The use of surface-plasmon polariton (SPP) resonance in the optical near field of a metallic mask to produce fine patterns with a resolution of subwavelength scale is proposed. Preliminary numerical simulations indicate that the critical resolution is determined mainly by the thickness of the metallic mask. The surface of the metallic mask on the illuminated side collects light through SPP coupling, and the interference of SPPs on the exit side of the metallic mask results in enhanced optical intensity with high spatial resolution, which can facilitate nanolithography efficiently by use of conventional photoresist with simple visible or ultraviolet light sources. Several schemes for sub-half-wavelength lithography based on SPPs are described. Inasmuch as the technique is not diffraction limited, nanostructures can be reproduced photolithographically.
©2004 Optical Society of America
Combined with wave-front engineering technologies, photolithography has remained a useful microfabrication technology because of its ease of repetition and suitability for large-area fabrication . The diffraction limit , however, restricts the fabrication scale of conventional photolithography . Potential solutions that have actually been pursued require increasingly shorter illumination wavelengths for replicating increasingly smaller structures. However, it is becoming more difficult and complicated to use the short optical wavelengths to reach the desired feature sizes. For example, the use of wavelengths in the deep-ultraviolet , the extreme-ultraviolet , or the x-ray regime  or in atomic lithography [7–9] requires significantly difficult adjustments of the lithographic process, including the development of new light sources, photoresists, and optics. Although the introduction of light sources with shorter-wavelength and wave-front engineering techniques should help to maintain the current rate of device miniaturization for several more years, it seems that a point will be reached at which the traditional approaches of shortening the exposure wavelength will no longer be able to produce the required feature sizes, so large-scale efforts to develop other approaches to nanolithography have been made. For example, quantum lithography has been explored in recent years, although it is far from application .
A relatively well-established method for the production of high-resolution patterns is the use of sequential techniques. One such technique is the use of focused particle beams, e.g., focused electron beams  or ion beams , which expose a resist layer as it is scanned across the substrate. Another involves the use of a local probe such as the tip of an atomic-force microscope  or the tip of the near-field scanning optical microscope . Although it produces high-resolution patterns, the sequential nature of this technique results in long writing times. Several other lithographic techniques under development, such as nanoimprinting [15,16], have the capability to overcome these limits, but any shift to a nonoptical lithographic technique will require the introduction of a new infrastructure of tools, materials, and processing technologies, the research and development costs of which will be huge.
Recently, however, optical contact or near-field lithography, with which it has been shown that sub-100-nm features can be produced with one-to-one amplitude masks brought into contact with a resist-coated substrate, has been developed experimentally as a promising parallel route to overcoming the diffraction limit. Several schemes that do not require short-wavelength light, such as contact printing through a transmission mask or a binary phase-shift mask [17,18], evanescent near-field lithography [19, 20], plasmon printing,  and the use of light-coupling masks , have been successfully demonstrated for performing near-field photolithography. Near-field contact lithography uses comparably simpler illumination sources without sophisticated imaging optics while maintaining large fields of exposure. The light coming from the apertures on the mask exposes the photoresist. However, according to standard diffraction theory, as the feature size on the mask shrinks much below the exposed wavelength, the amount of transmitted light is small, and light is diffracted into directions with large divergent angles . Especially on a nanoscale, the transmission of visible or ultraviolet light through two-dimensional apertures on a metallic mask is extremely low, thus limiting the exposure efficiency. This process suffers from a long exposure time and low contrast. The low transmission and low contrast are considered fundamental constraints on the achievable resolution and depth of exposure for technological purposes.
In this paper we propose a new technique named surface-plasmon polaritonic lithography (SPPL) that has the potential to produce subwavelength structures with high efficiency by the coherent illumination of a standard photoresist with ultraviolet or visible light. The key idea is to use surface-plasmon polaritons (SPPs) instead of photons as an exposure source. The wavelength of a SPP is much shorter than that of illumination light, so the spatial resolution is much enhanced. On thin metallic films, the wavelength of a SPP is determined mainly by the coupling of SPPs on both sides of the films. The smaller the thickness of the metallic film is, the shorter the wavelength of the SPP is. The materials close to the metallic interface with a large dielectric constant can also contribute a large resolution. In this sense, SPPL is similar to optical lithography for emersion in a high-index liquid or for a solid-emersion lens, but this effect is limited by the index of material that is used. The resolution of SPPL not only is related to the refractive index but also is determined by the thickness of the metallic film. The basic method of operation of SPPL employed in the study described in this paper is described in Section 2. Results of numerical simulations are detailed in Section 3. The discussion is given in Section 4.
