1. Introduction

Unique optical properties of two-dimensional periodic nanostructures continues to attract attention of researchers in many areas of optical science and technology [1]. Nowadays, periodic photonic and plasmonic nanostructures are applied in the development of plasmonic lasers [2], light emitting diodes (LEDs) [3], solar cells [4], and surface-enhanced Raman scattering (SERS) spectroscopy [5] or affinity biosensing [6, 7]. Interference lithography (IL) is an established method that enables rapid nanostructuring of the wafer-scale areas using intrinsically periodic interference patterns. The most straightforward IL approach used to produce two-dimensional patterns is based on multiple exposures of the photosensitive layer by the interference pattern formed by two intersecting coherent beams [8]. The IL techniques relying on the exposure by three or four beams were shown to provide higher contrast of the interference pattern with large number of possible lattice symmetries [9, 10]. Furthermore, fabrication of nanostructures with more complicated shapes and subwavelength feature sizes through careful selection of the mutual orientation and polarization of the interfering beams was reported [11, 12]. On the other hand, IL techniques employing more than three beams are known to be more prone to inhomogeneities of the interference pattern caused by even very subtle misalignments of the interfering beams [13, 14].

In various application areas (e.g. plasmonic sensing, solar cells) arrays of nanofeatures (holes, posts, discs, etc.) with dimensions much smaller than the period of the array (i.e. with low fill fraction) are needed. The minimum size of the features depends on the interference pattern contrast as well as the width of the interference maxima which are related to a wavelength and numerical aperture of the interfering beams. For example, IL employing four beams was reported to enable fabrication of periodic plasmonic arrays with features as small as 25% of the array period [13]. It has also been demonstrated that this typical size-to-period ratio can be further reduced by the addition of more coherent beams in order to suppress every second interference maxima of the original interference pattern, yielding an array with a doubled period yet having the same size of the features [15]. The drawback of such approach is the complicated beam alignment as the quality of resulting pattern depends strongly on mutual position, orientation and wavefront quality of all the interfering beams.

Recently, a non-contact optical lithography method based on the displacement Talbot lithography (DTL) has been reported [16, 17]. DTL is based on two-dimensional Talbot effect that is similar to the multiple-beam interference. In DTL, photosensitive samples are exposed to the quasi-periodic distribution of the light intensity (Talbot carpet) behind the transmission (amplitude or phase) mask. During the exposure of the sample, the mask-sample gap is varied to record the integral intensity distribution across the whole Talbot (self-repeating) distance. This approach enables robust and reproducible patterning of wafer-scale areas even on non-flat samples [16].

In this contribution, we present a novel approach to multiple-beam interference lithography enabling the fabrication of macroscopic areas of periodic sparse arrays of nanofeatures exhibiting long-range spatial-phase coherence. This method is based on the interference of eight or more coherent beams generated by the diffraction of large-diameter collimated beam on a transmission phase mask, see Fig. 1(a). The geometry (periods and profile depth) of the phase mask, which is depicted in Fig. 1(b), is designed to provide optimum diffraction efficiencies to all transmitted orders to yield an interference pattern with high contrast and narrow interference maxima, see Fig. 1(c).

 

Fig. 1 Scheme of a multiple-beam interferometric setup (a) used for the exposure of the photosensitive layer with 9 beams (overlap of all beams on the photosensitive sample is highlighted by the dotted line) transmitted through a 2D phase mask (b). The interference pattern (c) with periods Λ_x = Λ_y = 800 nm calculated for the phase mask with periods Λ_G,x = Λ_G,y = 800 nm (K_G = 2π/Λ_G) and linearly polarized incoming laser beam with the wavelength λ = 405 nm.

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This approach enables multiple-beam interference lithography with nearly perfect alignment of a large number of beams, as their mutual positions and directions are determined solely by the properties of the phase mask. Moreover, the high contrast of the interference pattern and utilization of orders with large diffraction angles enables the production of sparse arrays or arrays of arbitrary shaped nanomotifs (rods, dimers, rings, etc.) with high resolution. This can be achieved by changing the position of the photosensitive sample with respect to the phase mask during the exposure, i.e. by “drawing” the desired nanofeatures.

