Wavelength tunable diffractive transmission lens for hard x rays
C. David
a)
and B. No
¨
hammer
Laboratory for Micro- and Nanotechnology, Paul Scherrer Institut, CH-5232 Villigen-PSI, Switzerland
E. Ziegler
European Synchrotron Radiation Facility, B. P. 220, F-38043 Grenoble Cedex, France
共Received 1 February 2001; accepted for publication 24 April 2001兲
We report on the fabrication and testing of linear transmission Fresnel zone plates for hard x rays.
The diffractive elements are generated by electron beam lithography and chemical wet etching of
具110典 oriented silicon substrates. By tilting the cylindrical lenses with respect to the x-ray beam, the
effective path through the phase shifting zones can be varied. This makes it possible to optimize the
diffraction efficiency over a wide range of photon energies, and to obtain effective aspect ratios not
accessible with untilted optics. The diffraction efficiency of such a lens was measured as a function
of the tilt angles for various energies between 8 and 29 keV. Values close to the theoretical limit
were obtained for all energies. Because of the coherence preserving properties of diffractive optics,
the method opens up opportunities for experiments using coherent hard x rays. © 2001 American
Institute of Physics. 关DOI: 10.1063/1.1379364兴
The focusing of hard x rays (h
⬎ 8 keV) to submi-
crometer dimensions is an important prerequisite for many of
techniques such as microanalysis, microimaging, microspec-
troscopy, and microdiffraction. Reflective, grazing incidence
optics are most commonly used for this purpose, but submi-
cron spot sizes can only be obtained currently with great
difficulty due to aberrations stemming from imperfections of
the mirror surfaces.
1
Furthermore, high quality ellipsoidal
focusing mirror systems are difficult to align and expensive.
Due to their complexity, they are usually an integral compo-
nent of a synchrotron beamline, which limits their flexibility.
The first devices to achieve submicron hard x-ray focus-
ing in a routine fashion were Bragg–Fresnel lenses 共BFLs兲.
2
These devices usually consist of a Bragg crystal patterned
with a diffractive Fresnel lens. Although BFLs with zone
widths down to 100 nm and good diffraction efficiency have
been made,
3
there are some severe difficulties related with
their practical application. First, the optical axis of the setup
has to make a large additional angle, which—in contrast to
mirror optics—changes with the photon energy. Moreover,
the lense’s Bragg condition makes it only suitable for a nar-
row bandwidth and difficult to align when used in combina-
tion with a crystal monochromator. Therefore, BFLs are only
used in very few experimental setups. Focusing transmission
lenses avoiding these difficulties would be most useful in a
wide range of applications.
Some years ago it was recognized that compound refrac-
tive lenses 共CRLs兲 might provide an alternative way to focus
hard x rays without an additional angle in the optical axis.
CRLs were first proposed and patented by Tomie
4
and
shortly later experimentally verified by Snigirev et al.
5
Two
alternative arrangements are presently in use. The first type
consists of a linear array of holes along the optical axis
drilled into a block of low absorbing material, preferentially
Be. The cylindrical shape of the refracting surfaces leads to
inevitable spherical aberrations, which limit the obtainable
spot size to some microns. The second consists of low ab-
sorbing disks stacked along the optical axis with the refrac-
tive shape embossed into the surfaces of each disk. This
method gives the opportunity to avoid spherical aberrations
by using parabolic surfaces, and submicron focusing has
been demonstrated using Al as lens material. However, for
acceptable focal lengths the high absorption of Al limits the
transmission of these devices to about one percent.
6
The fab-
rication of aspherical refractive lenses from Be with adequate
quality has not been possible up to now due to its hardness
and brittleness.
Diffractive transmission lenses 共Fresnel zone plates兲
have been used successfully for x-ray focusing and imaging.
Spot sizes in the range of tens of nanometers for soft x
rays
7–11
and of about 100 nm for the multikilo-electron-volt
region
12
and for hard x rays
13
have been achieved. The dif-
fractive patterns are mostly generated by electron beam li-
thography. State-of-the-art lithography tools are capable of
positioning the zone structures with accuracies in the order
of nanometers. As the required accuracy to avoid aberrations
is in the order of one outermost zone width, the resolving
power of a zone plate is diffraction limited. Thus, the obtain-
able spot size is approximately equal to the width of the
outermost zones when the lens is irradiated with spatially
coherent light. This means, that in contrast to refractive or
reflective hard x-ray optics, the coherence of the incoming
light is preserved. This feature becomes increasingly impor-
tant in experiments taking advantage of the high coherence
provided by modern synchrotron sources.
