Interference lithography is an important method for fabricating periodical nano-structures. Its resolution, however, is limited with the minimum period being half the wavelength of light due to the diffraction limit. In this study, we presented bulk plasmon polariton (BPP) interference lithography with the resolution far beyond the diffraction limit. As a demonstrative result, a periodical line pattern of a 35 nm half-period (about 1/10 the wavelength of laser) over a large area (20 × 20 mm) was achieved in an experiment. The break of diffraction limit arises from exciting BPP modes with the high kx spatial frequency components inside hyperbolic metamaterial (HMM) composed by metal-dielectric multifilms. To enhance the contrast and intensity of the interference fringe field of two BPP modes, a metal cladding resist layer and optimized materials are employed. In addition, the period of interference patterns could be tuned by exciting BPP modes with variant kx spatial frequency. It is believed that the method with low cost, large area, and high resolution advantages has potential applications for manufacturing functional structures like gratings, polarizers and photonic crystals, etc.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Due to the advantages of cost-effective, efficient and large area, laser interference lithography has been widely used in fabricating a variety of periodic functional structures, such as, gratings , photonic crystals [2,3], biosensors [4,5], field-emission flat-panel displays , and optical storage media such as CDs or DVDs .etc. Suffering from the diffraction limit, the resolution of the traditional laser interference lithography is restricted to half of the illumination wavelength and the feature size smaller than one hundred nanometer is difficult to achieve. To obtain smaller features, much shorter wavelength is adopted in deep ultraviolet light (DUV)  or extreme ultraviolet light (EUV) lithography [9,10]. Unfortunately, the high cost of hardware such as the light source hinders practical applications of this method.
Surface plasmon (SP) lithography [11–17] has the ability of breaking diffraction limit and realizing the resolution around tens of nanometer. SP are electromagnetic excitations propagating at the dielectric/conductor interface, evanescently confined in the perpendicular direction. Because the wavelength of SP waves induced by free electron oscillations at the metal surface is much smaller than that of the excitation light, the smaller feature size beyond diffraction limit could be obtained [18–22]. In 2004, sub-100 nm lines were patterned lithographically using superlens in the optical near field excited by a wavelength of 436 nm and it should be considered as one rudimentary experimental demonstration of the SP lithography . Through employing the SP lithography method, metasurface holograms devices were fabricated in 2017 by our group .
It is worthy to note the gratings (mask) for SP lithography are usually the same scale with that of the lithography patterns. While the grating with the period beyond diffraction limit needs the expensive fabrication methods, such as focused ion beam (FIB) and electron beam lithography (EBL), thus the cost of SP lithography is also relatively high to some extent and needs to be reduced further.
In this paper, we demonstrated the large area and uniform deep subwavelength interference lithography through launching bulk plasmon polariton (BPP)  by employing HMM, which is composed of alternative metal and dielectric multi-films. The higher lithography period resolution could be achieved by employing this method. Moreover, in comparison with the aforementioned SP lithography, the period of the grating for launching SP is much larger than that of the interference pattern, promising this grating could be fabricated by the simple and low cost traditional laser interference lithography. As illustrative experiments, BPP interference lithography with half-period 35 nm (≈λ/10) and 20 mm × 20 mm area size are performed, which would promote the realization of ultra-small period, large area and low cost. Further, the pattern period could be easily tuned by simply changing the incident angles of a couple of asymmetrical beam. In addition, the field enhancement techniques were also introduced in our experiment to improve the lithography field intensity.
2. Methods and design
Figure 1(a) illustrates the schematic of BPP interference lithography structure with HMM. The proposed structure consists of a titanium dioxide (TiO2) grating, a spacer layer made by the remnant TiO2, HMM composed of alternatively stacked 5 pairs of SiO2/Al multifilms, a photoresist (PR) layer and an Al reflector. TiO2 grating are located at the bottom surface of the fused silica substrate, and are filled with adhesive layer. The thicknesses of the TiO2 grating, spacer layer, SiO2/Al film, PR layer and reflection Al film are 40 nm, 10 nm, 15 nm/15 nm, 30 nm and 70 nm, respectively. At the wavelength of 363.8 nm, the dielectric constants of Al, TiO2, SiO2 and PR are −12.19 + 2.83i, 7.68, 2.19 and 2.86 + 0.15i, respectively, which are measured with spectroscopic ellipsometry (SENTECH, SE850).