2. Multiple-beam interference patterns

In order to predict the interference pattern formed by multiple coherent collimated beams, each of the incident optical beams could be approximated by a harmonic plane wave with complex amplitude of the n^th wave described as:

In the interferometric setup considered in this work, all beams illuminating the photosensitive sample are transmission orders of the phase mask. Thus, their wave vectors are given by the periods of the phase mask Λ_G,x and Λ_G,y and the wave vector of the incident beam k_inc. The wave vectors of the transmitted orders can be expressed as:

 

Fig. 2 a) Wave vectors of 9 transmitted beams diffracted by a 2D phase mask with periods Λ_G,x and Λ_G,y. Schematic representation of the tangential components of the wave vectors for cases with: b) 13 beams and c) 21 beams. Red dots represents endpoints of the wave vectors of diffraction orders transmitted into the medium with refractive index n_T while the grey dots denote the evanescent orders.

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The number of transmitted diffraction orders (i.e. beams that participate in the multiple beam interference behind the phase mask) depends on the wavelength of the incoming light λ₀, grating vectors K_G,x and K_G,y and refractive index of the medium behind the phase mask n_T as the tangential component of the transmitted order $k^{xy}{}_{m,n}=\sqrt{{(m{K}_{G,x}^{})}^2+{(n{K}_{G,y}^{})}^2}$ has to be smaller than magnitude of the wave vector of the wave propagating in the medium n_T, $k^{xy}{}_{m,n}<k_T=2\pi n_T/{\lambda }_0$.

For the sake of simplicity, let us consider a phase mask with the same periods in both perpendicular directions, i.e. Λ_x = Λ_y = Λ, K_G,x = K_G,y = K_G and n_T = 1. In this case, the condition for existence of 9 transmitted beams may be written as $\sqrt{2}{K}_G<k_T<2K_G\Rightarrow \sqrt{2}{\lambda }_0<{\Lambda }_{9b}<2{\lambda }_0$, for 13 beams: $2{\lambda }_0<{\Lambda }_{13b}<\sqrt{5}{\lambda }_0$, Fig. 2(b), for 21 beams: $\sqrt{5}{\lambda }_0<{\Lambda }_{21b}<2\sqrt{2}{\lambda }_0$, Fig. 2(c), etc. The number of transmission beams taking part in the interference is of crucial importance for both the contrast and geometry of the resulting interference pattern. Examples of the interference patterns calculated for selected numbers of interfering beams are depicted in Fig. 3.

 

Fig. 3 Interference patterns calculated for three different numbers of interfering beams transmitted through the phase mask with period Λ and equal diffraction efficiencies for all beams. a) Λ = 530 nm, 4 beams (zeroth order neglected), b) Λ = 780 nm, 8 beams (zeroth order neglected), c) Λ = 1100 nm, 21 beams (zeroth order included); λ₀ = 405 nm.

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The patterns were calculated using Eqs. (2) and (3) for the wavelength of the incoming light λ = 405 nm. In Fig. 3(a), four orders: [-1,0], [0,-1], [0,1], [1,0], shown in blue in Fig. 2(a) are taken into account, while the [0,0] order is neglected (it is possible to block the zeroth order or to suppress it through the proper design of the phase mask). Due to the equal size of the normal component of the wave vectors of these orders ($k_{m,n}^{\perp }$), the interference pattern is invariant in z. The addition of second quartet of beams: [-1,-1], [-1,1], [1,-1], [1,1], results in more sparse interference pattern, see Fig. 3(b). The destructive interference between the two quartets of transmitted orders results in cancellation of every second interference maximum of the original 4-beam pattern, see Fig. 3(a). The utilization of additional higher orders leads to even sparser interference pattern, see Fig. 3(c).

In general, any interference pattern formed by beams with non-equal sizes of$k_{m,n}^z$will be changing along the z-direction. For example, the interference pattern in Fig. 3(b) is formed by two quartets of the beams [pictured in blue and red colors in Fig. 2(a)] with $k_{blue}^z=\sqrt{k_T^2-K_G^2}$ and $k_{red}^z=\sqrt{k_T^2-2K_G^2}$. The interference pattern is periodically repeating in z with the periodicity (or self-repeating distance)${\Lambda }_z=2\pi /\left(k_b^z-k_r^z\right)$, which is, in this particular case, about 2.3 µm. Similar dependence of the diffraction pattern on the distance from the mask was studied also in case of Talbot effect. In that case, a transmission mask with large period (Λ_G >> λ₀) and thus small diffraction angles is typically used and the use of paraxial approximation, yielding the self-repeating distance of the pattern $z_T=2{\Lambda }_G^2/\lambda$ (Talbot distance), is justified. However, MBIL utilizes also beams with high diffraction angles and thus the paraxial approximation cannot be used [19]. Especially with the increasing number of beams, the z-dependence of the MBIL pattern becomes more complex. The exact self-repeating distance can be determined from the differences between the $k_{m,n}^z$components of all pairs of participating beams $\Delta k_{mn}^z=k_m^z-k_n^z$. Each such pair produces modulation of the interference pattern with the period ${\Lambda }_{mn}^z=2\pi /\Delta k_{mn}^z$. The self-repeating distance than can be expressed as the least common multiple of all these periods ${\Lambda }_{LCM}^z$. In a situation depicted in Fig. 3(c), the interference pattern is formed by 21 beams encompassing 5 groups of beams with different $k_{m,n}^z$. The exact self-repeating distance for this case is astronomically high (~10²⁴ m); however, interference pattern with the contrast close to the optimum one (at z = 0) can be found much more frequently - in distances, where z approaches the integer multiple of the majority of periods${\Lambda }_{mn}^z$. For example, such plane with high-contrast pattern can be found at z = 11.2 µm, see Fig. 3(c). In general, increasing number of interfering beams in MBIL results in more complex behavior of the interference pattern in z direction, but provides stronger confinement of the light into interference pattern with higher contrast and lower fill fraction in the planes parallel with the phase mask.