14
The efficiency of a zone plate, i.e., the fraction of the
incoming radiation diffracted into the focal spot, depends on
the phase shift and attenuation caused by the diffractive
structures. For a given photon energy and zone plate mate-
rial, the maximum obtainable efficiency and the necessary
zone height to obtain this value can be calculated using the
scalar diffraction theory developed by Kirz
15
and the com-
plex refractive index n⫽ 1⫺
␦
⫺ i

tabulated for most ele-
ments by Henke et al.
16
For diffractive structures with a
a兲
Electronic mail: christian.david@psi.ch
APPLIED PHYSICS LETTERS VOLUME 79, NUMBER 8 20 AUGUST 2001
10880003-6951/2001/79(8)/1088/3/$18.00 © 2001 American Institute of Physics
square wave profile, the first order diffraction efficiency E
1
at a given x-ray wavelength is given by
E
1
⫽
1
2
共
1⫹ e
⫺ 2k
⫺ 2e
⫺ k
cos
兲
, 共1兲
where k⫽

/
␦
, and
⫽ 2
␦
t/ denotes the phase shift
caused by the diffracting structures. The maximum diffrac-
tion efficiency is high for a favorable ratio of absorption to
phase shift, i.e., for small values of k. In the case of the ideal
phase zone plate (k⫽ 0), a maximum first order diffraction
efficiency of 4/
2
⫽ 40.5% can be obtained for
⫽
.
Especially for energies just above the K edges of me-
dium weight elements like Ni or Ge and the L edges of heavy
materials like Ta, or Au, a significant fraction of radiation is
lost by absorption as can be seen from Table I. The obtain-
able efficiency of light elements like C or Si in this energy
range is close to the theoretical limit of an ideal phase zone
plate due to the absence of absorption edges. Unfortunately,
the required zone plate thickness to obtain a phase shift of
is more than 10
m, which results in enormous aspect ratios
for submicron structure widths. The fabrication of nanostruc-
tures using standard technologies like reactive ion etching is
limited to aspect ratios in the order of 10 due to a limited
control of the sidewall angles.
We used a simple technique to fabricate diffractive
lenses with significantly higher aspect ratios. The lenses
were made from 具110典 oriented Si substrates. First, mem-
branes of 15–20
m thickness were formed by photolithog-
raphy and reactive ion etching from the backside of the sub-
strate. The linear zone plate patterns were then defined by
electron beam lithography and transferred into 30-nm-thick
chromium structures by a lift-off process. On such substrates,
lines oriented in the 具112典 direction have sidewalls with 具111典
orientation. Using an ethylendiamine pyrocathecol solution
as orientation-selective wet etch resulted in structures with
vertical sidewalls.
17
Figure 1 shows a linear zone plate with
324 nm outermost zone width 共half-pitch兲 and 13
m struc-
ture height. A more detailed description of the lens fabrica-
tion process is given elsewhere.
18
This method is obviously limited to producing linear dif-
fractive structures and thus to one-dimensional focusing 关see
Fig. 2共a兲兴. To achieve two-dimensional focusing, we suggest
aligning two linear lenses with different focal lengths and
orthogonal orientation along the optical axis as indicated in
Fig. 2共b兲. In addition, diffractive optical elements with linear
structures leave an additional degree of freedom. By a tilt of
around an axis perpendicular to the diffractive structures
and the optical axis, the effective path through the structures
can be increased by a factor of 1/cos
关Figs. 2共c兲–2共d兲兴.
The diffraction efficiency of a wet etched Fresnel zone
plate fabricated by this technique with 5.5
m high Si struc-
FIG. 1. Scanning electron microscopy images of linear Fresnel zone plates
fabricated by electron beam lithography and wet chemical etching of 具110典
oriented silicon substrates. The outermost zone width is 324 nm, the zone
height is 13
m, corresponding to an aspect ratio of 40.