A schematic of the SSPL process is shown in Fig. 1(a). The mask consists of a thin metallic film with apertures much smaller than the wavelength of the illumination light. In a traditional situation this is a typical diffraction-limited exposure, so a resolution of less than approximately λ/2 cannot be achieved. In SPPL, however, the excitation of SPPs on the metallic surfaces gives us a way to circumvent this limit (Fig. 1(b)). The resultant enhanced optical field close to the metal surface can cause increased exposure of the resist layer with enough contrast directly below the mask patterns with high resolution.
When a metallic mask is placed in an optical field, it can exhibit collective electron oscillations known as SPPs, which are charge density waves that are characterized by intense electromagnetic fields confined to the metallic surface. For a weak corrugation upon a semi-infinite silver surface, the dispersion of SPPs can be approximately replaced by that of a smooth metal film :
where ω is the excitation frequency, k sp is the wave vector of SPP, εd is the dielectric constant of the interface medium, and εm is the dielectric constant of the metal. The dispersion of SPPs on semi-infinite silver is shown in Fig. 2 (red curve). If the metal layer is sufficiently thin, plasma waves at both metal interfaces are coupled, resulting in symmetric and antisymmetric SPPs [25, 26]. For a thin metallic film with thickness d specified by ε 2 surrounded by media specified by ε 1 and ε 3, the coupling equations are as follows :
where k 0 is the value of the wave vector of illumination light, k is the value of the wave vector of SPP, kr and ki are real part and imaginary part of SPP wave vector. Solving the coupling equations in a silver film yields the dispersion curves of SPPs for silver masks with different thickness that are shown in Fig. 2. The frequency-dependent dielectric constant of silver is incorporated by use of a second-order polynomial fitted to tabulated data over the 350–900-nm range . The surrounding refractive index is 1.7, which is within the range of refractive indices of photoresists. For a semi-infinite silver film the wave vector of a SPP is larger than that of the light line when the optical frequencies are below 3250 meV. However, for the thin films (100, 60, and 50 nm) the wave vectors of SPPs are always larger than that of the light line. In particular, when the illumination frequency is close to 3250 meV, the wave vectors of SPPs are much larger than that of an illumination wave, so the resolution can be enhanced greatly compared with that of traditional kinds of photolithography, for which the resolution is diffraction limited.
Figure 3 shows the critical resolution of SPPL obtained by the interference of SPPs on metallic films. When there is no SPP effect, the resolution limit is just half a wavelength of illumination light. However, with SPP excitation the critical resolution is much smaller than the illumination wavelength. For a g-line (one spectrum from mercury light), which has an optical energy of 2843 meV that corresponds to 436 nm in wavelength, the resolution of SPPL is ~50 nm (dashed line). However, the critical resolution of traditional g-line photolithography without SPP excitation is just 218 nm (dashed–dotted line). The smaller the thickness of the metallic mask is, the higher the resolution enhancement that is obtained. For example, the maximum resolution of a mask with a thickness of 50 nm can reach 20 nm when the energy approaches 3250 meV (dotted line).
For a periodic mask, one can excite the SPP by coupling the illumination light with the grating momentum :
where k sp is the surface-plasmon wave vector, k x is the in-plane component of the incident wave vector, G x and G y are the reciprocal lattice vectors in the x and y directions, and mx and my are integers. With the help of reciprocal lattice vectors, input light with long wavelength can excite SPPs. For normal incidence, k sp=±mx G x±my G y, which means that k sp=±mx G x and k sp=± my G y may be excited simultaneously. That is to say, the SPP waves on the mask have opposite propagating directions along the metallic films. The interference of the SPP waves results in standing waves along the metallic film. For one-dimensional patterns, the resonant wavelength λ at normal incidence is
The positions that correspond to selected values of mx agree well with the far-field transmission peaks, as has been shown theoretically [29–36]. One can tune the wavelength at which resonance occurs by changing the pitch, the incident angle, or the refractive index of the surrounding material in the mask. For example, for a given photoresist (the refractive index is 1.7), when the pitch is 400 nm, exposure sources with a wavelength of 436 nm can be used. When the pitch is changed to 300 nm, the resonant wavelength is shifted to 365 nm.
If the parameters of the patterns on the exit side of the metallic mask are much smaller than the illumination wavelength, the oscillating charges produce an oscillating dipole field about the structured surface, which produces a localized distribution of the electromagnetic field about the metal part. If the resonance frequency falls within the sensitivity range of a photoresist, the field enhancement can be used to locally expose a thin layer of resist. For example, using standard g-line or i-line photoresist requires a resonance wavelength of 300–460 nm.