3. Materials and methods

3.1. Design of the phase mask

As the periodicity and contrast of the interference pattern are dependent on the number of the transmitted diffraction orders and their intensities (given by the diffraction efficiencies), diffraction of the monochromatic light by 2D relief gratings of various surface geometries was theoretically modeled using 2D rigorous coupled wave analysis (RCWA). The diffraction efficiencies can be effectively increased for suitable directions of the diffracted orders through the shape of the grating surface analogously to 1D blazed diffraction gratings. In this work, gratings with 2D sinusoidal surface modulation were considered, as they can be easily manufactured by the two-beam interference lithography.

3.2. Fabrication of the phase mask

The phase masks – relief diffraction gratings with 2D periodic modulation - were fabricated using sequential two-beam IL. In the first step, cleaned polished glass slides were spin-coated with AZ 701 photoresist (Microchemicals, Germany) layer with a final thickness between 500 nm and 1000 nm. The photosensitive layers were then exposed by 1D sinusoidal interference pattern formed by two crossed coherent collimated beams in a Mach-Zehnder interferometer. The light emitted from the coherent UV-Violet laser (λ₀ = 325 nm for IK3031R-C from Kimmon Koha, Japan or λ₀ = 405nm for DL405-40-S from CrystaLaser, USA) was focused, transmitted through a pin-hole, collimated and split using a custom-made beam splitter. Two collimated beams were then redirected by two mirrors to illuminate the photosensitive sample. The period of the interference pattern Λ_G was controlled though the angle between the interfering beams θ and the wavelength of the used laser λ₀: ${\Lambda }_G={\lambda }_0/[2sin(\theta /2)]$. After the first interferometric exposure, the sample was rotated by 90 degrees and the exposure was repeated to yield a 2D sinusoidal pattern in the photoresist layer. The photoresist layer was then baked at a temperature of 160°C for 1 minute and, after cooling down back to the room temperature, developed in AZ 726 developer. The developed layer was bleached using flood exposure with the UV light to increase its transmittance in the subsequent multiple-beam interferometric exposure.

3.3. Multiple-beam interferometric setup

The arrangement of the multiple beam interferometer based on transmission phase mask is depicted in Fig. 4. The beam emitted from a single frequency laser (λ = 405 nm, DL405-40-S from CrystaLaser, USA) was coupled to a polarization maintaining (PM) single-mode optical fiber and transmitted towards a collimating lens. The collimated laser beam was then transmitted through a special wedge prism with the phase mask attached to its back face using refractive index matching oil. The prism and the glass substrates of both the phase mask and the photosensitive sample were made of the same glass (H-ZF1, refractive index 1.68 at 405 nm). This glass was selected to match the refractive index of the used photoresist and thus to reduce the unwanted reflections on the photoresist-glass interfaces. The wedge prism was used to deflect the back reflected light from the exposed photoresist. Substrate with the photosensitive layer was mounted to the nanopositioning stage (P-563.3CD, Physik Instrumente, Germany) in close vicinity (typically between 0.5 mm and 2 mm) to the phase mask and aligned to be parallel to it. To reduce the reflections from the back side of the illuminated sample, another glass (H-ZF1) substrate with opaque and blackened back side was optically connected to the substrate with photosensitive sample during the exposure.

 

Fig. 4 Schematic drawing of the multiple-beam interferometric setup based on a transmission 2D phase mask.