The dispersion relation of the coupled BPP modes is given by (kx2 + ky2)/εz + kz2/εx = k02, where the propagation direction is perpendicular to the x-y plane. k0 is the wavevector of the light in vacuum, kx, ky and kz are the wavevector component along x-, y- and z-direction, respectively. Since the wavevector of coupled BPP is larger than that of in vacuum, the coupled BPP modes could be used in lithography to obtain smaller half-period. The HMM could be regarded as an anisotropy medium, and thus effective medium theory (EMT) [22–24] could be utilized for calculating the dielectric tensor of HMM. For the HMM defined in Fig. 1, εx = εy = −5.31 + 1.46i and εz = 5.23 + 0.26i, which are calculated through EMT at λ = 363.8nm. In another case, the TE polarization wave is restrained due to the negative sign of εx. For the TM waves, however, the equi-frequency contour (EFC) surface in EMT approximation shows a cylindrical hyperbolic profile, enabling light propagation with infinite large transverse wavevector kx and ky, as shown in Fig. 2(a). Additionally, the light with kx and ky confined by the circle kx2 + ky2 = εk02 would not propagate inside the structure.
The optical transmission function (OTF) for the HMM defined in Fig. 1 calculated by RCWA shows a filter window in Fig. 2(b). The peak denoted by the red dashed curve could be explained by two surface modes confined at the interface between the HMM and the dielectric medium [25,26]. Herein, the BPP modes are highly confined within metal/dielectric metamaterial and exponentially decay outside [26,28]. Especially, only diffraction light with the wavevector in the narrow range could be coupled to the BPP modes inside HMM and show the propagation behavior. According to the OTF window, wavevectors from 2k0 (BL) to 3.6k0 (BH) could propagate through the structure, while wavevectors beyond this range would be inhibited as the imaginary part of kz is larger than zero in Bloch Theory . Therefore, diffraction orders with suitable wavevector kx should locate in the passband of OTF window. Furthermore, the grating function could be written as follows, kx = nk0sin(θ) + 2πm/Λ, where kx is the transmitted transverse wavevector; θ and m are the incident angle and diffraction order, n is the refractive index of incident material. In this paper, only perpendicular illumination is considered. So, the grating function could be rewritten as kx = 2πm/Λ, which reveals the wavevector of the diffraction light only depends on the diffraction order and the grating period.
In this paper, a specially designed structure acts as a spatial frequency filter, allowing a pair of symmetrical diffraction orders of light to reach the PR layer and producing uniform interference patterns. By adjusting the period of grating to λ/2.6, only ± 1st orders of diffraction light with the wavevector of 2.6k0 are located in the passband of the OTF window. As depicted in Fig. 2(b), the zero-order transmitted light is restrained while a pair of symmetrical diffraction orders light around 2.6 k0 could pass through it. Hence, the half-period of interference fringes in PR layer could reach λ/10.
The key of plasmonic interference lithography with small period is to reliably select symmetrical diffraction orders of light [22,27,28]. The expected diffraction modes could be selected through the structure with the bandpass transmission property, while the other orders of diffraction modes are restrained. However, the narrow passband in waveguide plasmonic interference lithography structure may bring obstacles in matching the diffraction modes with the waveguide modes . In contrast, a wider passband (Δkx = 1.6k0) of the OTF window depicted in Fig. 2(b), has predominant tolerance in alleviating the match difficulty. From the diffraction equation at normal incident light, it could be concluded that there exists 2.6k0 intervals between adjacent diffraction modes. Thus, the wanted diffraction modes with the drifting transverse wavevector from the ideal value of 2.6k0 could be also transmitted under the wide transmission passband. Under this condition, other unwanted diffracted orders of modes introducing the serious distortion of the interference patterns, would also not transmitted from the OTF passband. Moreover, the interference fringes in waveguide plasmonic interference lithography heavily rely on the film thickness of metal/PR/metal structure . Therefore, the parameters of the interference structure should be updated to produce interference fringe with the new half-period. Considering the wider passband of OTF in Fig. 2(b) for the fixed HMM as defined in Fig. 1 and the wider intervals between diffraction modes, the half-period of the interference fringe could be adjusted only by tuning the angles of a couple of symmetrical incident light as shown in Fig. 3. Here, the ± 1st diffraction orders were located at the high cut-off wavevector (BH) as shown in Fig. 2(b) by set the grating period to 110 nm under normal incidence. Clearly, the transmitted transverse wavevector kx could be tuned by changing the incident angle, thus the spatial frequencies of the launched BPP modes changes correspondingly. As a result, the period of the interference pattern is continuously altered as shown in Fig. 3. Figure 3(a) illustrates the electric field intensity distribution of the interference fringe normalized by that under the normal incidence, which proves the period tenability of BPP interference lithography. The period resolution of the interference patterns could be tuned from 55 nm to 95 nm as depicted in Fig. 3(b). And the image contrasts when tuning pattern period are meet the requirement of the positive photoresist.
