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Surface Plasmon Interference Nanolithography
Surface Plasmon Interference
Nanolithography
Zhao-Wei Liu, Qi-Huo Wei, and Xiang Zhang*
,
NSF Nanoscale Science and Engineering Center (NSEC), 5130 Etche</i>V<i>erry Hall,
Uni</i>V<i>ersity of California, Berkeley, California 94720-1740, and Applied
NanoBioscience Center, Arizona State Uni</i>V<i>ersity, Main Campus, P.O. Box 874004,
Tempe, Arizona 85287-4004
Received March 31, 2005; Revised Manuscript Received April 7, 2005
ABSTRACT
A new nanophotolithography technique based on the interference of surface plasmon waves is proposed and demonstrated by using computer
simulations. The wavelengths of the surface plasmon waves at metal and dielectric interfaces can reach the nanometer scale while their
frequencies remain in the optical range. As a result, the resolution of this surface plasmon interference nanolithography (SPIN) can go far
beyond the free-space diffraction limit of the light. Simulation results show that one-dimensional and two-dimensional periodical structures
of 40 100 nm features can be patterned using interfering surface plasmons launched by 1D gratings. Detailed characteristics of SPIN such
as field distribution and contrast are also investigated.
As the most widely used form of lithography for almost
all micromanufacturing purposes, photolithography was
limited by the physics of diffraction. To achieve nano-
meter feature sizes, either the working wavelength has to
be reduced,
1-3
or alternative techniques of pattern trans-
fer such as nanoimprinting lithography (NIL)
4,5
have to be
adopted. The main approach to reducing the working
wavelength is to directly use light sources of higher photon
energy such as extreme ultraviolet light (EUV) or soft
X-rays.
1-3,6-7
However, accompanying with this reduction
of the exposing wavelengths is the drastic increase of
complexity and cost for instrumentation and processing.
Another approach, called immersion photolithography,
1-3,8-9
interposes a liquid medium between the optics and the wafer
surface to replace the usual air gap. Even though the wave-
length of the light can be reduced by a factor equal to the
refractive index of the liquid, the resolution improvement is
limited owing to the relative low refractive index of the
available materials. It has also been shown that a solid-
immersion lens could be used for increasing the resolution
of photolithography.
10
A new scheme to achieve photolithographic nanopatterning
is proposed recently,
11-13
which is based on the unique
properties of surface plasmons (SP). The dispersion relation
for the surface plasmons at an interface between semi-infinite
metal and dielectric materials can be written as:
14
where k
sp
and k
0
are the wave vectors of the surface plasmons
and the light of the same frequency in a vacuum.
m
and
d
are the permittivities of the metal and dielectric materials,
respectively. Owing to the collective excitations of conduc-
tion electrons in metals such as Au, Ag, and Al,
m
for these
metals is strongly wavelength dependent and negative at
optical frequencies. The wave vector of surface plasmons
can thus become significantly larger than that of the free
space light at the same frequency when the real part of
m
approaches -
d
. The frequency at which Re(
m
) ) -
d
is
called the resonant surface plasmon frequency sp
. At
frequencies close to sp
, surface plasmons possess an optical
frequency, but a down to X-ray wavelength. As a result,
utilizing surface plasmon waves for lithography may dra-
matically increase the pattern resolution.
Lately it was demonstrated that the use of surface plasmons
in the optical near field of a metallic mask can produce fine
patterns with a subwavelength resolution.
12,15,16
Especially,
using a silver grating mask with 300 nm periodicity,
lithography with 100 nm pitch has been demonstrated by
using the interference of surface plasmon waves within the
grating area.
15
In this paper, we numerically demonstrate surface plasmon
interference nanolithography (SPIN). In contrast to previous
work,
12-13,15-16
multiple one-dimensional gratings are used
to convert free-space light into surface plasmon waves, and
* Corresponding author, E-mail: xiang@berkeley.edu University of California, Berkeley. Arizona State University.
k
sp
) k
0
m d
m
+
d
(1)
NANO
LETTERS
2005
Vol. 5, No. 5
957-961
10.1021/nl0506094 CCC: $30.25
© 2005 American Chemical Society
Published on Web 04/21/2005 those waves propagating outside the grating area form an
interference pattern when they encounter each other. By using
a different number of gratings or surface plasmon waves,
various interference patterns such as periodic lines and two-
dimensional dot arrays can be obtained. The numerical results
show that the resolution can go far beyond the free-space
diffraction limit by tuning the excitation light frequency close
to the resonant surface plasmon frequency. This SPIN
technique promises various practical fabrication applications
since it only requires UV photoresists.
