lenses showed zones formed
within the designed annular region with the predicted zone
width of 60 nm, i.e., two times smaller than the EBL-written
structure width in the mask (Fig. 3).
The performance of the condenser lenses made with
EUV holography was measured at the same XIL beamline. A
pinhole was used to illuminate the FZP under test with co-
herent x rays. The intensity profile of the image formed by
the lens was measured with a knife edge scan, which showed
that this large lens of about 1.4-mm diam focused the light to
a 0.77-
m
m-diam spot as measured between the 20% – 80%
points of the scan (Fig. 4). We attribute the difference be-
tween the achieved spot size and the diffraction-limited size
FIG. 1. The principle of achromatic holography for making a FZP. A mask
containing two zone plates with focal lengths f
1
and f
2
is illuminated with
spatially coherent EUV light from the left-hand side. At the image plane
sz =sd the diverging and converging diffraction orders from the two zone
plates intersect at equal angles to form a zone plate pattern with half the
zone width of the parent zone plates. The inner and outer radii of the parent
zone plates can be chosen so that in a certain annular range at the image
plane, the undesired diffraction orders are absent. A schematic frontal view
of the mask is shown in the upper right-hand side.
FIG. 2. Intensity distribution calculated with the method of stationary
phases near the image plane for (a) monochromatic, and (b) wide spectrum
sDl/ l= 0.04d illumination. The fringes are part of the elliptical curves cor-
responding to the constant optical path difference surfaces between the two
sources located at the respective foci of the two parent zone plates. In this
calculation we assumed the duty cycles of the two parent zone plates, and
hence their diffraction efficiencies to be the same. The focal lengths and the
dimensions of the parent zone plates were the same as the ones used in the
experiment.
Appl. Phys. Lett., Vol. 85, No. 14, 4 October 2004 Solak, David, and Gobrecht 2701
of 0.20
m
m to the zone placement errors in the EBL-written
parent zone plates. In fact, we measured these errors to be
more than 300 nm (i.e., much larger than the zone width)
with a SEM equipped with an interferometer controlled
stage. The achieved performance is satisfactory for the func-
tion of the condenser lens, which is to illuminate samples
with a high numerical aperture beam rather than to produce a
spot size comparable to the outer zone width of the lens.
Maintaining the zone placement accuracy is much easier
with smaller optics (microzone plates) typically used in high-
resolution x-ray imaging.
9
This experiment confirms our the-
oretical predictions and demonstrates the practicality of the
approach with an available EUV source and beamline.
The scheme depicted in Fig. 1 can be used to make
ring-shaped FZP with an obstructed region in the center cov-
ering more than 50% of the radial range. The condenser lens
reported in this Letter required a large obstructed region
(84% of the lens radius), which is responsible for the reduc-
tion in the predicted resolution down to 0.2
m
m from a value
close to the outermost zone width of 60 nm. This impact on
resolution, which is much less severe for achievable, smaller
obstruction ratios, has to be taken into account in the design
and use of FZP made with this technique.
When used with state of the art EBL-made zone plates,
spatial-frequency multiplication should readily lead to
zone plates with 10-nm resolution.
3,9
The ultimate limit in
the holographic fabrication is equal to one-quarter of the
wavelength used, which corresponds to about 3.5 nm for a
13.4-nm wavelength. The use of laser holography for making
the parent zone plates can free the process from the artifacts
of EBL. The achromatic scheme makes it possible to utilize
the full bandwidth of the wideband source to perform the
exposures in practical times. As zone-plate-based x-ray mi-
croscopy matures into a commercialization phase, this
method offers a high throughput means for fabrication of the
necessary optics with exposures taking seconds, instead of
hours, required for EBL. Other x-ray optical elements de-
manding high spatial resolution, such as variable period
spectrometric gratings and linear zone plates, can be made
with the described achromatic EUV holography.
The authors thank J. F. van der Veen, L. Heyderman, and
B. Nöhammer for discussions. Part of this work was per-
formed at the Swiss Light Source, Paul Scherrer Institute,
Villigen, Switzerland.
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FIG. 3. SEM images of the holographically made FZP after the recorded
pattern was etched into the Cr film and the Si
3
N
4
support membrane. (a)
Low-resolution image showing Moiré fringes in the annular range where the
zone structures were formed. The Moiré fringes are formed between the
SEM scan lines and the circular zone structures. The schematic inset indi-
cates the area of the ring-shaped FZP where the SEM image was acquired.
(b) Higher-resolution image showing etched zones with about 66-nm zone
width. The image was taken approximately in the middle of the annular
range shown in (a).
FIG. 4. Theoretically calculated and measured knife edge scans across the
focused beam. A lithographically made open slit measuring 203 100
m
m
2
in
a thin, but opaque, membrane was used for this purpose. A photodiode
behind the slit was used to measure the transmitted light intensity. The
measured data was normalized but no background was removed. The calcu-
lated curve includes the broadening effect of the illuminating spectrum. For
this test the monochromator in the beamline was set to provide a spectral
bandwidth of Dl/ l=3310
−4
.
2702 Appl. Phys. Lett., Vol. 85, No. 14, 4 October 2004 Solak, David, and Gobrecht
