Analysis of a scheme for de-magnified Talbot lithographyL. Urbanski, M. C. Marconi, A. Isoyan, A. Stein, C. S. Menoni et al. Citation: J. Vac. Sci. Technol. B 29, 06F504 (2011); doi: 10.1116/1.3653507 View online: http://dx.doi.org/10.1116/1.3653507 View Table of Contents: http://avspublications.org/resource/1/JVTBD9/v29/i6 Published by the AVS: Science & Technology of Materials, Interfaces, and Processing Related ArticlesThermally reflowed ZEP 520A for gate length reduction and profile rounding in T-gate fabrication J. Vac. Sci. Technol. B 30, 051603 (2012) Formation of large-area GaN nanostructures with controlled geometry and morphology using top-downfabrication scheme J. Vac. Sci. Technol. B 30, 052202 (2012) Resist–substrate interface tailoring for generating high-density arrays of Ge and Bi2Se3 nanowires by electronbeam lithography J. Vac. Sci. Technol. B 30, 041602 (2012) Real-time measurements of plasma photoresist modifications: The role of plasma vacuum ultraviolet radiationand ions J. Vac. Sci. Technol. B 30, 031807 (2012) Electron beam lithography on vertical side faces of micrometer-order Si block J. Vac. Sci. Technol. B 30, 041601 (2012) Additional information on J. Vac. Sci. Technol. BJournal Homepage: http://avspublications.org/jvstb Journal Information: http://avspublications.org/jvstb/about/about_the_journal Top downloads: http://avspublications.org/jvstb/top_20_most_downloaded Information for Authors: http://avspublications.org/jvstb/authors/information_for_contributors

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Analysis of a scheme for de-magnified Talbot lithography

L. Urbanski and M. C. MarconiNSF ERC for Extreme Ultraviolet Science & Technology and Electrical and Computer Engineering,Colorado State University Fort Collins, Colorado 80523

A. IsoyanSynopsys, Inc., Hillsboro, Oregon 97124

A. SteinCenter for Functional Nanomaterials, Brookhaven National Laboratory, New York 11973

C. S. Menoni and J. J. RoccaNSF ERC for Extreme Ultraviolet Science & Technology and Electrical and Computer Engineering,Colorado State University Fort Collins, Colorado 80523

(Received 22 June 2011; accepted 23 September 2011; published 10 November 2011)

The authors describe a photolithographic scheme based on the replication of a periodic transparent

mask in a photoresist utilizing the coherent self-imaging Talbot effect. A periodic two-dimensional

diffractive structure (or Talbot mask) composed of unit tiles distributed in a square matrix was

illuminated by a coherent extreme ultraviolet (EUV) beam from a table top EUV laser. The

illumination beam was reflected in a spherical mirror and the Talbot mask was placed in the path

of the convergent beam. At designed locations determined by the Talbot distance, reduced replicas

of the mask were obtained and used to print the slightly de-magnified copies of the mask on the

surface of a photoresist. Experimental results showing the de-magnification effect are in good

agreement with the diffraction theory. The limits of the technique are discussed. VC 2011 AmericanVacuum Society. [DOI: 10.1116/1.3653507]

I. INTRODUCTION

In recent years, novel applications of nano-structures that

are now impacting many fields have been demonstrated. Of

particular interest are the periodic structures with nanometer

dimensions replicated over large areas, that allowed the

implementation of unique devices such as stimulated surface

Raman scattering detectors, plasmonic structures capable to

focus light beyond the diffraction limit or “superlenses,”

novel approaches to nano-lithography based on plasmon in-

terference, etc.1–4 The rapid advancement of nano-

technology that has allowed the practical demonstration of

these new devices and techniques, along with the develop-

ment of new applications made possible by nanostructures

will be favored by easy access to a versatile method used to

produce such nano-structures in a cost effective manner.

