A novel nanofabrication technique based on 4-beam interference lithography is presented that enables the preparation of large macroscopic areas (>50 mm2) of perfectly periodic and defect-free two-dimensional plasmonic arrays of nanoparticles as small as 100 nm. The technique is based on a special interferometer, composed of two mirrors and a sample with photoresist that together form a right-angled corner reflector. In such an interferometer, the incoming expanded laser beam is split into four interfering beams that yield an interference pattern with rectangular symmetry. The interferometer allows setting the periods of the array from about 220 nm to 1500 nm in both directions independently through the rotation of the corner-reflector assembly around horizontal and vertical axes perpendicular to the direction of the incident beam. Using a theoretical model, the implementation of the four-beam interference lithography is discussed in terms of the optimum contrast as well as attainable periods of the array. Several examples of plasmonic arrays (on either glass or polymer substrate layers) fabricated by this technique are presented.
© 2014 Optical Society of America
Periodic nanostructures play an important role in numerous fields of research including optics, plasmonics, and microelectronics with applications such as photonic crystals , optical metamaterials , substrates for plasmonic sensing  or surface enhanced Raman scattering , and many more. Interference lithography (IL) is a powerful technique for the rapid fabrication of wafer-scale periodic nanostructures [5, 6]. Although it does not provide the same flexibility and resolution of electron or ion beam lithography (EBL or IBL), it is superior in terms of patterning speed and coherence of the periodic pattern on scales larger than the one write-field used in EBL or IBL processes (typically several hundreds of micrometers). In applications where a long-range order of the nanostructure is required, IL is also preferred over colloidal (nanosphere) lithography, a bottom-up fabrication technique based on layer of self-assembled nanospheres that acts as a mask for deposition or removal of the material onto or away from the surface of interest . The long-range order of the nanostructures prepared by colloidal lithography is affected by the non-zero size dispersion of the individual building blocks, leading to the formation of defects and the division of the structure into differing domains (typically smaller than 100 µm). In case of IL, the nanostructure homogeneity is dictated by an intrinsically periodic interference pattern limited only by the size of the interferometer optics and coherence length of the laser source, which can be as large as tens of centimeters and tens of meters, respectively. It has been shown that interference patterns with all possible lattice symmetries both in 2D and 3D can be prepared using the interference of three  or four  non-coplanar beams. Several arrangements of three-beam IL, including those utilizing an extended Lloyd’s mirror  or a special optical prism , were reported as efficient tools for the fabrication of large (~cm2) 2D periodic nano-arrays with a hexagonal symmetry. An addition of the fourth beam enables the preparation of arrays with square or rectangular symmetry, but it also complicates the alignment of the interfering beams, as their mutual orientation and phase relations have to be set within very narrow limits [12, 13]. Even a slight deviation from the optimum geometry will result in artifacts and inhomogeneities of the periodic pattern . These technical difficulties can be partially circumvented by applying multiple exposures of only two interfering beams [12, 15], as the two-beam interference is much less sensitive to the angle between the interfering beams; however, this technique yields an interference pattern with a rather poor contrast. Interference of three or more laser beams and careful design of their orientation and polarization improves the pattern contrast, enabling the fabrication of more complex nanostructures having a deeply sub-wavelength features [16–18]. Nevertheless, due to the previously mentioned strong dependence of the pattern homogeneity on the alignment of all interfering beams, implementations of previously reported four-beam IL have demonstrated to yield only small areas of homogeneous nanostructures (typically tens of µm) [16, 19–21].
Here we report a novel technique for fabrication of large areas of defect-free periodic nanostructures based on four-beam interference lithography. The technique utilizes a right-angled corner reflector-like interferometer, which is in fact an extension of the well-known Lloyd’s mirror configuration used for two-beam interference lithography. This proposed configuration allows for the precise alignment of all four interfering beams, and furthermore, enables flexible tuning of their mutual orientation by the rotation of the whole corner reflector with respect to the incident beam. This facilitates the settings of the recorded nanostructure periodicity in both lattice vector directions without the need for realignment of the interferometer mirrors.
