## Abstract

We propose an effective method for fabricating dual-periodic structures using the combination of multi-beam interference lithography and evanescent wave exposure. Four-beam evanescent wave interference lithography (EWIL) is used as a prototype to demonstrate the fabrication feasibility of one-dimensional (1D) micro-grating structures covered with nanodots and two-dimensional microdot structures filled with subwavelength fringes by designing reciprocal lattice vectors of interference fringes. We experimentally fabricated 1D nano-/micro-grating structures with periods of 140 nm and 12.5 µm and microdots filled with subwavelength gratings of 450 nm period by four-beam EWIL. These structures are applicable to superlattice photonic crystals and subwavelength structured surfaces.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Owing to their unique optical properties, periodic nanostructures such as photonic crystals (PhCs) [1] and subwavelength structured surfaces (SWSs) [2] have gained considerable attention in recent years. Single-periodic PhCs have demonstrated great [ABS]potential in the development of photonic waveguides [3], surface emitting diode lasers [4], integrated photonic circuits [5], and biosensors [6]. Further, one-dimensional (1D) and two-dimensional (2D) subwavelength grating structures have been used for the development of birefringent waveplates [7], guided-mode-resonance filters [8], and antireflection coatings [9]. However, lack of structural freedom in single-periodic structures limits their application in the fabrication of super-lattice PhCs and advanced micro/nanostructures. The spatially graded PhCs facilitate a better manipulation of electromagnetic waves than the single-periodic PhCs [10]. For example, a moth-eye shaped biomimetic nanostructure [9], which is composed of hemispherical compound eyes in several hundred of microns covered with subwavelength dots with a diameter of several hundred nm, shows multiple functions including antireflection and water-repellency because of its multi-scale structure. Therefore, the fabrication of dual-scale structures with subwavelength (>150 nm) periodicity or a dual periodicity of several tens of microns and has garnered significant attention. Until now, these spatially variant periodic structures have been fabricated using several methods such as direct laser writing [11], two-photon lithography [12], self-organization [13], stereolithography [14], and interference lithography [15–19].

Interference lithography (IL) is a powerful technique for the fabrication of periodic micro/nanostructures due to its advantages: low-cost, high throughput, and large-area fabrication [15]. Here, holographic patterns formed by the interference of two or more coherent beams are projected onto a photoresist and periodic relief patterns are fabricated after the development process. Several studies have used multi-beam IL for fabricating 2D and three-dimensional (3D) periodic structures [15]. Multi-beam interference patterns are basically superposition of 1D interference fringes. Three-beam IL and four-beam IL have been used for the fabrication of hexagonal and square dot patterns, respectively [15]. These methods utilize the superposition of the same pitch fringes with different angles for the fabrication of single-periodic 2D patterns. However, a different approach based on spatial beating has also been proposed for the fabrication of dual-scale periodic structures [16]. Here, asymmetric incident condition or superposition of slightly different fringes enables the formation of interference fringes with µm order modulation. Six-beam IL has been used for the fabrication of hexagonal microcell filled with 2D dots [16] and moth-eye shaped structures with periods of several hundred microns [17]. Y. Lin et al. developed a more flexible multi-beam IL system composed of the spatial light modulator (SLM), and fabricated dual-periodic [18], five-folds [19], holographic patterns to improve the functions of PhCs. Although theoretical minimum pitch of IL is a half-wavelength, the practical minimum pitch was ∼sub-µm due to some experimental limitations. Hence, the processing fineness of IL was insufficient for the actual size of PhCs with the visible light (less than several hundred nm).

In this study, we have employed evanescent wave interference lithography (EWIL) to fabricate subwavelength and dual-periodic microstructures for improving the performance of PhCs and other subwavelength structures. Two-beam EWIL has one of the highest numerical aperture (NA) among the existing lithography techniques, and it facilitated the achievement of a fringe pitch of less than λ/3 [20–24]. However, few studies have reported the applicability of EWIL for multi-scale structures. The combination of EWIL and multi-beam interference enabled us to fabricate fine patterns with a period of ∼140 nm, grating structures with the dual periodicity of several tens of microns, and subwavelength gratings array in micro-lattice, which is an adequate size for the visible light applications of PhCs and SWSs.