FIG. 2. A linear zone plate can be used to produce a line focus 共a兲, while a
combination of two such devices will result in two-dimensional focusing
共b兲. By tilting of the lenses, the effective path through the phase shifting
structures can be varied 共c, d兲 in order to match the phase shift over a wide
energy range and to increase the obtainable aspect ratio.
TABLE I. Maximum first order efficiencies E
max
and optimum structures
heights t
opt
of a binary diffractive optical element for a selection of elements
commonly used in zone plate fabrication at different photon energies.
Element
10 keV 15 keV 20 keV
E
max
共%兲 t
opt
共
m兲 E
max
共%兲 t
opt
共
m兲 E
max
共%兲 t
opt
共
m兲
C 40.4 13.6 40.5 27.6 40.5 34.0
Si 38.7 12.6 39.7 19.3 40.1 26.0
Ni 30.1 3.4 34.9 5.1 37.0 6.9
Ge 38.0 6.8 32.7 9.3 35.5 12.5
Ta 26.4 2.4 29.5 3.2 33.0 4.3
Au 32.7 2.0 27.3 2.9 31.4 3.7
1089Appl. Phys. Lett., Vol. 79, No. 8, 20 August 2001 David, No
¨
hammer, and Ziegler
tures, an aperture of 200
m, a length of 2.5 mm, an outer-
most zone width of 350 nm, and 5
m support membrane
thickness was measured at the BM5 bending magnet beam-
line of the European Synchrotron Radiation Facility 共ESRF兲.
The diffraction efficiency for the untilted lens is expected to
be optimum at 4.9 keV photon energy. Due to air absorption,
we were not able to measure the diffraction efficiency for
energies below 8 keV. In addition we were restricted by the
geometry of the Si具111典 double crystal monochromator to
values below 29 keV. The lens was mounted with the dif-
fracting structures oriented horizontally, thus, focusing in the
vertical direction. A slit with an opening of approximately 20
m height and 200
m width was scanned through the focal
plane of the lens while recording the transmitted signal using
a photodiode. The first order diffraction efficiency can be
obtained by evaluating the integral over the focal peak. This
method was previously developed to characterize Bragg–
Fresnel lenses.
3
It has proven to be very accurate, as it does
not require exact knowledge of the slit dimensions.
The calculated efficiency data and the measured values
for 8, 10, 13.3, 20, and 29 keV photon energy are plotted in
Fig. 3. The curves reach their maxima at 55.8°, 63.6°, 70.9°,
77.5°, and 81.5° tilt angle, respectively, which corresponds to
a phase shift of
. Oscillations at higher tilt angles with
minima for values equivalent to even integers and maxima
for odd integers of
phase shift can be observed. We were
able to measure the diffraction efficiencies up to tilt angles of
85°, corresponding to an aspect ratio of 150. The measured
data for 10 and 29 keV photon energy very closely follow the
theoretical curves, whereas for the other energies, the mea-
sured data are somewhat lower than expected. This is prob-
ably due to a slight angular misalignment around the axis
perpendicular to the optical axis and the tilt axis, which
would lead to a tilt of the structures sidewalls with respect to
the beam.
The wet etched Si lens used in a tilted arrangement can
thus be used over a wide energy range without any compli-
cated realignment. Although the aspect ratio of the untilted
device is already fairly high 共15.7兲, the wet etching technique
is capable of exceeding this value at least by a factor of 2 as
shown in Fig. 1. It is, therefore, possible to fabricate lenses
with higher structures for even harder photon energies or to
reduce the outermost zone width and, thus, the achievable
spot size down to the 100 nm range. The technique to in-
crease the aspect ratio by tilting could also be applied to zone
plates with blazed zone profiles.
19,20
This would be of special
interest for two-dimensional focusing using two linear
lenses. A combination of two binary lenses limits the total
efficiency to a maximum value of (40.5%)
2
⫽ 16.4%, while
a combination of ideal blazed zone plates could give up to
100% efficiency. Furthermore, it should be noted, that the
described techniques are also suited to produce other diffrac-
tive optical elements than merely lenses. Such devices could
include wavefront-shaping elements or linear gratings to be
used as beam splitters for interferometric
21,22
or holographic
applications.
The authors wish to thank Bianca Haas for her support in
fabricating the Si具110典 membranes. The technical staff of the
Laboratory for Micro- and Nanotechnology is acknowledged
for the excellent working conditions in the Nanofab facility.
