Flexible method based on four-beam interference lithography for fabrication of large areas of perfectly periodic plasmonic arrays M. Vala and J. Homola* Institute of Photonics and Electronics, ASCR, Chaberská 57, Prague, Czech Republic *[email protected]
Abstract: 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 OCIS codes: (260.3160) Interference; (220.3740) Lithography; (220.4610) Optical fabrication; (250.5403) Plasmonics.
References and links 1.
J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light 2nd Edition, 1–286 (Princeton University Press, 2008). 2. W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications, 1–200 (Springer, 2010). 3. M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008). 4. M. L. Jin, V. Pully, C. Otto, A. van den Berg, and E. T. Carlen, “High-Density Periodic Arrays of Self-Aligned Subwavelength Nanopyramids for Surface-Enhanced Raman Spectroscopy,” J. Phys. Chem. C 114(50), 21953– 21959 (2010). 5. S. R. J. Brueck, “Optical and interferometric lithography - Nanotechnology enablers,” P IEEE 93(10), 1704– 1721 (2005). 6. J. H. Seo, J. H. Park, S. I. Kim, B. J. Park, Z. Q. Ma, J. Choi, and B. K. Ju, “Nanopatterning by Laser Interference Lithography: Applications to Optical Devices,” J. Nanosci. Nanotechnol. 14(2), 1521–1532 (2014). 7. X. Y. Zhang, A. V. Whitney, J. Zhao, E. M. Hicks, and R. P. Van Duyne, “Advances in contemporary nanosphere lithographic techniques,” J. Nanosci. Nanotechnol. 6(7), 1920–1934 (2006). 8. L. Z. Cai, X. L. Yang, and Y. R. Wang, “Interference of three noncoplanar beams: patterns, contrast and polarization optimization,” J. Mod. Opt. 49(10), 1663–1672 (2002). 9. L. Z. Cai, X. L. Yang, and Y. R. Wang, “All fourteen Bravais lattices can be formed by interference of four noncoplanar beams,” Opt. Lett. 27(11), 900–902 (2002). 10. J. de Boor, N. Geyer, U. Gösele, and V. Schmidt, “Three-beam interference lithography: upgrading a Lloyd’s interferometer for single-exposure hexagonal patterning,” Opt. Lett. 34(12), 1783–1785 (2009). 11. L. J. Wu, Y. C. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, “Fabrication of large area two- and threedimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86(24), 241102 (2005). 12. A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney, and M. D. Perry, “Methods for fabricating arrays of holes using interference lithography,” J. Vac. Sci. Technol. B 15(6), 2439–2443 (1997).
#212311 - $15.00 USD (C) 2014 OSA
Received 19 May 2014; revised 10 Jul 2014; accepted 13 Jul 2014; published 25 Jul 2014 28 July 2014 | Vol. 22, No. 15 | DOI:10.1364/OE.22.018778 | OPTICS EXPRESS 18778
13. A. Fernandez and D. W. Phillion, “Effects of phase shifts on four-beam interference patterns,” Appl. Opt. 37(3), 473–478 (1998). 14. M. Ellman, A. Rodriguez, N. Perez, M. Echeverria, Y. K. Verevkin, C. S. Peng, T. Berthou, Z. Wang, S. M. Olaizola, and I. Ayerdi, “High-power laser interference lithography process on photoresist: Effect of laser fluence and polarisation,” Appl. Surf. Sci. 255(10), 5537–5541 (2009). 15. N. D. Lai, W. P. Liang, J. H. Lin, C. C. Hsu, and C. H. Lin, “Fabrication of two- and three-dimensional periodic structures by multi-exposure of two-beam interference technique,” Opt. Express 13(23), 9605–9611 (2005). 16. X. Zhang, M. Theuring, Q. Song, W. D. Mao, M. Begliarbekov, and S. Strauf, “Holographic Control of Motive Shape in Plasmonic Nanogap Arrays,” Nano Lett. 11(7), 2715–2719 (2011). 17. X. Zhang and S. Strauf, “Formation of triplet and quadruplet plasmonic nanoarray templates by holographic lithography,” Appl. Phys. Lett. 102, 093110 (2013). 18. W. D. Mao, G. Q. Liang, H. Zou, and H. Z. Wang, “Controllable fabrication of two-dimensional compound photonic crystals by single-exposure holographic lithography,” Opt. Lett. 31(11), 1708–1710 (2006). 19. A. Rodriguez, M. Echeverria, M. Ellman, N. Perez, Y. K. Verevkin, C. S. Peng, T. Berthou, Z. B. Wang, I. Ayerdi, J. Savall, and S. M. Olaizola, “Laser interference lithography for nanoscale structuring of materials: From laboratory to industry,” Microelectron. Eng. 86(4-6), 937–940 (2009). 20. H. H. Solak, C. David, J. Gobrecht, L. Wang, and F. Cerrina, “Four-wave EUV interference lithography,” Microelectron. Eng. 61–62, 77–82 (2002). 21. H. H. Solak, C. David, J. Gobrecht, L. Wang, and F. Cerrina, “Multiple-beam interference lithography with electron beam written gratings,” J. Vac. Sci. Technol. B 20(6), 2844–2848 (2002). 22. J. L. Stay and T. K. Gaylord, “Contrast in four-beam-interference lithography,” Opt. Lett. 33(13), 1434–1436 (2008). 23. B. Auguie, X. M. Bendana, W. L. Barnes, and F. J. G. de Abajo, “Diffractive arrays of gold nanoparticles near an interface: Critical role of the substrate,” Phys. Rev. B 82(15), 155447 (2010).