## 2. Theoretical analysis

The principle of multi-beam EWIL is theoretically described as follows. Multiple evanescent wave interference can be explained by considering that *n* beams are incident on the *xy-*plane (Fig. 1) from the negative *z* direction and evanescent fields are generated in the positive *z* direction. The intensity distribution can be described as a superposition of the electric field vectors. The electric field vector of the *n*_{th} evanescent wave with any linear polarization can be expressed as

*xy*-plane, $\hat{{\textbf r}}$ is the position vector in

*xy*-plane, $\omega $ is the angular frequency of the light, and ${\beta_n} = {k_0}{(n_\textrm{p}^2{\sin ^2}{\theta_n} - n_\textrm{r}^2)^{1/2}}$ is the attenuation constant. It is clear from Eq. (1) that $1/{\beta_n}$ is the attenuation height at which the amplitude of the electric field is 1/

*e*of its value at the boundary (

*z*= 0). ${k_0}(2\pi /\lambda )$ is the wave vector in vacuum, $\lambda $ is the wavelength, ${\theta_n}$ is the incident angle of the beam, and ${n_\textrm{p}}$ and ${n_\textrm{r}}$ are the refractive indices of the prism ($z < 0$) and resist ($z \ge 0$), respectively. ${\hat{{\textbf P}}_n}$, ${\hat{{\textbf k}}_n}$, and $\hat{{\textbf r}}$ in Eq. (1) are defined as

*xy*-plane, and polarization angle ${\psi_n}$ is defined as the angle between the plane of polarization and the incidence plane containing the wave vector ${\hat{{\textbf k}}_n}$. Here, ${\psi_n} = $0,

*π*corresponds to P polarization, while ${\psi_n} = $

*π*/2, 3

*π*/2 corresponds to S polarization. In general, the relative phase of each beam can affect the interference patterns. However, the change of the relative phase generally causes 2D translations of the interference patterns under our assuming conditions. The transitions had little influence on the periodicity of the interference pattern which was our main interest. Therefore, the phase terms of each beam were omitted in Eq. (1). The intensity of

*n*-beam interference is expressed as follows:

As shown in Eq. (5), the total interference pattern is described as the superposition of all the two-beam interference patterns. Each interference fringe has orientation perpendicular to the reciprocal lattice vector ${\hat{{\textbf k}}_b} - {\hat{{\textbf k}}_a}$, and the fringe pitch is $2\pi /|{\hat{{\textbf k}}_b} - {\hat{{\textbf k}}_a}|$. The total number of interference terms can be calculated as $_n{C_2}$. In addition, $n - 1$ reciprocal lattice vectors of two-beam interference can be independently chosen for designing the total interference pattern and other fringes are automatically fixed by these vectors. The intensity of the interference attenuates along the *z* axis at the rate of ${\beta_a} + {\beta_b}$.

The basic properties, i.e., pitch and visibility of interference can be elucidated by assuming simple and symmetric two-beam interference as follows. Here, two beams have the same incident angle, i.e., ${\theta_a} = {\theta_b} = \theta $ and the azimuth angle difference $|{\phi_a} - {\phi_b}|= \delta \phi $. The fringe pitch ${d_{ab}}$, which represents the fringe pitch of two-beam interference with ${\hat{{\textbf E}}_a}$ and ${\hat{{\textbf E}}_b}$, can be expressed as