We have previously reported the feasibility of generating

periodic nano-structures of arbitrary design arranged in a

two-dimensional structure on the surface of a photoresist by

a photolithographic method based on self-imaging using a

table top EUV laser.5 A similar approach was recently used

by Zanke et al. to print large areas of periodic circular holes

in a hexagonal lattice in what was reported as coherent dif-

fraction lithography.6 The approach allows the fabrication

of periodic nanostructures patterned in the photoresist by

the exact replication of a diffractive transparent mask pro-

duced by the coherent self-imaging effect also known as

the Talbot effect.7 In our former experiment we extended

the original concept of the Talbot effect to arbitrary diffrac-

tive units (or tiles) that we referred to as generalized Talbot

imaging.5

In this work we demonstrate that it is possible to replicate

and simultaneously scale the size of the printed nanostructure

by adequately illuminating the diffractive mask with a conver-

gent coherent beam. The de-magnification is a consequence

of the extra phase introduced in the illuminating beam by the

reflection on a spherical mirror. It depends on the optics used

and the geometry of the setup. A theoretical description of the

self-imaging effect and the de-magnification factor is pro-

vided based on the Kirchhoff–Fresnel formalism. The limita-

tions for this method are further discussed.

The experimental setup is schematically shown in Fig. 1. It

is composed of a concave multilayered mirror with the peak

reflectivity centered at 46.9 nm, for an incidence angle of 18�

and a focal length of f¼ 25 cm. The Talbot mask is placed at a

distance, s, from the mirror in the path of the converging beam.

The distance between the focal plane, F, and the Talbot planes

where the samples to be printed are placed is denoted as z.The Talbot effect that produces the self-imaging of periodic

structures can be explained using the Kirchhoff–Fresnel diffrac-

tion theory. To simplify the formalism, let us consider the sim-

ple case of a one-dimensional structure. Let T(x) be the one-

dimensional transmission function of a periodic object with a

period, p, such that T(x)¼T(xþ p). The transmission function

can be expressed in terms of its Fourier series as

TðxÞ ¼X

m

Cm exp i2pmx

p

� �; (1)

where Cm is the amplitude of the mth Fourier component.

After the reflection in the spherical mirror, the wave-front

acquires an extra phase given by

06F504-1 J. Vac. Sci. Technol. B 29(6), Nov/Dec 2011 1071-1023/2011/29(6)/06F504/4/$30.00 VC 2011 American Vacuum Society 06F504-1

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M �exp ik

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðx� x0Þ2 þ f 2

q� �� �

f; (2)

where x and x0 are the coordinates in the mirror’s plane and

in the mask’s plane, respectively, and f is the mirror’s focal

distance.

Assuming a plane wave illumination with unitary

amplitude, the transmitted optical field, UT, after the mask

will be,

UT ¼ �1

ik

ðþ1�1

TðxÞM exp �ikRf gR

dx; (3)

where R ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðx� x0Þ2 þ z2

q:

The transmitted optical field can be calculated by solving

Eq. (3). Replacing the expressions from Eqs. (1) and (2), the

transmitted field will be proportional to,

UT /X

m

Cm exp i2pðf � sÞ

pzðx� x0Þ

� �

exp i2pðf � sÞkðf � s� zÞ

2p2z

� �: (4)

The original transmission function, T(x), is reproduced when

the last term in (4) is equal to 1, with a scale factor given by

d¼ z/(f – s). The locations of the Talbot planes will be given

by the condition,

ðf � sÞðf � s� zÞz

¼ 2mp2

k; (5)

where m is an integer number. A Talbot image with a de-

magnification, d, will be obtained at distances, d, given by

d ¼ f � s� z ¼ 2mp2ðf � sÞ2mp2 þ kðf � sÞ : (6)

At these distances, the Talbot image will have a period

p0given by

d ¼ p0

p¼ zj j

f � s: (7)

For this experiment we used the Talbot mask which was

described in more detail in Ref. 5. The Talbot mask was

written by e-beam lithography on an �60 nm thick layer of

hydrogen silsesquioxane (HSQ) resist deposited on an ultra-

thin (30 nm) SiN membrane. The thin membrane allowed for

�13.5% transmission at 46.9 nm, the wavelength of the table

top EUV laser used in this test, while the 60 nm thick layer

of HSQ was sufficiently opaque to provide a good contrast

for the diffractive mask. The units of the mask were standard

test patterns with a period of 4.845 lm. An electron micro-

scope micrograph of the mask is shown in Fig. 2.