In order to calculate the properties and contrast of the four-beam interference pattern, we will approximate each of the incident optical beams as a harmonic plane wave with the complex amplitude of the nth (n = 1,.., 4) wave described as:22].
Let us choose the coordinate system to be coupled with the corner reflector, so that the x and y axis are in directions normal to the mirrors II and I, respectively, and the normal vector of the sample plane is parallel with the z axis, see Fig. 1. In this case, the wave vectors of the incident interfering beams can be written as:Fig. 1(a). The four-beam interference will occur only if the incident beam can be reflected by both mirrors. This is fulfilled when the angles between the incident beam and the corner reflector lie within the ranges of θ = (0, π/2) and φ = [-arctan(cosθ), arctan(cosθ)]. By introducing expressions in Eq. (3) into Eq. (2), one can directly obtain the dependence of the spatial period Λ of the interference pattern in the direction of both the x- and y-axis:
From Eq. (3), it is clear that the beams denoted as 1 and 4, and beams 2 and 3 both lie in the same planes of incidence denoted in Fig. 1(c) as σ14 and σ23, respectively, and the angle of incidence α is the same for all four beams , see Fig. 1(b). The resulting interference pattern has a rectangular symmetry, where the difference between the periods Λxand Λy increases with the angle φ. In the special case of φ = 0, the planes σ14 and σ23 are perpendicular to each other (β = π/2), and the interference pattern has a square symmetry.
Another important parameter of the interference pattern is its contrast. A higher contrast is desirable as it allows for more reproducible preparation of structures with smaller critical dimensions and sharper features (steep sidewalls of the developed photoresist is a crucial prerequisite for reliable lift-off of the sacrificial photoresist layer). For the preparation of periodic nanostructures, it is useful to define the global contrast as Vglobal = (Imax-Igap)/(Imax + Igap), where Imax and Igap are the intensities in the maximum of the interference pattern and local maximum intensity between the two (global) maxima, respectively.
If the mirrors used in the interferometer provide a reflectivity close to 100%, we may approximate the intensities of all four beams incident to the sample to be equal: I1 = I2 = I3 = I4. Furthermore, the phase relations between interfering beams are simplified here, as all four interfering beams originate from (different parts of) a single coherent collimated beam incident on the corner reflector interferometer. The initial phase differences in Eq. (2) would be equal to zero if no phase shifts occurred upon the reflection from the mirrors. The differences among the initial phases are also independent of the orientation of the incident beam (given by anglesand). This can be seen directly in the point x = y = z = 0, where all the four beams coincide. In our calculations, we took into account phase shifts caused by the reflection from each mirror (π and 0 for the TE-polarized and TM-polarized component of the incident wave, respectively). These phase shifts affect both the shape and contrast of the resulting interference pattern, as they cause a change of the direction of the polarization vector e of the reflected wave, thus affecting the contrast coefficients Vmn. The global contrast is then solely dependent on the contrast coefficients Vmn in each of the interference terms, and the initial phases n in Eq. (2) can be omitted. In the optimum case when the vectors of polarization of all incident waves are parallel, it follows that Vmn = 1, for all n,m = 1..4, n≠m, as the Imax = 16Iinc and Igap = 0. In this case the global contrast will reach its maximum value of Vglobal = 1. It is unreasonable to set the polarization of each interfering beam independently (due to the space limitations inside the interferometer); therefore, we will analyze the possibilities to optimize the contrast by only changing the polarization of the incoming beam (before it reaches the corner reflector interferometer). Here we will consider a linear polarization of the incident beam with an arbitrary orientation of the polarization vector described by angle νpol (measured from the vertical direction, i.e. νpol = 0, when the vector of the electric field is parallel to the z-axis for θ = 0 and φ = 0).