In order to improve the interference field intensity, the dielectric grating was introduced to enhance the coupling between the diffraction modes and the BPP modes inside HMM. Moreover, the ± 1st orders of diffraction light rather than the higher diffraction orders of light were selected for the interference lithography to increase the lithography energy efficiency, because the excitation efficiency of ± 1st orders diffraction light are larger than that of the higher orders diffraction light at normal incidence. Besides, the back reflection technique was also introduced to improve the intensity of interference field by enhancing the resonance coupling of the BPP modes inside the cavity, which composed of top Al film, PR layer and bottom reflective Al film.
Two same structures but with TiO2 or Au grating layer (including grating and spacer) were prepared to prove our method. The grating layer illustrated in Fig. 1 (red region) composed of TiO2 could highly improve the coupling between the diffraction light and the HMM compares to the Au grating. More details could be obtained in Fig. 4(a) and 4(b). It shows the |Ex|2 and |Ez|2 at the interface between TiO2 grating layer and HMM is much more strongly than that between Au grating layer and HMM, which implies the coupling between TiO2 grating and the HMM is larger than that between Au grating and HMM. This could be explained by the great difference between the permittivity imaginary part of TiO2 and Au, as the absorption of the Au is greater than that of TiO2. Here, |Ex|2TiO2/|Ex|2Au and |Ez|2TiO2/|Ez|2Au are respectively defined as the normalized magnitude ratio of electric field components between the HMM with TiO2 grating and the HMM with Au grating at the grating/HMM interfaces. And their calculated values are 6.4 and 25.3, respectively, as presented in Fig. 4(c). Meanwhile, all those structures have the ability to suppress other orders, like 0th and ± 2nd orders, diffraction light with the transverse wavevector of 0k0 and 5.2k0, which could be seen from the Fourier spectrum analysis presented in Fig. 4(d). Benefiting from the filter characteristic of HMM, the magnitude ratio |Ez|/|Ex| at 2.6k0 in the middle PR layer shows almost the same value in Fig. 4(d) for both structures. Moreover, the amplitude transmission of ± 1st orders diffraction light of the HMM with TiO2 grating layer is greater than that of the HMM with Au grating layer as depicted in Fig. 4(e), which is calculated by the rigorous coupled wave analysis (RCWA) method .
Numerical simulation with finite element method for 1D mask is performed to demonstrate light intensity distribution inside the structure. The normalized light intensity is defined as |E|2/|E0|2, where |E0|2 is the incident light intensity. Meanwhile, the image contrast is defined as (|Emax|2-|Emin|2)/(|Emax|2 + |Emin|2). The simulated normalized |E|2 distribution maps of two different structures in the x-z plane are given in Fig. 5(a) and 5(b). And Fig. 5(c) gives light intensity distribution along horizontal lines in the center of PR layer. Obviously, the light intensity of TiO2/HMM/PR/Al is almost 16 times higher than that of the Au/HMM/PR/Al, which proves the higher energy efficiency of TiO2 grating layer. Moreover, the image contrast for interference fringes in the whole PR layer are both larger than 0.98 for two structures as presented in Fig. 5(d), which is attributed to the good filter performance of HMM and the image enhancement of Al reflector. In addition, the nonuniformity of light intensity among the whole PR layer in Fig. 5(d) (defined as (|Emax|2-|Emin|2)/(|Emax|2 + |Emin|2)) for two structures are both equal to 0.12, which is small enough and plays the key role in fabricating uniform patterns in practical application as illustrated in Fig. 8(e) and 8(f).