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3.4. Fabrication of plasmonic arrays

Cleaned H-ZF1 glass slides (AW Optics, China) were spin-coated with AZ 701 photoresist (Microchemicals, Germany) diluted with PGMEA to yield a final thickness of about 200 nm. Coated samples were exposed in a multiple-beam interferometric setup and baked at 120°C on a hot plate for 1 minute. Then, samples were let to cool down to a room temperature and developed in AZ 726 developer (MicroChemicals, Germany). The plasmonic gold layer (thickness ~30 nm) was deposited in a vacuum evaporation apparatus (Classic 570 from Pfeiffer, Germany). A thin (~1 nm) layer of titanium was deposited on the substrate prior to the deposition of gold to promote its adhesion to glass. The lift-off step was performed by immersing the samples in an ultrasonically agitated acetone bath (kept at a temperature of 50°C) leaving only gold nanoobjects on glass in places where gold was deposited directly on the surface of glass through the holes in the photoresist layer.

To demonstrate the potential of the proposed method based on multiple-beam interference lithography, we have fabricated 2D periodic plasmonic arrays of different geometries using either single exposure or multiple consecutive exposures of the photosensitive sample.

4. Results

4.1. Single exposure

The simplest 2D nanostructure attainable by the MBIL is a periodic array of nanoobjects with round or elliptical footprint (holes, discs or pillars) defined by the shape of the maxima of the interference pattern. Examples of the prepared plasmonic arrays with three different periods are shown in Fig. 5.

 

Fig. 5 Plasmonic arrays fabricated using three different phase masks with periods a) Λ = 750 nm, b) Λ = 1260 nm and c) Λ = 1800 nm. The SEM micrographs of the prepared arrays are shown before and after the lift-off of the photoresist layer. The theoretical patterns (top) are shown for comparison.

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The geometry of the fabricated arrays shows a good agreement with the patterns predicted using Eq. (2) at the zero distance from the phase mask (z = 0). Amplitudes of the interfering beams (transmission diffraction orders of the phase masks with the periods 750 nm, 1260 nm and 1800 nm) were calculated by the 2D RCWA method, in which the phase masks were approximated by a 2D crossed relief grating with the sinusoidal profile and a modulation depth of 650 nm. The refractive index of the modeled phase mask material at λ = 405 nm was 1.69.

As expected, the periods of the fabricated arrays corresponds to the periods of the phase mask. The size of the holes in the patterned photoresist (and therefore also the size of the plasmonic nanofeatures after lift-off) is affected by the width of the interference maxima, exposure dose and development time. The total exposure doses used in the fabrication of arrays shown in Fig. 5 were following: a) D_9b = 33.7 mJ/cm² for 9 beams, b) D_29b = 52.9 mJ/cm² for 29 beams and c) D_61b = 35.1 mJ/cm² for 61 beams. The exposure dose was determined from the exposure time and the intensity of the collimated beam (measured before entering the prism, see Fig. 4). The minimum dimensions of the nanoobjects in the selected arrays presented in Fig. 5 are around 200 nm, which is in accordance with the diffraction limited width of the interference maxima W_Imax = λ₀/(2nsinθ_max), where n denotes refractive index of air (n = 1), θ_max is the maximum diffraction angle (here θ_max~π/2, sinθ_max~1) and λ₀ is the wavelength (λ₀ = 405 nm). As discussed in section 2, the complexity of the diffraction pattern in the z direction is increasing with an increasing number of interfering beams. This requires precise alignment of the photosensitive sample to be parallel with the phase mask. In our interferometric setup, we were able to control the parallelism of the mask and the photosensitive sample within 10⁻⁴ rad using He-Ne laser beam prior to each exposure. This level of control enabled fabrication of plasmonic arrays across areas as large as several mm².

4.2. Multiple exposures

By virtue of the sparse nature of the multiple-beam interference pattern, the MBIL technique enables recording of arrays of complex-shaped nanostructures by means of several MBIL exposures at distinct positions of the interference pattern on the sample. The position of the interference pattern can be easily altered by changing the mutual position of the phase mask and illuminated sample. The movements of the interference pattern can be done during the exposure or between the consecutive exposures. We have demonstrated this “nano-drawing” capability of the MBIL following the second approach that we selected to avoid the exposure during the settling time of the nanopositioning stage. The photoresist-coated sample was shifted only in the directions parallel to the surface of the phase mask. The distances between the individual positions of the exposure were selected to be smaller than the dimensions of the unit cell of the lattice. The fabricated arrays of selected nano objects (nanodisc dimers, nanorods and bowtie antennas) are shown in Fig. 6.