Although the ideal conditions, and thus the maximum contrast, are not attainable in real experiment, it is possible to nearly fulfill the parallelism of polarization vectors of all interfering beams under certain circumstances. The first case is the grazing incidence, i.e. α→90° (θ→0), where the polarization of the incoming beam is close to the TM (νpol~0), see Fig. 2(a) and (b). The second case is a nearly normal incident linearly polarized beam, where the optimum global contrast is found also for TM-polarized incoming beam, i.e. νpol = 0,Fig. 2(c). In all of these cases, the global contrast is close to 1, e.g. Vglobal>0.93 for geometries in Fig. 2(a)-(c).
For the angles of incidence between these two extremes, it is somewhat difficult to find an optimum polarization state to optimize the global contrast. Let us consider an example of θ = 30° (and φ = 0 = > β = 90°). In this case, the TM-polarized incident beam will yield a slightly skewed interference pattern, shown in Fig. 2(d), with the global contrast below its optimum value of Vglobal>0.7, which would be obtained when the polarization plane of the incoming beam is declined by angle νpol = 21°, see Fig. 2(e). The global contrast in this optimized geometry is still considerably higher than that obtained via sequential two-beam interference lithography, where a 1D interference pattern is recorded twice into a photoresist with the second exposure having the interference pattern perpendicular to the first one . In such situation, the maximum global contrast is Vglobal = 1/3 as the intensity between the maxima fulfills Igap = Imax/2, see Fig. 2(f).
3. Materials and methods
3.1. Interferometer setup
A custom made corner reflector-like interferometer was used for the exposure of the photoresist-coated samples. A simplified scheme of the optical layout is shown in Fig. 3(a). A beam from He-Cd laser (IK3031R-C, from Kimmon Koha, Japan) emitting a linearly polarized light with vertical orientation and 325 nm wavelength was transmitted through the half-wave plate and wire-grid polarizer to obtain the desired rotation of the polarization plane. The beam was then focused using a UV objective (LMU-40X-NUV from Thorlabs), and transmitted through a 10 μm diameter pin-hole to improve its spatial coherence. The divergent beam was subsequently collimated using a special custom made optical doublet lens with corrected spherical aberration (VOD Turnov, Czech Republic) and impinged on an interferometer, where the parts of the beam reflected from the dielectric mirrors (6 cm x 10 cm, reflectivity >90% for angles of incidence up to 60 deg) interfered with the part of the beam, which was impinging on the photoresist layer directly, resulting in a four-beam interference. The whole right-angled corner reflector assembly was mounted on a custom made rotation platform depicted in Fig. 3(b) that allowed rotation of the interferometer around the horizontal and vertical axes by angles θ and φ.
3.2. Alignment of the interferometer
The preparation of large areas of periodic nano-arrays requires the precise alignment of the interfering beams. It is worth noting here that the interference pattern formed by four beams in a right-angled corner-reflector interferometer is invariant in the direction of z-axis, as the z-components of the wave vectors are identical, see Eq. (3). This means that the orientation of the photoresist-coated sample and its perpendicularity to the mirrors is not critical and small deviations result only in negligible variations in the periods of the recorded pattern. The most critical parameter influencing the quality of the resulting interference pattern is the angle between two interferometer mirrors. When the angle differs from 90° by a small angle γdev, it can be shown that the interference pattern will be altered in one direction, resulting in a Moirè-like pattern made of interference patterned stripes of high contrast as well as intermediate zones between those stripes where the contrast is poor, see Fig. 4(a). Each stripe is shifted by Λ/2 in the perpendicular direction and the period of these fringes is ΛM = Λ/(2sin2γdev), (Λ = Λx and Λ = Λy for patterns closer to the mirror I and II, respectively, see Fig. 1). Considering this, we can directly derive the maximum deviation γdev for given dimensions of the nanostructure, where we need the contrast to be within certain limits. For example, when we demand the interference pattern Vglobal to be better than 80% of its optimum value (optimum contrast can be found in the center of each stripe, at y = mΛM, where m is integer) within the stripe at least 1 mm wide, the period of the stripes ΛM would have to be at least 4 mm. With this assumption with a period of the structure having e.g. Λx = Λy = 400 nm, the deviation of the mirrors has to be less than 25 μrad.
