Based on surface plasmon resonant enhancement, a method to realize photolithography beyond diffraction limit by using polystyrene spheres (PSs) self-assembled on silver slab was proposed in this paper. The optimum parameters for PS with different diameters were presented. In order to verify this method, numerical simulation on a typical configuration with 1.5µm diameter of PS was carried out by using the finite-difference time-domain (FDTD) method, and the minimum feature size of 88nm beyond diffraction limit at 365nm working wavelength was obtained.
© 2008 Optical Society of America
Photolithography is a useful micro-fabrication technology for the ease of repetition and suitability for large-area fabrication . The diffraction limit, however, restricts the critical size of conventional photolithography. To reduce the critical size and meet the wide use of nano scale device, several technologies such as focused ion beam (FIB) lithography , e-beam lithography , and near-field scanning optical microscopes lithography  have been studied in many laboratories. However, they all use point-by-point scanning rather than forming the whole image at once and suffer from the disadvantages of low efficiency, high expenditure, and incompatibility for larger area fabrication.
The discovery of superlens has attracted increasing interest. Unlike conventional optical components, it will substantially enhance the evanescent waves and then focus both the propagating spectra and the evanescent waves, thus capable of achieving diffraction-free imaging [5-9]. Recently, superlens nano lithography is carried out by X. Zhang group [10-12]. As a newly developed technique, it provides a potential solution of the problems encountered by the traditional photolithography. However, this technique has two serious problems that must be overcome before putting it to practical use. The first is that the fabricated nano structures in photoresist (PR) are inseparable from the template, which makes the transfer of the fabricated structures to optical material impossible. The second is that the nano scale features on the template are fabricated usually by FIB  or e-beam lithography  which suffers from the disadvantages mentioned above.
In this paper, we improved the superlens nano lithography system by forming the template using polystyrene spheres (PSs). The template fabricated by this method can be conveniently separated from PR. Larger area PS monolayer on silver slab is obtained by self-assemble [13, 14] and the contact points of the PS with the silver slab are in nano scale, thereby it is highly efficient and economic to acquire template with larger area nanostructure which is beyond the diffraction limit. Then, the principle to achieve nanopattern with feature size smaller than the diffraction limit using this template was presented, and the numerical simulation was also presented in detail. After that, the discussion on the optimization of the template design was carried out.
In superlens photolithography, the evanescent wave which carries the higher spatial frequency about the object is enhanced by surface plasmon (SP) excitation and participates in imaging. The key to the experiment design is to carefully select the nano scale object and thin metal slab with negative permittivity in order to enhance the evanescent wave.
To realize efficient SP excitation, a structure which is composed of PS, silver slab, PR, and substrate, is designed in our method, as shown in Fig. 1. The PS is used in this structure for two main reasons. First, PSs can be treated as convergent lenses with high numerical apertures and short focal length. Most of the incident light is concentrated to the contact point of PS and silver slab by the strong convergent effect of PS [15-17]. The convergent light supplies sufficient energy for the object imaging and reduces the background light, which increases the contrast in image plane. Second, its contact point with the metal slab is close to infinitesimal when it is regard as rigid PS. The contact point can be regard as an infinitesimal nano object for the imaging sub-wavelength features, and it also can convert the wave vector to meet the need of SP excitation.
At normal incidence, most of convergent light is converted into evanescent wave with k x≫k 0(k x is the wave vector of the evanescent wave and k 0 is that in vacuum) by the nano point. Localized SP (LSP) can be excited by the evanescent wave [10, 18] which carries the nano information about the nano point and an image with feature size smaller than the diffraction limit can be obtained on the other side of the silver slab. In imaging procedure, as surface charges accumulate at the interface, the match between the metal and its adjacent dielectric medium is crucial to ensure the evanescent enhancement across the slab. When -ε 1≈ε 2(ε 1 is the permittivity of metal and ε 2 is that of the dielectric medium), most of the evanescent wave transmits the silver slab and is enhanced by the SP excitation, resulting in the tunneling effect . For the evanescent substantially enhancement, a thin silver slab is chosen as the superlens with a negative permittivity (ε 1=-2.4012+i0.2488)  at a wavelength of 365 nm, and its real part matches close to that of the surrounding dielectric material, PS (ε 2 PS=2.5281) . On the other side of the silver slab, an i-line positive PR with relative permittivity ε 2 PR=2.886+i0.059  is spun on the substrate for nanopattern recording. Even though there is a slight mismatch of the ε 2 PR and ε 2 PS, an asymmetric lossy superlens still supports the efficient coupling of the evanescent fields between two surfaces of the silver film . The evanescent wave transmission coefficient of the silver slab is calculated by Pendry as following :
Where k x, k y and k z is the wave vector at x, y, and z direction, respectively, d is the slab thickness. From Eq.1, the amplitude of evanescent wave increases exponentially with the thickness of the slab, and lead to larger amplitude of the back side than that of the front side.