The amplitude transmission difference between |Ex| and |Ez| for the BPP interference lithography is essential for high contrast interference fringes in the measure of |Ez|2 + |Ex|2 and uniformity. To ensure high contrast and uniformity of interference patterns, an Al reflector was adopted. Figure 6(a) and 6(b) shows the intensity distribution of |Ex|2, |Ez|2 and |Ex|2 + |Ez|2 for the same structure without and with Al reflector, in which the dashed rectangles indicate the corresponding position of gratings. It’s obvious that the |Ex|2 and the |Ez|2 have almost the same amplitude for structure without Al reflector, which brings greatly blurred interference fringes with the contrast value about 0.1. Owing to the adoption of Al reflection enhancement technique, there exist a shift of π/2 phase between the |Ex|2 and |Ez|2 . Benefitting from the inhibition of |Ex|2 component, the magnitude ratio |Ez|/|Ex| being 13 which is about 15 times larger, the image contrast is 0.98 which is about 10 times larger than that of structure without Al reflector. Due to the high magnitude ratio |Ez|/|Ex| being 14.3 and 14.6 at 2.6k0 for two structures in Fig. 4(a) and 4(b), the interference fringes exhibit high uniformity of 0.988 and contrast of 0.986. The high contrast and intensity in the PR layer ensure the exposure stability and feasibility in experiments.
3.1. Sample fabrication
The fabrication procedures of BPP interference structure and lithography process are illustrated in Fig. 7. Two types of grating and spacer layers (TiO2 and Au) with the same HMM multilayer were used for exposure. Firstly, we introduce the fabrication of structure with TiO2 grating and spacer layer. First, Au (20 nm) film was deposited on Si substrate by thermal evaporation (C-VAC400-I, Xiwoke LTD.) with 2.5Å/s, chamber pressure of ~5 × 10−4Pa and ambient temperature. Afterwards, the TiO2 film with 50 nm thickness was deposited on Au film by magnetron sputtering system (DE500, DE Technology Inc.), with which conditions were power of 200 W in radio frequency mode, Ar gas flow rate of 6.8 sccm, and at a base pressure of ~1 × 10−4Pa. Then, the AR-3170 positive photoresist (ALLRESIST GmbH, Strausberg) was spin coated on the grating layer at 4000 rpm for 30 seconds and baked for 10 min at 100°C. After that, 1D grating (20 mm × 20 mm) with 140 nm period and 50% duty cycle, which was prepared on the photoresist layer by large area laser immersion interference lithography (325 nm wavelength, HeCd laser, Kimmon Koha Co., LTD), was transferred to TiO2 grating layer by Ion Reactive Etching (IRE-3, Beijing JinShengWeiNa Techonology Co., LTD). The etching conditions were set as power of 100W, CHF3 flow rate of 30 sccm, and the etching rate is about 7 nm/min. In order to reserve a thin remnant layer on the grating layer, the height of grating was etched to 40 nm. Next, the grating and sacrifice layer (Au film) was attached to another fused silica substrate with UV curable epoxy resin adhesive (X31213 produced by ZYMET) and then cured by ultraviolet light at 365 nm central wavelength and energy intensity of 100J/cm2. Due to the weak adhesion between the sacrifice layer and the Si substrate, the grating layer and sacrifice layer glued to the new fused silica substrate was stripped off from the original one by outside force. Then, a planar and smooth transfer surface with small roughness of 0.7 nm root-mean-square (RMS) measured by AFM (NT-MDT) was obtained, which copies the surface morphology of the Au film, after the dissolution of it.
The Au grating was produced as follows. Au film with the thickness of 50 nm was deposited on the Si substrate by thermal evaporation as mentioned above. Then, the same 1D grating prepared on the photoresist layer coated on the Au film was transferred directly to it by Ion Beam Etching (IBE-150B, Beijing JinShengWeiNa Techonology Co., LTD). The etching condition were set as the ion beam current of 40 mA, acceleration voltage of 200 V, Ar gas flow rate of 3.0 sccm and vacuum pressure of ~5 × 10−4Pa. The grating height was etched to 40 nm leaving a 10 nm transfer layer. Afterwards, the Au grating layer was transferred to the new substrate by the same method mentioned above.