The precise adjustment of the right angle between the interferometer mirrors can be done using a special interferometric approach, see Fig. 4(b). We used a special shear plate, a slightly wedged glass plate, to generate the interference fringes. The interferometer was rotated so that the both mirrors were oriented vertically (θ = 0). The waves reflected from both mirrors were than directed back to the shear plate and after the reflection on its front and back surfaces they illuminated the screen where the interference pattern was formed, see Fig. 4(b). The slope and spacing of the interference fringes formed in the areas denoted as I, II and III were set to be identical by the adjustment of the angle between the interferometer mirrors. Using this interference-based alignment technique in combination with the fine screw-driven adjustment of the mirror tilt, it was possible to control the angular deviation of the mirrors γdev to be smaller than 10 μrad.
3.3. Fabrication procedure
Standard microscope glass slides or polished slides made of SF2 glass (Schott, Malaysia) were used as substrates. Prior to the spin-coating with photoresist, all substrates were cleaned in a UV ozone cleaner (UVO cleaner 42, Jelight, USA) for 20 minutes, followed by rinsing in ethanol and DI water and drying by a N2 stream. A high-resolution positive photoresist AZ 701 MiR (MicroChemicals GmbH, Germany) was diluted with PGMEA (AZ EBR solvent) so that a layer with a desired thickness (from 160 nm to 650 nm) could be prepared using a spin-coater (SCS G3, Specialty coating systems, USA). After spin-coating, the samples were soft-baked at 95°C for 60s on a hotplate, followed by laser exposure in the interferometer (see section 3.1), post-exposure bake on a hotplate for 60s at 110°C and development in AZ 726 MIF (also from MicroChemicals GmbH), see Fig. 5.
Nanostructured surfaces of the samples were then inserted into a thermal evaporator apparatus PLS 570 (Pfeiffer, Germany) onto a tilted rotating sample holder and coated with an SiO2 contact mask (Fig. 5, step 3) to restrict the size of the openings in the photoresist and shield the photoresist sidewalls for the subsequent deposition of the plasmonic metal (gold). In cases where the sidewalls of the developed photoresist were steep enough and it was not desired to decrease the size of the individual nano-features to be fabricated, the gold layer was deposited directly onto bare photoresist layer, without the use of the masking layer. In the last step, the sacrificial layers (photoresist and contact mask) were lifted-off in an acetone bath (50°C) assisted by 80 kHz ultrasonic agitation for several minutes.
4. Results and discussion
In order to demonstrate the possibilities and versatility of the four-beam interference lithography implemented using a corner reflector-like interferometer, we fabricated several macroscopic periodic plasmonic arrays and characterized them morphologically by both scanning electron microscopy (SEM) and atomic force microscopy (AFM). The periods of the arrays were set by the choice of the orientation of the corner-reflector interferometer with respect to the incoming laser beam (angles θ and φ) according to Eq. (4). The range of the incident angle θ was limited to be approximately 10°<θ<80° for φ = 0 due to geometrical restrictions during the exposure, as the area of the photoresist exposed by all four beams was decreased considerably for angles outside this interval. In cases where φ≠0 the usable range of θ is proportionally lower. These geometric restrictions limit the attainable periods to about 220-1500 nm. For the arrangement of each interferometric exposure, an optimum declination of the linear polarization from the vertical direction νpol was selected in order to maximize the contrast of the interference pattern. Optical exposure doses defined here as Dinc = Iinc.te, where Iinc is intensity of the incoming beam before its incidence on the interferometer and te is exposure time, were within the range (10.2-17.1) mJ/cm2. The results of the theoretical calculations indicate that the intensity of the maxima of the interference pattern is about 12 to 16-times higher than Iinc (for ideal mirrors, see Fig. 2); therefore, the estimated exposure doses at those maxima were within Dmax = (110-200) mJ/cm2, which was sufficient for the clearing of the photoresist.