Most of background light with transverse wave vector k(k<k 0) is restrained for the reflecting and absorbing of the silver slab. Due to the evanescent wave increasing and the background light decreasing, for the transmitted light, the proportion of background light to evanescent wave is decreased. The enhanced evanescent wave is dominant in imaging. Hence the evanescent waves, carrying sub-wavelength information about the contact point, compensate the loss of the spatial frequencies and restore the image below the diffraction limit. The image with the feature size smaller than the diffraction limit can be formed in PR.
3. Simulation results and analysis
In order to verify above principle, the energy field was investigated. Based on the symmetry character of the sphere, a circular symmetry spot will be generated. The energy distribution of a slice across the spot is sufficient for studying the beam size. Therefore, the simulation is carried out by two-dimensional finite-difference time-domain (FDTD) method for simplicity. The parameters in simulated structure are selected as following: PR ranged from 1.668 µm to 3 µm along z direction, silver film thickness 18nm, PS diameter 1.5µm. The incident electromagnetic wave is TM-mode rectangular wave at wavelength 365nm. The relative permittivity of the silver slab, the PS, and the PR are ε 1=-2.4012+i0.2488, ε 2 PS=2.5281 and ε 2 PR=2.886+i0.059, respectively. To obtain energy field for the periodically arranged PSs, the period boundary condition was used. For contrast analysis, the model without silver slab was also simulated with PR ranged from 1.65 µm to 3 µm. The simulated results for the two cases are all shown in Fig. 2 and analyzed in following, respectively.
The energy field in the case without silver slab is shown in Fig. 2(a). The incident plane waves are focalized in PR by the PS, as shown in Fig. 2(a). The zoomed picture shows the energy distribution of one beam in PR within the 50nm scope away from the surface. It can be seen that the relation between the beam width and the distance is inconspicuous.
When the silver thickness is 18nm, the energy distribution is shown in Fig. 2(b) and that of the 50nm scope from the PR surface was zoomed. Comparing Fig. 2(b) with Fig. 2(a), the energy distribution is different in two aspects. First, in Fig. 2(b), there are a series of peaks in the PSs resulting from the reflected light which comes back and meets the incident forming stationary wave, but there are not such peaks in Fig. 2(a). Second, the width of the beam on the surface of PR in Fig. 2(b) is almost half of that in Fig. 2(a), which is because of the silver slab imaging the nano scale contact point on the surface of PR. In the imaging procedure, the evanescent waves converted by the nano point are enhanced through the silver slab by LSP excitation and participation in the image. Since it decay exponentially in PR after leaving the silver slab, the beam width increased quickly with the increasing of the transmission distance, as shown in the zoomed picture of Fig. 2(b).
Slices on the surfaces of the PR for above two cases are shown in Fig. 2(c). The dashed curve shows the normalized energy without silver slab, whose Full-Width-Half-Maximum (FWHM) is 180nm. The solid curve shows the normalized energy with silver slab, whose FWHM is 88nm which breakthroughs the diffraction limit because of the evanescent waves participation.
From above results, the energy distribution without silver slab is greatly different from that with silver slab. In PR within 300nm of the surface at x=0, the normalized energies for both without and with silver slab are shown in Fig. 2(d). In the former case, as the dotted curve shown, the energy has the maximum value at focus position (144nm distance). However, the latter case is quite different from the former case, because a larger energy peak resulting from the enhanced evanescent waves presents on the surface of the PR (0nm distance) besides the energy peak at focus position (232nm distance), as the solid curve shown.
The FWHM of beams are also different from each other for above two cases. In Fig. 2(d), it can seen that the FWHM of the beam is associated with the corresponding energy distribution. Take the former case without silver slab as an example, the FWHM curve (triangle symbol curve) is in the opposite direction trend of the energy curve (dotted curve) along the x direction, so there is only one minimum FWHM values at the focus position. For the latter case with silver slab, the relation between FWHM (square symbol curve) and the corresponding energy distribution (solid curve) is similar to the former case and there are two vale FWHM values corresponding to the two peak energy positions. The minimum FWHM value is on the surface of the PR (88 nm) due to the enhanced evanescent wave participation which carries higher spatial frequency. With the distance extending, the evanescent wave decays exponentially and the background light becomes dominant, which leads to the FWHM increases quickly and approaches to that in the former case at 21nm distance, so the silver slab benefits smaller image limited to within 21nm of the PR surface. The expectant feature size can be obtained by modulating the exposure dose in order to ensure the development depth less than 21nm.
In the case with silver superlens for 1.5 µm diameter, since the values of FWHM increase rapidly with respect to the distance from the surface, the consistent contacting is crucial to obtain the consistent photolithography. This problem can be solved in the way that PS is embedded into an elastomeric thin film which has the instinctive appetency to the silver slab [15, 21].