The illumination source was a highly coherent EUV table

top laser developed at Colorado State University. The energy

per pulse provided by the laser was approximately 0.1 mJ

and 1.2 ns full width at half maximum (FWHM) duration. It

was operated at the repetition rate of 1 Hz. The laser wave-

length, k¼ 46.9 nm, corresponds to the 3s1P1-3p1S0 transi-

tion in Arþ8. The laser emission is produced by exciting Ar

with a fast discharge through a ceramic capillary. The cur-

rent pulse was approximately 21 kA, a 10–90% rise time of

approximately 55 ns, and a first half-cycle duration of

approximately 135 ns.8,9 The relative band width of the

EUV laser is approximately Dk/k¼ 3.5� 10�5, yielding a

coherence length of approximately 840 lm. The spatial co-

herence length of the beam improves with longer capillaries

reaching a fully spatially coherent illumination for the 36 cm

capillary. In this experiment it was calculated to be 740 lm

at the distance where the exposure took place.

The EUV laser impinges a spherical multilayer mirror

that focuses the beam and simultaneously spectrally filters

the EUV plasma background. The mirror has a reflectivity of

approximately 40%, optimized at an incidence angle of 18�.After the mirror, the Talbot mask and the sample coated

with photoresist were placed in a translation stage which

allows for moving the set mask-sample along the path of the

converging beam. The distance between the Talbot mask

and the sample was adjusted for the first Talbot plane, in this

case 960 lm. The sample was a 0.5 mm thick silicon wafer

covered with a 100 nm thick layer of poly-methyl-methacry-

late photoresist deposited by spin coating. The recording of

the photoresist required an exposure of approximately 300

shots. The laser was set to operate at 1 Hz, yielding an

FIG. 1. (Color online) Scheme of the experimental set up. The set mask-

sample is placed at different distances, s, from the focusing mirror. Solidly

moving these two elements along the direction of the convergent beam

(positions 1 and 2 in the figure) allows for different de-magnification

factors.

FIG. 2. Scanning electron micrograph of the Talbot mask. The mask was

defined in 50 nm thick HSQ deposited on a 30 nm thick SiN membrane.

06F504-2 Urbanski et al.: Analysis of a scheme for de-magnified Talbot lithography 06F504-2

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exposure time of 5 min in order to record one image. This

time can be reduced if the laser is operated at a higher repeti-

tion rate, at a maximum of 4 Hz. After exposure, the samples

were developed in a mixture of methyl-isobuthyl-ketone and

isopropanol for 1 min. Subsequently, they were rinsed with

pure isopropanol and dried using ultra high purity nitrogen.

The developed samples were scanned using an atomic

force microscope. Figure 3 shows the images of the prints

obtained at different positions along the converging beam.

The set mask-sample was solidly moved along the path of

the converging beam to distances of d1¼ 22 cm, d2¼ 24.4

cm, and d3¼ 24.5 cm from the mirror. These distances yield

calculated de-magnification factors of d1¼ 0.96, d2¼ 0.85,

and d3¼ 0.82, respectively.

The scan size of all images is 20� 20 lm2. From the

images, the period of the structures was measured to be

p1¼ 4.69 lm, p2¼ 4.35 lm, and p3¼ 4.24 lm, yielding to

measured de-magnification factors, dM1¼ 0.97, dM2¼ 0.89,

and dM3¼ 0.87, respectively.

The discrepancy between the measured and calculated

de-magnification values may stem from two facts. One of

them being the measurement error of the s distance, that in

our set up was estimated to be (1 mm), while the other is due

to the variation in the effective focal length of the mirror due

to the natural divergence of the illumination beam (�5

mrad). Considering these two factors, the calculated and

measured values are within the experimental errors.