Before conducting the entire fabrication procedure (see section 3.3), the interferometric exposure step was performed multiple times with different settings, thus yielding different geometries of the fabricated nanostructures to verify the accuracy of the theoretical calculations used to model the interference pattern (based on Eqs. (2) and (3) with input parameters θ, φ and νpol). Examples of the patterned photoresist layers measured by the AFM and corresponding calculated interference patterns are shown in Fig. 6. Photoresist layers with thicknesses of 250 nm Fig. 6(a) and (b) and 620 nm Fig. 6(c) were used. Due to the precise alignment of the interferometer mirrors, it was possible to prepare periodically nanostructured photoresist without defects on area larger than 50 mm2.
To demonstrate the capability of the proposed four-beam interference technique to produce large areas of periodic patterns without defects, a nanostructured photoresist layer was prepared on a silicon wafer and subsequently coated by a gold film (to improve contrast in SEM measurements). Figure 7(a) shows a photograph of a nanopatterned surface having defect-free periodic structures (marked with a red dashed line) over an area of more than 60 mm2. SEM micrographs collected from six different locations within this area are shown in Fig. 7(b).
The periods of the structures do not change throughout much larger areas (~cm2); however, the shape and size of the individual nanoholes are slightly modulated with increasing distance from the point (x = y = z = 0) coinciding with the bottom right corner of the sample in Fig. 7(a). This is most likely a consequence of the aberration of the wavefronts of the interfering beams, caused by the collimation of the large-diameter incident beam and its reflection on the imperfectly planar mirrors. The effect of these slight deviations from ideal planar wavefronts on the quality of the interference pattern increases with the distance from the point x = y = z = 0, where the interference of beams originating from more distant (and thus more dissimilar) parts of the wavefront of the initial large-diameter beam is taking place.
Plasmonic arrays were fabricated from the nanostructured photoresist by gold deposition through the periodically arranged holes, with a subsequent lift-off of the photoresist layer. Due to the high contrast of the photoresist pattern, the sidewalls of the nanostructured photoresist were steep enough to enable successful lift-off even without the use of a contact mask [Fig. 5, (step 3)]. Examples of the plasmonic arrays prepared by direct deposition of the gold layer on the nanostructured photoresist are shown in Fig. 8. It is worth noting that due to the absence of the dry etching step, which is often included in other nanofabrication techniques (e.g. IL techniques with poor contrast or hole-mask colloidal lithography), plasmonic arrays can be prepared using the proposed 4-beam IL-based technique on a broader range of materials including polymers that would be attacked by a dry etching. The utilization of polymer bottom layers can be useful in certain applications; for example, in affinity sensing on plasmonic arrays in a refractive index-symmetric environment, where the presence of a low refractive index layer below the plasmonic array is desirable . The capability of the 4-beam IL technique to prepare plasmonic arrays on top of a low-index polymer Cytop (AGC, Japan) is demonstrated in Fig. 8(b).