In summary, both the energy distribution and the spot size of the structure without silver slab are greatly different from that with silver slab. In the former case, evanescent waves, which carry the information of nano scale about object, decay exponentially along z direction and are lost before reaching the observed plane. The incident plane waves are converged by the PS and the size of the spot is larger than the diffraction limit because of the absence of the evanescent wave. In contrast, in the latter case, the silver slab can image the contact point at the back side of the slab. Evanescent waves are enhanced by the silver slab and the loss of the higher spatial frequencies information is compensated, moreover, most of the background light is restrained for the reflecting and absorbing of the silver slab. Thus an image of the point which below the diffraction limit is formed. After leaving the silver slab, the evanescent wave decay exponentially in PR, while the spot size increases quickly. The proportion of background light to evanescent wave is increased as the transmission distance increases, and the focusing action of the background light becomes dominant gradually resulting in the second energy peak.
The simulation results and analysis demonstrate that image with feature size smaller than the diffraction limit can be realized with PS and silver slab. Several factors influence the feature size (FWHM) of the beam. The most important factors are the silver thickness and the PS diameter.
4.1. Silver thickness-dependent minimal feature size
The silver thickness is crucial to the feature size of the beam. The beam size and the transmitted energy were simulated with varying silver thickness using FDTD. Fig. 3(a) shows thickness-dependent beam feature size and transmitted energy at out-plane of the silver slab with PS diameter of 1.5 µm. The dashed curve (180nm) and the black curve show the feature size without silver and that with varying silver thickness, respectively. The blue curve is the enhanced transmission corresponding to the varying silver thickness. Due to the competition between LSP resonance and intrinsic loss in the metal, the optimum thickness is 18nm in which case exists the maximum evanescent field enhancement and minimal feature size (88nm). The smallest beam size is half of that without silver and beyond the diffraction limit. Smaller beam size than that without silver slab all can be obtained with the silver thickness ranged from 15nm to 45nnm. However, improper thickness, such as larger than 45 nm or smaller than 15 nm, often leads to diminishing the enhancement resulting in a diffraction-limited image.
4.2. PS diameter-dependent feature size
The feature size also strongly depends on the diameter of the PS. In order to achieve better mini size feature by maximizing the enhancement of the evanescent wave, silver thicknesses must be designed for different diameter PSs. Fig. 3(b) shows thickness-dependent beam feature size to several diameters. When the diameter larger than 700nm, it can be seen that the optimum silver thickness and smallest feature size exist, and the relations between feature size and silver thickness is similar to that of 1.5 µm diameter. As shown in Fig. 3(b), the feature size decreases as the diameter decreases. Because PS with smaller diameter, has a shorter focal length and a smaller spot size than the bigger PS, additionally a smaller contact point with silver slab is produced, and all these result in larger k x which ultimately leads to smaller feature size. On the other hand, larger k x induced by smaller diameter PS results in the optimum silver thickness shifting to larger values [19, 22], as shown in Fig. 3(b).
As the diameter gets smaller, the focal length decreases continually. When the PS diameter is smaller than 700nm, the focus position is inside of the PS. The scattering spot on the surface of the silver slab make only a little fraction of incident light convert into evanescent wave. The transmitted background light is much stronger than the evanescent wave and dominates the spot size. Thus, the influence of silver thickness on the FWHM is not distinct, as shown in Fig. 3(b) by the i curve which shows the case of diameter of 600nm. Modulating the ratio of the refractive index between the PS and the surrounding medium, we can make the focus position always being on the surface of the silver slab whether the PS diameter is larger or smaller than 700nm.
From above analysis, an optimum silver thickness exists due to the competition between LSP resonance and intrinsic loss in the metal. It is unique for a given diameter PS because the concrete tangent manner leads to the concrete evanescent wave vector. Modulating the ratio of the refractive index between the PS and the surrounding medium can make the focus position always being on the surface of the silver slab no matter the diameter of the PS larger or smaller than 700nm.
In conclusion, an optimized superlens nano-patterning method is put forward in this paper. By designing the PS diameter and silver thickness, nano scale photolithography can be realized by employing LSP excitation. Our simulation results demonstrate that the obtained spot size is smaller than the half of that without superlens. Nano patterns such as holes with different sizes, periods, and arrangement can be fabricated using the super image of contact points by special designed arrangement, diameter, and silver thickness. By introducing the characteristic of the method, the superlens nanolithography has a promising future to practicality and popularization for the low cost and conveniently separated template. This is an effective method for nanofabrication with the advantages of high efficiency, simplicity, economy and ease for large area fabrication by single-step lithography.
This work was supported by 973 Program of China(No.2006CB302900), 863 Program of China (2007AA03Z332) and the Chinese Nature Science Grant (60727006, 60678035). The authors thank Shaoyun Yin and Changtao Wang for their kind contributions to the work.
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