3. Electric field distribution
In what follows, we analyze the behavior of the electric field distribution on a metallic mask based on rigorous coupled-wave theoretical models  that provide a qualitative, idealized illustration of some of the quantitative support of this technique. Several conditions are defined in our description. The numerical values of refractive indices for the substrate of the mask and the resist used in simulation are 1.46 and 1.7, respectively. The dielectric constant of the silver is taken from the experimental measurement . The perfect boundary condition is used for both top and bottom metal interfaces. For a deep corrugation the resonant condition of light leaving a structured mask in contact with a substrate varies with the parameters of the configuration and the details of the implementation. The wafer layer is not included in this simulation because of the small decay length of the near field. Here we give the electric field distributions under SPP excitation for several different plasmon masks. For simplicity, two-dimensional simulation is performed in the study reported in this paper; however, the simulation can be extended to three dimensions.
3.1 Symmetric perforated plasmon mask
Figure 4 shows the electric field distribution on a mask consisting of an array of metallic holes (we refer it as a perforated plasmon mask). The thickness of the mask is 50 nm. The line/space ratio on the masks is fixed to 1:10. The wavelength of the illumination light is 436 nm, which corresponds to 2843 meV in energy. The electric field distribution represents the case in which a photoresist layer in the near field of the mask is indexed matched to its supporting substrate, which is experimentally possible with appropriate choices of materials.
In Figs. 4(a), 4(b), 4(c), and 4d the periodicities of the masks are 450, 600, 900, and 1200 nm, respectively. The corresponding pattern numbers of the interference of SPPs between the adjacent slits are 4, 6, 8, and 12, which means that for different periodicities the number of high-intensity ranges near the mask is different. Close to the metallic surface, a high-intensity range with a spatial resolution of ~50 nm can be observed, which we attribute to the interference of SPPs with large wave vectors. Because the illumination wavelength and the thickness of the mask are not changed, the obtainable resolution does not change obviously when the width of the metal between the apertures on the mask is modified. The emission from the holes’ locations decays rapidly with increasing distance from the bottom surface of the mask. The field that originates from the metal parts decays slowly, which clearly indicates that a large portion of the field emanates from the metal surfaces. So most of the light transmitted is found not at the locations of the holes but on the metal surfaces. These phenomena are similar to the observations studied by Hohng et al . The field distribution shows that the interference of SPPs causes a highly directional high intensity range, which results in a finite depth of the electric field in the surrounding materials. In this sense, conformal contact is not needed during exposure. In experiment, a layer of refractive-index-matched material is necessary to be added on the bottom side of the mask as a protection layer. The width of the exposed pattern can be controlled by changing the thickness of the protection layer.
Qualitatively similar results are obtained when the mask and the substrate layers are not index matched. We believe that the presence of these phenomena is an intrinsic feature caused by the interference of SPP waves. The result suggests that, in this type of geometry, it is possible to fabricate resist pattern groups with different numbers of features according to requirements by changing the periodicity of the mask.
3.2 Symmetric unperforated plasmon mask
In this subsection we propose another approach to achieving SPPL. The distinguishable physical characteristic of the mask is that all the holes or slits are sealed with some metal. It is generally thought that either an increase in thickness or the presence of additional metal layers can drastically reduce the transmission of visible light owing to absorption and reflection. However, our recent study has shown that light can be transmitted through unperforated metallic structures to the far field , which provides us a hint for doing lithography with unperforated metallic plasmon masks. Without loss of generality, we studied the electric field distribution under SPPs excited by visible light.
The mask that we studied had an array of periodic grooves corrugated on both surfaces with a periodicity of 900 nm, a groove width of 180 nm, and a center layer with a thickness of 10 nm. On the illumination side, one collects photons by exciting SPP modes and then by tunneling the plasmon through the grooves to establish the SPP modes on the other side. Finally, the interference of the SPPs on the exit side results in high spatial resolution. Figure 5 shows the electric field distribution at the resonant condition achieved by excitation of the SPP on the interface between the mask and the photoresist with a wavelength of 932 nm, which corresponds to 1328 meV in energy. Because of the coupling between the modes on opposite sides, the SPP on the illuminated side is magnified through a metallic slab  and reaches a maximum on the exit side with a resolution of ~180 nm, which is approximately one fifth of the illumination wavelength. The field is located mainly in the photoresist. Another significant new feature is the appearance of strong bright spatial intensity distribution with a size of 20 nm at the aperture corner. The influence of the edge effects can be removed by addition of a thin layer of index-matching materials with a thickness of 5–10 nm on the bottom side of the metallic mask. The results show that the near-field distribution of SPPs has high field intensity and high spatial resolution with enough contrast. It is good for subwavelength lithography.