The dependence of the de-magnification with the distance

from the mirror is governed by expression (7) and changes

very rapidly when approaching the focal plane. This depend-

ence is shown in Fig. 4, where the de-magnification factor

p0/p is plotted as a function of the normalized distance from

the mirror, s/f. The solid curve is the analytical expression of

the de-magnification as a function of the mirror–mask dis-

tance, s, normalized to the focal distance, f. The circles are

the actual data points. The graph shows that the de-

magnification changes very little throughout almost all of

the range, s, and only close to the focus (s/f¼ 1), does the de-

pendence becomes more pronounced.

One limiting factor for this method is the spherical aber-

ration introduced by the mirror that produces slightly differ-

ent focal distance values for the tangential and sagittal

directions. This is clear in the prints obtained, which showed

a slightly different period in the two directions indicating an

astigmatic image. This problem can be solved by replacing

the spherical mirror by an off-axis parabolic mirror or, alter-

natively, designing the Talbot mask with the appropriate cor-

rection for the spherical aberration.

The main limitation on setting a large value of the demag-

nification factor arises from its strong dependence with the

distance when the Talbot plane is located close to the focal

plane. We may assume that to have a clear print the mask

should be positioned within the depth of focus (DOF) which

is typically a few microns. Even for this small distance, close

to the focal plane the de-magnification factor variation is so

strong that the print is degraded. We can see this effect if we

consider that the error in determining the demagnification

factor is given by

Dd ¼ zT

Z2ðDOFÞ;

where the depth of focus is DOF ¼ k½ð1þ 2p2=kWÞ2�, W is

the size of the mask, and Z is the distance from the mask to

FIG. 3. (Color online) Atomic force micrographs of the prints obtained at

different distances from the focusing mirror. The period decreases when the

set mask-sample moves towards the focus. The de-magnification factors and

distances measured from the focusing mirror are: (a) dM1¼ 0.97, d1¼ 22

cm, (b) d M2¼ 0.89, d2¼ 24.4 cm, and (c) d M3¼ 0.87, d3¼ 24.5 cm.

06F504-3 Urbanski et al.: Analysis of a scheme for de-magnified Talbot lithography 06F504-3

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the focal plane. The error in positioning the mask diverges

when reaching the focal plane. It is thus not possible to set

large demagnification factors and this method is only re-

stricted to modest de-magnification values.

II. SUMMARY

In summary, we have analyzed the effect that a conver-

gent beam illumination has on the size of the printed fea-

tures utilizing Talbot lithography. The de-magnification

effect becomes apparent when the sample is located close

to the focal plane of the focusing mirror. In the vicinity of

the focal plane the de-magnification factor changes very

fast with the distance, and the error in determining its value

with respect to the distance from the mask to the focal

plane diverges, limiting the range that can practically be

achieved. This method utilizes a periodic mask and focus-

ing optics, which makes the setup relatively simple to

implement at EUV wavelengths. It is noncontact, high fi-

delity, and capable of printing over relatively large areas

with high resolution.

ACKNOWLEDGMENTS

The authors are indebted to the early contributions of F.

Cerrina to this project. This work was supported by the

National Science Foundation (Award No. ECCS 0901806),

the NSF ERC for Extreme Ultraviolet Science and Technol-

ogy (Award No. EEC 0310717). This research was carried

out in part at the Center for Functional Nanomaterials, Broo-

khaven National Laboratory, which is supported by the U.S.

Department of Energy, Office of Basic Energy Sciences,

under Contract No. DE-AC02-98CH10886.

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FIG. 4. De-magnification factor, d, as a function of the normalized distance,

s/f. The solid curve corresponds to the predicted values according to the

Kirchhoff–Fresnel theory and the red circles correspond to the measured

values.

06F504-4 Urbanski et al.: Analysis of a scheme for de-magnified Talbot lithography 06F504-4

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