Numerical simulations were performed using the com-
mercial software package CST Microwave Studio (MWS).
With the aim of validating the simulation method and
reviewing quantitatively some fundamental properties of
surface plasmon waves, which are important to SPIN, we
first studied a simple situation where only a one-dimensional
grating is used.
The simulated structure consists of a transparent glass as
the mask substrate, an aluminum mask, and a semi-infinite
photoresist (PR) layer (Figure 1a). The thickness of the Al
mask is assumed to be 100 nm, which is sufficiently thick
to block the direct transmitted light, ensuring that all fields
at the Al/PR interfaces outside the gratings originate from
surface plasmon waves and that the Al film can be treated
as semi-infinite. Ag is another good material candidate for
SPIN mask considering its plasmon frequency sp
is also
located at UV range (Au mask is not appropriate for
lithography purposes because its sp
locates at visible range).
Al is chosen as an example here because of its relatively
long SP propagation length at UV excitation. A one-
dimensional grating with periodicity
is used so that the
momentum difference between the incident light and the
surface plasmons can be compensated.
The refractive indices used for the glass and the PR (from
AZ Electronic Materials data sheets for AZ5200-E) are 1.52
and 1.7, respectively. The permittivity of the Al mask is
described by the Drude model,
Al
(
) ) -
p2
/[
( -
iV
c
)], where the high-frequency bulk permittivity ) 1,
the bulk plasmon frequency p
) 2.4 × 10
16
rad/s, and the
electron collision frequency V
c
) 1.1 × 10
15
rad/s, are
obtained by fitting the model to the experimental data taken
from the literature.
17
The incident light, polarized along the
x direction or perpendicular to the grating, is normal to the
substrate. Based on the conservation of momentum, surface
plasmon waves with a wave vector k
sp
) 2/ can be
resonantly excited.
The electrical field magnitudes at the Al/PR interface at
different distances from the grating edges are shown in Figure
1b as functions of the excitation frequencies. For a grating
with the period
) 205 nm, clear resonant peaks can be
seen around the frequency 8.22
× 10
14
Hz, or a vacuum
excitation wavelength at 365 nm (Figure 1b,c). From the local
field distribution at the frequency 8.22
× 10
14
Hz, surface
plasmon waves can be observed propagating and decaying
in magnitudes with the distance away from the grating edge
(Figure 1d).
Key physical parameters obtained from this simulation
agree well with analytical predictions. (1) For a grating with
period
) 205 nm, theoretical calculations based on eq 1
yield a resonant excitation wavelength at
) 377 nm, which
agrees with the simulation result within 3%. This slight
deviation in the resonant wavelength is ascribed to the coarse
meshing size in the simulation. (2) The propagation length
along the surface, which dictates the maximum interference
area with sufficient contrasts, is obtained by exponential
fitting to the electrical field curve versus the distance from
the grating (Figure 2a). The simulation results yield about
1.8
µm propagation length for both E
x
and E
z
, which agrees
with the theoretical prediction 1/
{
Im
}
(k
sp
)
1.74 µm. (3)
The decay length of SP waves in the z direction, on the other
hand, determines the exposure depth in the photoresist. The
simulation data (Figure 2b) yield approximately 84 nm for
both E
x
and E
z
, while the theoretical estimation 1/
|k
z
| )
/2
| ( Al
+
PR
)/(
PR
2
)
| is about 82.3 nm. (4) The ratio E
z
/
Figure 1.
(a) Schematic configuration of the simulated structure
which is composed of a transparent glass substrate, a 100 nm thick
aluminum mask, and a semi-infinite photoresist. The grating
periodicity
is 205 nm and the grating slit d is 60 nm. The
amplitudes of electric field components (b) E
x
and (c) E
z
versus
the excitation frequency at 20 nm