Many thanks are also due to Joanna Hoszowska of ESRF for
her help during the efficiency measurements at BM5.
1
E. Ziegler, O. Hignette, Ch. Morawe, and R. Tucoulou, Nucl. Instrum.
Methods Phys. Res. A 共in press兲.
2
S. M. Kuznetsov, I. Snigireva, A. Snigirev, P. Engstrom, and C. Riekel,
Appl. Phys. Lett. 65,827共1994兲.
3
C. David and A. Souvorov, Rev. Sci. Instrum. 70,4168共1999兲.
4
T. Tomie, Japanese Patent No. 06045288 共1994兲, US Patent No. 5,594,773
共1997兲, German Patent No. DE1995019505433 共1998兲.
5
A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 共London兲 384,
49 共1996兲.
6
B. Lengeler, C. Schroer, J. Tu
¨
mmler, B. Benner, M. Richwin, A. Snigirev,
I. Snigireva, and M. Drakopoulos, J. Synchrotron Radiat. 6,1153共1999兲.
7
E. Anderson and D. Kern, in X-Ray Microscopy III, edited by A. G.
Michette, G. R. Morrison, and C. J. Buckley 共Springer, Berlin, 1990兲,
p. 75.
8
D. Weiss, M. Peuker, and G. Schneider, Appl. Phys. Lett. 72, 1805 共1998兲.
9
G. Schneider, T. Schliebe, and H. Aschoff, J. Vac. Sci. Technol. B 13,
2809 共1995兲.
10
S. J. Spector, C. J. Jacobsen, and D. M. Tennant, J. Vac. Sci. Technol. B
15, 2872 共1997兲.
11
C. David, B. Kaulich, R. Medenwaldt, M. Hettwer, N. Fay, M. Diehl, J.
Thieme, and G. Schmahl, J. Vac. Sci. Technol. B 13, 2762 共1995兲.
12
M. Panitz, G. Schneider, M. Peuker, D. Hambach, B. Kaulich, S. Oester-
reich, J. Susini, and G. Schmahl, in X-Ray Microscopy: Proceedings of the
Sixth International Conference, edited by W. Meyer-Ilse, T. Warwick, and
D. Atwood 共American Institute of Physics, Melville, NY, 2000兲,p.676.
13
W. Yun, B. Lai, Z. Cai, J. Maser, D. Legnini, E. Gluskin, Z. Chen, A. A.
Krasnoperova, Y. Vladimirsky, F. Cerrina, E. Di Fabrizio, and M. Gentili,
Rev. Sci. Instrum. 70, 2238 共1999兲.
14
J. Baruchel, P. Cloetens, J. Ha
¨
rtwig, W. Ludwig, L. Mancini, P. Pernot,
and M. Schlenker, J. Synchrotron Radiat. 7, 196 共2000兲.
15
J. Kirz, J. Opt. Soc. Am. 1,301共1974兲.
16
B. L. Henke, E. M. Gullikson, and J. C. Davis, At. Data Nucl. Data Tables
54,181共1993兲.
17
For a review of vertical silicon wet etching see for example: D. L. Ken-
dall, J. Vac. Sci. Technol. A 8,3598共1990兲.
18
C. David, E. Ziegler, and B. No
¨
hammer, J. Synchrotron Radiat. 8, 1054
共2001兲.
19
E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini,
and R. Barrett, Nature 共London兲 401, 895 共1999兲.
20
C. David, Microelectron. Eng. 53, 677 共2000兲.
21
P. P. Naulleau, C. H. Cho, E. M. Gullikson, and J. Bokor, J. Synchrotron
Radiat. 7, 405 共2000兲.
22
U. Bonse and M. Hart, Appl. Phys. Lett. 6, 155 共1965兲.
FIG. 3. First order efficiency of a linear Fresnel zone plate with 5.5
m high
Si structures for photon energies between 8 and 29 keV as a function of the
zone plate tilt angle. The lens aperture was 200
m. The upper horizontal
axis indicates the effective aspect ratio of the 350 nm wide outermost zones.
1090 Appl. Phys. Lett., Vol. 79, No. 8, 20 August 2001 David, No
¨
hammer, and Ziegler