The visibility of fringes formed by each two-beam interference at $z = 0$ is determined by the ratio of amplitudes ${A_a} ({A_b})$ and $|{\hat{{\textbf P}}_a} \cdot {\hat{{\textbf P}}_b}|$. We call the latter term as the visibility factor for convenience. The amplitudes are considered as equal here for simplicity. Figures 2(a) and (b) show the visibility factor $|{\hat{{\textbf P}}_a} \cdot {\hat{{\textbf P}}_b}|$ for ${\theta_a} = {\theta_b} = \theta $ and the azimuth angle difference $|{\phi_a} - {\phi_b}|= \delta \phi $ for P (${\psi_{a,b}} = 0$) and S (${\psi_{a,b}} = \pi /2$) polarizations. It is evident in Fig. 2 that no interference fringes are formed when the two beams are polarized in the perpendicular directions; P-polarized beams satisfy ${\sin ^2}\theta + {\cos ^2}\theta \cos \delta \phi = 0$ and S-polarized beams are incident at $\delta \phi = \pi /2$. In addition, P polarization shows better visibility factor than S polarization in most cases. Therefore, the incident and azimuth angles of multi-beam EWIL should be carefully chosen to improve the interference contrast or suppress unnecessary interferences [25].

We have employed four-beam EWIL to demonstrate the fabrication of microstructures and nanostructures. To simplify the incident condition, the intensity corresponding to the interference of the counterpropagating 4-beams in the same incidence plane with pairs of different incident angles was calculated by Eq. (5) using our experimental parameters ($\lambda = $488 nm, ${n_\textrm{p}} = 1.81$, ${n_\textrm{r}} = 1.70$). The amplitude of all beams was set to ${A_{1 - 4}} = $1 and all the beams were S-polarized (${\psi_{1 - 4}} = $*π*/2). The incident angles and azimuth angles were set as $({\theta_{1 - 4}},{\phi_{1 - 4}}) = $ (70.5°, 0°), (70.5°, 180°), (86.9°, 0°), and (86.9°, 180°). Figure 3 shows the configuration and total intensity distribution of four-beam EWIL. According to Eq. (5), six interference distributions were obtained, which were reduced to four due to symmetrical incident conditions. The four intensity distributions are shown in Figs. 4(a)–4(d), where the fringe pitch is ${d_{12}} = $135 nm, ${d_{34}} = $143 nm, ${d_{13}} = {d_{24}} = $139 nm, and ${d_{14}} = {d_{23}} = $4826 nm, respectively. The attenuation height of each combination is ${({\beta_1} + {\beta_2})^{ - 1}} = $267 nm, ${({\beta_1} + {\beta_3})^{ - 1}} = $102 nm, and ${({\beta_3} + {\beta_4})^{ - 1}} = $63 nm. One of the drawbacks of EWIL is that the attenuation height is less than the wavelength. However, some studies have resolved this issue by utilizing waveguide resonance, which resulted in the aspect ratio as high as 1.8 with a pitch of 111 nm [22]. Anisotropic etching techniques can also improve the aspect ratio of the patterned structure [26]. It was found that the pitch of micro-envelope and fine-fringes corresponded to the fringe pitch of ${d_{13}}( = {d_{24}})$ and averaged pitch of ${d_{12}}, {d_{14}}( = {d_{23}}),\textrm{ and }{d_{34}}$. Therefore, we can design the structures with nano- and micro-periodicity by choosing appropriate reciprocal lattice vectors.

As discussed previously, three reciprocal lattice vectors of two-beam interference can be independently chosen to design the total intensity distribution of four-beam interference. We chose three wavevectors to design the dual-scale structures of 1D micro-fringe covered with 2D nanodots and the combination of 2D microdots and 1D subwavelength fringe. The calculated 1D micro-grating and 2D nanodot pattern are shown in Fig. 5(a). Here, the incident conditions are $({A_{1 - 4}},{\theta_{1 - 4}},{\phi_{1 - 4}},{\psi_{1 - 4}}) = $(1, 77°, 185°, 0°), (1, 77°, 265°, 0°), (1, 77°, 275°, 0°), and (1, 77°, 355°, 0°). The pitch of micro-grating and fine 2D dots are 1.59 µm and 204 nm. This dual-scale pattern has the potential to combine the functions of diffraction gratings and anti-reflection coating. Figure 5(b) shows the 2D microdots and 1D subwavelength grating pattern. The incident conditions are $({A_{1 - 4}},{\theta_{1 - 4}},{\phi_{1 - 4}},{\psi_{1 - 4}}) = $(1, 71°, 315°, 0°), (1, 71°, 225°, 0°), (1, 87°, 315°, 0°), and (1, 87°, 225°, 0°). Microdots are aligned in a face-centered rectangular grid with a period of 5 µm and fine fringes have a pitch of 360 nm.