Characterization of the plasmonic arrays prepared by the direct deposition of gold onto a nanostructured photoresist revealed that the lower limit of the size of the individual nano-features was about 40% of the array period. However, for applications where a smaller ratio of the feature size to array period is demanded, certain modifications of the fabrication procedure can be used (e.g. utilization of a photoresist with more non-linear photosensitivity or wet development performed at lower temperatures). Here we utilize a technique based on the deposition of an additional masking layer that constricts the openings in the nanostructured photoresist layer, through which the plasmonic metal is deposited in the last step of the fabrication procedure. This additional step also improves the reproducibility of the lift-off process, as the masking layer shields the sidewalls of the photoresist during the gold deposition, which leaves the sidewalls accessible for the solvent used to remove the photoresist. Micrographs of the plasmonic arrays prepared on an SF2 glass substrate with the assistance of a contact mask taken before and after the lift-off of the sacrificial layers are shown in Fig. 9. Interferometric exposure was performed under the incidence angles θ = 44°, φ = 0.5°by a linearly polarized beam with νpol = 35°. The exposure dose was Dinc = 12.65 mJ/cm2 and the development time td = 20s. Nanostructured photoresist (with the initial thickness of 160 nm) was then coated with a contact SiO2 mask on a rotating holder tilted by 75° with respect to the SiO2 deposition source. A gold layer with a thickness of 50 nm was deposited onto a mask-coated photoresist from the direction of a surface normal [Fig. 9(a)] followed by the lift-off of the sacrificial layers. This technique yielded periodic plasmonic arrays with a decreased size of the individual nano-features, down to 25% of the period [Fig. 9(b)-(d)].
In order to assess their ability to support localized surface plasmons, the fabricated plasmonic arrays were characterized by optical spectroscopy. For this characterization we used a sample prepared under similar conditions as that shown in Fig. 9, saved for a longer development of td = 30s, which resulted in slightly larger dimensions of the individual nanoparticles (91 nm × 125 nm). The transmission spectra collected over a 5 mm2 area of the sample are shown in Fig. 10, where the polarization of the incoming light was along both the longer and shorter axes of the nanoparticles. The spectra calculated using the finite-difference time-domain (FDTD) method (FDTD Solutions from Lumerical Solutions Inc., Canada) are shown for comparison (dashed lines).
The spectral dips in Fig. 10 correspond to two modes of localized surface plasmons excited by two orthogonally polarized incident optical waves, present due to the elliptical shape of the individual nanoparticles. The measured spectra show good repeatability across different locations of the sample, confirming the homogeneity of the plasmonic array within the area of examination. The comparison with the calculated spectra reveals that the experimentally measured dips are broader and shallower with respect to theoretical calculations. We believe that these differences are primarily due to the size dispersion of the individual nanoparticles, with additional differences stemming from the roughness of the nanoparticle surfaces - an effect that was not included in the theoretical model.
We have presented a novel technique for fabrication of large areas of perfectly periodic plasmonic arrays based on 4-beam interference lithography utilizing a special corner reflector-like interferometer. The method was analyzed theoretically using a 4-beam interference model, and the possibility to attain an interference pattern with high contrast was shown for various geometries of the interferometric exposure. The potential of this technique to fabricate defect-free macroscopic plasmonic arrays with rectangular symmetry was demonstrated through the fabrication of several nano-arrays of different periods prepared on different types of substrates, including low-index polymer layer. The smallest dimensions of the individual nano-features in the fabricated arrays were about 40% of the array period in the case of direct deposition of the plasmonic metal through the patterned photoresist, and about 25% when an additional contact SiO2 mask was used to reduce the cross-section of the holes in photoresist. This interferometric method required a precise alignment of the angle between the interferometric mirrors, a variable that drastically affects the quality of the resulting pattern. Precise alignment of this angle enabled the successful fabrication of homogeneous plasmonic arrays on an area larger than 50 mm2. The attainable periods of the arrays with the used laser source (λ = 325 nm) ranged from 220 to 1500 nm, and could be easily changed by a simple rotation of the whole interferometer with respect to the incident beam without the necessity of realignment of the interferometer mirrors. Prepared samples were characterized morphologically using both atomic force and scanning electron microscopies. Based on the presented results and flexibility of the adjustment of the interference exposure geometry, this technique is expected to be used as a powerful and flexible tool for the rapid fabrication and optimization of truly macroscopic and defect-free plasmonic arrays.
This research was supported by Praemium Academiae of the Academy of Sciences of the Czech Republic and the Czech Science Foundation (contract P205/12/G118).
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