3.3 Asymmetric unperforated plasmon mask
The mask with symmetric grooves on the opposite faces shows a strongly radiative response. How about the mask with asymmetric grooves on both sides? As another example of SPPL, we designed an asymmetric unperforated silver mask that has separate arrays of periodic grooves corrugated on the illuminated side and on the resist side with 180° phase shift. The parameters are as follows: The groove depth is 30 nm, the thickness of the center layer is 30 nm, the groove width is 140 nm, the periodicity is 700 nm, and the illumination wavelength is 539 nm, which corresponds to 2300 meV in energy. Figure 6 shows that at the resonant condition the grooves on the illuminated (upper) face collect light by improving the coupling-in efficiency, whereas the grooves on the lower face redistribute the field distribution with a spatial resolution of 140 nm, which is almost one fourth of the illumination wavelength. The density of the interferential patterns increases to four times compared with that of the pattern features on the mask.
From the discussion above, one can see how to control the density of the resist patterns by changing the parameters of the mask. Inasmuch as the electric field strength drops off gradually with increasing distance from the bottom surface of the mask, the intensity and the width of the high-intensity features gradually become smaller when the distance between the exposure location and the bottom side of the metallic mask increases (Figs. 3–6), so the size of the exposed area and the exposure time will depend on the intensity and the duration of the exposure.
From the electric field distribution discussed above, our type of lithography is different from previously used contact lithography. In our case the exposure field comes from the metal surface, whereas in previous methods the exposure field came from the location of the holes in the mask . It should be noted that the effect of resist absorption on the plasmon resonance has not been taken into account in these calculations. For a highly absorbing resist layer, the absorption may reduce the magnitude of the field enhancement.
We have demonstrated a method for obtaining subwavelength resolution that is based on the interference of SPPs in the near field of a metallic mask. The spatial patterns are determined by the coherent interference of scattered SPP waves. For the same resolution, the electric field distribution has different spatial configurations when the apertures on the mask are different. The interference of the SPPs causes a highly directional intensity range with high intensity in a finite depth of electric field, which is good for noncontact exposure. From the field distribution in this paper, we can see the electric-field intensity at the edge of the apertures on the mask is much higher than that from the flat part, so the contact-exposed result will not be uniform. However, the high intensity from the edges decay very fast with increasing distance from the bottom surface of the mask, while the field from the flat part decays slowly. By utilizing the decay properties, the edge effect can be removed by adding a layer of refractive-index-matched material. For example, photoresist is one good candidate to be attached on the bottom surface of the plasmon mask as a protection layer to get rid of edge effect. The detail information of the protection layer will be analysised elsewhere. In this paper our purpose for introducing periodicity is to excite SPPs. Once the SPPs are excited, the interference of SPPs can result in high spatial resolution, so the number of periods is not critical. For example, a metallic film mask can be designed in this way: Periodic structures are introduced on both ends of a flat metallic film. Then light is shone on one of the periodic structures to excite a SPP. The SPP propagates along the flat metallic film. It will be reflected by the periodic structure on the other end of the film when it meets the structure on the other end. The reflected SPP interferes with the original SPP to form standing SPP waves along the metallic film. One possible way to achieve much higher resolution is to decrease the thickness of the metallic mask. Figure 7 shows the resolution of thin metallic masks of different thicknesses. The smaller the thickness of the metallic film is, the higher the resolution that can be obtained. Another way is achieve higher resolution is to excite SPPs by tuning the illumination energy to 3250 meV. When the illumination frequency is smaller than 3250 meV, the resolution of SPPL is much larger than the critical resolution of traditional optical lithographies. For a metallic film of 20 or 10 nm the resolution can be several nanometers, which can be comparable with the resolution obtained by x-ray lithography, although the illumination frequencies are just within the optical frequency range. In this case, although the wavelength of SPP is very short, the lithographic scheme has to be changed because the film has already become transparent, which causes worse contrast. For example, a metallic film with a thickness of 10 nm can be used for excitation of a SPP that has a short wavelength, and other metallic tips can be introduced to guide the SPP to expose photoresist. For arbitrary features we can use an unperforated mask to obtain isolated or arbitrary patterns by modifying the metallic patterns on the exit side of the mask or use metallic tips.
In conclusion, we have demonstrated that subwavelength photolithography beyond the diffraction limit can be attained with SPPs excited by optical frequency. Several schemes for fabricating resist patterns were proposed. The effective wavelength of the exposure is that of the SPP, which is much smaller than that of the illumination light because of the coupling between photon and fluctuating electrons, so the resolution is improved. One can produce arbitrary patterns by optimizing the configuration on the exit side of the unperforated metallic mask. SPPL satisfies the requirements of many single-step lithographic applications. However, the difference between the patterns on the mask and the patterns in the resist remains open to subsequent investigation. The simplicity, utility, and economy of the approach nevertheless make high-resolution, high-density optical lithography a practical reality in nanotechnology.
We thank L. Jay Guo of the University of Michigan and S. Tikhodeev and N. Gippius of the Russian Academy of Sciences for valuable discussions and suggestions.
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