It may be noted that these subwavelength fringes show form birefringence, which can be applied to waveplates [27]. Therefore, we believe that this structure can be applied to micro-waveplate arrays using the form birefringence. The simulated results in Fig. 5 suggest the feasibility of this method for the fabrication of nano/micro dual-scale structures.

## 3. Experiment

We developed an experimental system to demonstrate the four-beam EWIL technique, which is shown in Fig. 6. A monochromatic and continuous wave (cw) semiconductor laser (Sapphire 488 LP, Coherent) was used as the light source. The beam diameter and the size of exposure spot on the substrate were 0.7 mm and 0.7 mm × 2.0 mm with the incident angle of 80° respectively. The polarization of all the beams was controlled by a half waveplate and polarizer. The output beam was split into four beams by two beam splitters. The incident and azimuth angles of the incident beams were controlled with the precise rotation of the three separate mirrors to generate the four evanescent waves. The cubic glass prism (${\textrm{n}_\textrm{F}}$ =1.81; S-TIH 11, Ohara, Inc.) was aligned to realize total internal reflection (TIR) with a positive tone resist (${\textrm{n}_\textrm{F}}$ =1.70, AZ P1350). In the fabrication process, a quart substrate (SK-1300) was firstly spin-coated by hexamethyldisiloxane (HMDS) for hydrophobization. A resist of 500 nm thickness was spin-coated on the substrate at 6000 rpm. It was then baked at 100°C by a hot plate for 6 minutes to remove the solvent. For facilitating the exposure of evanescent waves on the resist, the top surface of the coated resist was mounted upside down on top of the prism. The gap between the resist and prism was filled with index matching liquid (${\textrm{n}_\textrm{F}}$ =1.81, Cargile Labs) to obtain optical contact between them. The details of the exposure conditions are described later. After the exposure, the resist was developed for 60 s using a commercial developer (AZ Developer). It was then rinsed with distilled water, and the fabricated structures were visualized by atomic force microscopy (AFM).

For simplicity, the azimuth angles of the four evanescent waves were chosen in the same incident plane (*y *= 0), and the azimuth angles were ${\phi_{1,3}} = 0$° and ${\phi_{2,4}} = 180$°, as obtained in the theoretical simulations. The incident angles were adjusted according to the pitch of micro-envelope, which was 12 µm. Consequently, the incident angles were ${\theta_{1,2}} = $71° and $\theta_{3,4} = $76°. The corresponding critical angle was 69.9°. The average incident irradiance of each beam ${\hat{{\textbf E}}_{1,2}}\textrm{ and }{\hat{{\textbf E}}_{3,4}}$ was ∼100 and 170 mW/cm^{2}, respectively, and the exposure dose was ∼540 mJ/cm^{2}. All the four beams were S-polarized. Figure 7 shows the AFM images of the fabricated structures using only two-beam EWIL (${I_{12}}$, ${I_{34}}$) for the confirmation of the desired incident conditions. The fringe pitch in Figs. 7(a) and 7(b) are 143 and 139 nm, which are in excellent agreement with calculated values of 142.6 and 138.9 nm, respectively. These pitches are obtained from the spatial spectrum of long range line-scan AFM data (20 µm scan with 1024 sampling points), which correspond to the interference with exposure NA of 1.71 and 1.76. The cross-sectional profile is not exactly the inverse of the intensity distribution because the developing process is a nonlinear chemical process. The shape can be more accurately simulated by the cellular automaton method [23]. A line and space pattern with a period of 12.5 µm, which is fabricated using the proposed four-beam EWIL, is clearly seen in Fig. 8(a). The AFM images of the fabricated nano/microstructures are shown in Fig. 8(b). Figure 8(c) shows the micro- and nano-fringe profile (A-A’ in Fig. 8(b)), which is averaged over 100 nm width along with the profile; the asymmetry of the image has been removed by the linear fitting. Therefore, the micro-envelope of the nano-grating was not affected by higher order fitting process. The height of fine gratings with a pitch of 140 nm was changed from 12.5 nm to about 0 nm according to the envelope of the intensity distribution.