 

Fig. 6 Fabricated arrays consisting of a) nanodisc dimers, b) nanorods and c) bowtie antennas prepared by multiple exposures of the photoresist layer at different positions of the phase mask with respect to the photosensitive sample. From top to bottom, layout of the designed geometry of the array and SEM micrographs of gold-coated patterned photoresist and final (gold on glass) nanoarrays are shown.

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The arrays of nanomotifs fabricated by combination of 2 to 6 exposures shows a good agreement with the design. Exposure doses at each position of the nanopositioning stage were a) D_dimer = 21.4 mJ/cm² (two exposures), b) D_rod = 15.6 mJ/cm² (three exposures) and c) D_bowtie = 15.6 mJ/cm² (six exposures). The exposure doses were determined in the same manner as described in section 4.1.

5. Discussion

The main advantages of the presented MBIL technique are its simplicity, patterning speed and versatility. Using MBIL, large areas of surface can be patterned by complex periodic nanostructures at relatively low cost with the use of an optical setup utilizing a simple 2D periodic grating (phase mask). While the splitting of laser beam into a set of interfering beams and their exact alignment to form homogeneous high-contrast interference pattern is managed by the phase mask, control of the air gap between the phase mask and photosensitive surface remains a technical challenge. In this work, we did not measure the size of this gap with the precision sufficient to be able to align the photoresist layer with a desired plane in the interference pattern with optimum contrast, see Fig. 3. However, we were able to expose the sample to these optimum-contrast areas of the interference pattern by introducing a slight tilt (less than 1 mrad) between the phase mask and the photosensitive sample. This resulted in up to several mm wide stripes on a photoresist layer that were exposed by an interference pattern with optimum contrast. Furthermore, the real-time imaging of the interference pattern behind the phase mask is possible using standard optical microscopy. We have confirmed feasibility of this active control of the interference pattern contrast; however we did not incorporated it in the presented MBIL interferometric setup. Next generation of the MBIL system will be designed to allow for real-time control of the pattern in the plane of the exposed sample surface.

The presented method is currently capable of fabrication of arrays with the minimum nanoparticle dimensions below 200 nm and interparticle distances around 100 nm. On gold nanoparticles of such dimensions, plasmonic resonances can be excited in the near infrared and shortwave infrared regions. In order to improve the resolution of the MBIL method and to reach resonances in the visible part of the spectrum, several modifications of the MBIL can be considered. As it was already discussed in section 4.1, the resolution of the MBIL is constrained by the width of the interference maxima that can be approximately expressed as W_Imax = λ/(2nsinθ_max). Apparently, a higher resolution can be attained by the use of light with a shorter wavelength. Further improvement can be achieved when a medium of a high refractive index is used to fill the gap between the phase mask and the exposed sample. However, this approach may introduce unwanted contamination of both sample and phase mask (in case of liquid immersion) or hamper the alignment and nanopositioning between the sample and the phase mask (in case of phase mask and the photosensitive layer situated on the opposite sides of a transparent solid material, e.g. glass). Apart from increasing the lithographic resolution through stronger localization of the light around interference maxima, it can be improved also through the use of photoresist with a steeper contrast curve. Through the use of nonlinear or multiphoton photoresists or development process at low temperatures and careful control over the exposure dose, the resolution can be pushed beyond the diffraction limit.

The selected non-contact geometry of the phase mask and a sample separated by an air gap is beneficial not only for the alignment and nanopositioning of the interference pattern on the sample. Contrary to the contact photolithography based on geometrical shadow printing, the resolution is not reduced with the increasing distance from the mask. Furthermore, interference pattern at greater distances from the phase mask is not affected by the point defects of the phase mask as these are not propagated farther than few Talbot distances from the mask [19]. Importantly, the presence of the air gap also prevents the damage of the phase mask and sample during the exposure and manipulation with the sample.

6. Conclusion

In conclusion, we have demonstrated a novel optical nanofabrication technique based on multiple-beam interference lithography and demonstrated that the technique is suitable for rapid fabrication of periodic plasmonic nanostructures with motifs of arbitrary shapes with a deeply sub-micron resolution. Although the fabrication of plasmonic arrays was selected as a showcase of this method, the multiple-beam interference utilizing a 2D transmission phase mask can be performed at broad range of wavelengths and applied to a variety of tasks benefiting from the concentration of light into periodically ordered submicron volumes in two or three dimensions, such as fabrication of periodic structures (photonic crystals, metamaterials, diffractive elements), optical trapping or Talbot grid-based microscopy.