Subsequently, 5 pairs SiO2/Al (15 nm/15 nm) films were alternatively deposited on the grating layer by magnetron sputtering. In order to reduce the surface roughness of Al film, Al target alloyed with 3% Cu was adopted in the sputtering process. The optimized sputtering conditions were power of 200W in radio frequency mode, Ar gas flow rate of 6.8 sccm, and at a base pressure of ~6 × 10−5Pa. The deposition rate for Al and SiO2 film are 3 and 0.6 Å/s, respectively. A SiO2 layer with 10 nm thickness used as protect layer was then deposited on the multilayer at the same sputtering parameters, then the 30-nm diluted AR-3170 positive PR layer was spin coated on it and baked for 5 min at 100°C. Finally, in order to enhance the pattern contrast in the PR layer, a 70 nm Al reflective layer was deposited on it by thermal evaporation at chamber pressure of ~1 × 10−5Pa and deposition rate of 1.5 Å/s, which could avoid the unwanted ultraviolet light exposure in sputtering process.
3.2. Exposure process
The 363.8 nm TM polarized light from the Ar-ion laser with its electric field perpendicular to the grating direction was vertically illuminated to the grating from the fused silica substrate side. The exposure times are 60s and 700s at the same exposure light intensity for two structures with TiO2 and Au gratings, respectively. After exposure process, the cladding reflect Al layer were dissolved by phosphoric acid and then the PR layer were developed in AR 300-35 developer for 20 seconds, rinsed by deionized water and dried by N2 in order. After that, the morphology of exposed PR layer is measured by Scanning Electric Microscopy (SEM).
4. Results and discussions
In order to compare and analysis the efficiency of energy utilization, two identical structures but respectively combined with TiO2 and Au grating layer were chosen. Figure 8 (a) and 8(b) shows the SEM images of TiO2 grating and Au grating after etching process. The TiO2 grating is planarized with the measured 7.5 nm peak-to-valley (PV) value and 0.6 nm RMS copying the morphology of sacrifice film Au as shown in Fig. 8(c). Meanwhile, the top surface of Au grating layer, after the lift-off process, shows 4 nm PV profile and 0.37 nm RMS roughness, which is consistent with the morphology of Si substrate in Fig. 8(d). Figure 8(e) and 8(f) show the SEM images of the resulting fringes obtained in the PR layer after dissolving the back reflection Al film and developing process. Clearly, nearly uniform dense periodic line with 35 nm half-period were obtained, which is less than 1/10 of the incident light wavelength. The patterns area of BPP interference lithography is about 20 mm × 20 mm. Figure 8(g) exhibits the cross-section SEM image of the BPP interference lithography structure. The ear-like structures on the top edge of the grating were caused by assembling of Au atoms reflected at the Ion Beam Etch (IBE) processing.
Both fringes show almost the same image contrast, as could be seen in the simulation of Fig. 5(d). The exposure time of the structures with Au grating layer is almost 12 times longer than that with TiO2 grating layer, which is consistent with the theoretical results. The slightly distortion of interference patterns in the SEM images depicted in Fig. 8(e) and 8(f) are mainly attributed to the film roughness, which delivers the random fluctuation of interference intensity and reduces fingers uniformity. So, controlling the roughness of the multifilms as small as possible is very necessary in experiment. In order to obtain the large aspect ratio, much thicker PR layer should be considered. In the simulations as depicted in Fig. 9, the image contrast hold well and larger than 0.8 when the thickness of PR layer is lower than 60 nm. At the same time, the light intensity for 60 nm PR layer is only 13% of that for 30 nm PR layer. With the PR layer thickness increasing from 60 nm, the contrast decreases dramatically attributed to the damped mode coupling from the bottom reflector Al film.
In conclusion, we accomplished BPP interference lithography with small half-period, large area and high lithography energy efficiency based on HMM composing of Al/SiO2 multifilms. Our design is based upon spatial frequency selection of a couple of symmetrical diffraction modes, which results in a uniform deep subwavelength periodic interference field in the PR layer. In contrast to the previous SP lithography, the grating was fabricated by the low-cost laser interference lithography. By tuning the incident angles of a couple of symmetrical light, the spatial frequency of the selected BPP mode would change continuously and thus the pattern period. Benefiting from those interference field enhancement methods, the lithography energy efficiency was increased by two orders of magnitude. This method was applied to achieve 20 mm × 20 mm and uniform periodic subwavelength lines with a half-period (35nm) about λ/10.
973 Program of China (2013CBA01700); National Natural Science Foundation of China (NSFC) (61575202, 61175204, 61405200).
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