The procedure for the fabrication of 2D microdots and 1D nano-grating structures is described as follows. The incidence conditions were similar to that used in Fig. 5(b). Azimuth angles were $\phi_{1 - 4} =$ 287.6, 252.4, 288, and 252°. Incident angles were ${\theta_{1,2}}$, ${\theta_{3,4}}$ = 71 and 76°. According to Fig. 2, all the four beams were set to be P-polarized as they exhibit higher interference contrast than S-polarized beams under the above incident and azimuth angles. The calculated intensity distribution of the structure, in which 2D elliptical dots filled with subwavelength fringes (450 nm) are aligned in a face-centered rectangular grid, is shown in Fig. 9(a). The fabricated structures in Fig. 9(b) shows good agreement with the calculated results. The 2D microdot pattern was aligned with periods of 25 and 43 µm and it was tilted by ∼81° due to the misalignment of the incident beams. The norm of the reciprocal lattice vector of the micro-envelope was about 50-100 times smaller than that of the fine fringes. Thus, the pitch and orientation of micro-fringes were more sensitive to alignment errors. The AFM images are shown in Figs. 9(c) and 9(d), and fine 1D fringes are clearly seen in the dots. These structures can be applied to a micro-waveplate arrays using form birefringence. Further, the proposed method can be used for the integration of conventional micro-optical elements like diffraction gratings, computer generated hologram, and micro-lens array with nano-optical elements such as antireflection coatings, form birefringence, and guided mode resonance filters.

## 4. Conclusion

We have demonstrated the fabrication of dual-scale nano/microstructures by multi-beam EWIL using the spatial beats. Theoretical analysis based on the decomposition of each two-beam interference was used to obtain clear insights for the total intensity distribution of four-beam EWIL. The simulated superposed interference patterns had a micro-beat envelope and nano-grating structure with a pitch of less than λ/3, which is a sufficient processing finesse for the fabrication of PhCs and SWSs. In the four-beam interference, three reciprocal lattice vectors of each two-beam interference can be independently designed to obtain desired dual-scale structures by controlling the incident and azimuth angles. For example, 1D micro-/nano-grating, 1D micro-grating covered with a 2D nanodot pattern, and 2D microdots filled with nano-gratings were analyzed, which can be realized experimentally under specific incident conditions. The typical drawbacks of EWIL are limited penetration depth in a photoresist for high aspect-ratio and the requirement of a prism with a large refractive index for large-area fabrication. However, some methods have been proposed to overcome these limitations [22,24], which may facilitate a more flexible fabrication using EWIL. The experimental results showed good agreement with the theoretically calculated 2D interference pattern in the *xy*-plane. The fabricated 1D nano-/micro-grating structures had 140 nm nano-fringes and their height was modulated with a pitch of 13 µm. Another fabricated structure comprised of 2D elliptical dots, which were aligned on a rectangular grid with a period of 25 and 43 µm, filled with 450 nm subwavelength fringes. The multi-beam EWIL method exhibits significant improvement over conventional multi-beam IL, and it is potentially useful for the fabrication of versatile multi-scale structures with sufficiently fine periodicity.

## Funding

Japan Society for the Promotion of Science (JP 15H02214, JP 18J21820); Amada Foundation.

## Acknowledgments

We thank Dr. Kudo (Kansai University) for helpful discussions and comments on the photoresist.

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