1. Introduction Periodic nanostructures play an important role in numerous fields of research including optics, plasmonics, and microelectronics with applications such as photonic crystals [1], optical metamaterials [2], substrates for plasmonic sensing [3] or surface enhanced Raman scattering [4], 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 [7]. 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 [8] or four [9] non-coplanar beams. Several arrangements of three-beam IL, including those utilizing an extended Lloyd’s mirror [10] or a special optical prism [11], 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 [14]. 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 #212311 - $15.00 USD (C) 2014 OSA
Received 19 May 2014; revised 10 Jul 2014; accepted 13 Jul 2014; published 25 Jul 2014 28 July 2014 | Vol. 22, No. 15 | DOI:10.1364/OE.22.018778 | OPTICS EXPRESS 18779
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 rightangled 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. 2. Theory 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: E n = En en exp ( ikn ⋅ r + φn ) ,
(1)
where En is a real amplitude of the electric field, en is a unit vector of polarization, kn is a wave vector ( kn = kn0 2π / λ , kn0 is a unit vector in the direction of kn and λ is a wavelength), and φ n is the initial phase. In our case, where four coherent waves are all present at some point r, the total intensity given by the interference of these four waves can be written as: 4
4
I ( r ) = Em2 + 2 Em En Vmn cos ( km − kn ) ⋅ r + φm − φn , m =1
(2)
m=2 n0.93 for geometries in Fig. 2(a)-(c).
Fig. 2. Calculated interference patterns for λ = 325 nm and different angles of incidence and declinations of the polarization plane νpol of the incoming beam: a) θ = 5°, φ = 0, νpol = 5°, b) θ = 5°, φ = 25°, νpol = 0, c) θ = 75°, φ = 0, νpol = 0, d) θ = 30°, φ = 0, νpol = 0, e) θ = 30°, φ = 0, νpol = 21°. Interference pattern obtained by superimposition of two, two-beam interference patterns (angle between coherent beams in each of two-beam interference is 90°) perpendicular to each other (f).
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 #212311 - $15.00 USD (C) 2014 OSA
Received 19 May 2014; revised 10 Jul 2014; accepted 13 Jul 2014; published 25 Jul 2014 28 July 2014 | Vol. 22, No. 15 | DOI:10.1364/OE.22.018778 | OPTICS EXPRESS 18782
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 [15]. 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.
Fig. 3. a) Layout of the 4-beam interferometer based on right-angle corner reflector-like interferometer made of two mirrors and base plate with the photoresist-coated substrate. b) Photograph of the corner reflector-like interferometer with two rotation axes.
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
#212311 - $15.00 USD (C) 2014 OSA
Received 19 May 2014; revised 10 Jul 2014; accepted 13 Jul 2014; published 25 Jul 2014 28 July 2014 | Vol. 22, No. 15 | DOI:10.1364/OE.22.018778 | OPTICS EXPRESS 18783
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.
Fig. 4. a) Modulation of the interference pattern as a consequence of the misalignment of the mirrors by γdev = 2 deg. b) Scheme of the optical adjustment of the perpendicularity of the interferometer mirrors using a shear plate (transparent plate with the front and back surface oriented to form a slight wedge).
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 spincoater (SCS G3, Specialty coating systems, USA). After spin-coating, the samples were softbaked 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.
#212311 - $15.00 USD (C) 2014 OSA
Received 19 May 2014; revised 10 Jul 2014; accepted 13 Jul 2014; published 25 Jul 2014 28 July 2014 | Vol. 22, No. 15 | DOI:10.1364/OE.22.018778 | OPTICS EXPRESS 18784
Fig. 5. Scheme of the fabrication procedure used herein: 4-beam interferometric exposure (1), wet development (2), optional deposition of a contact mask (3), deposition of plasmonic metal (4), and lift-off of the sacrificial layers with or without the contact mask (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°
Abstract: 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 OCIS codes: (260.3160) Interference; (220.3740) Lithography; (220.4610) Optical fabrication; (250.5403) Plasmonics.
References and links 1.
J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light 2nd Edition, 1–286 (Princeton University Press, 2008). 2. W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications, 1–200 (Springer, 2010). 3. M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008). 4. M. L. Jin, V. Pully, C. Otto, A. van den Berg, and E. T. Carlen, “High-Density Periodic Arrays of Self-Aligned Subwavelength Nanopyramids for Surface-Enhanced Raman Spectroscopy,” J. Phys. Chem. C 114(50), 21953– 21959 (2010). 5. S. R. J. Brueck, “Optical and interferometric lithography - Nanotechnology enablers,” P IEEE 93(10), 1704– 1721 (2005). 6. J. H. Seo, J. H. Park, S. I. Kim, B. J. Park, Z. Q. Ma, J. Choi, and B. K. Ju, “Nanopatterning by Laser Interference Lithography: Applications to Optical Devices,” J. Nanosci. Nanotechnol. 14(2), 1521–1532 (2014). 7. X. Y. Zhang, A. V. Whitney, J. Zhao, E. M. Hicks, and R. P. Van Duyne, “Advances in contemporary nanosphere lithographic techniques,” J. Nanosci. Nanotechnol. 6(7), 1920–1934 (2006). 8. L. Z. Cai, X. L. Yang, and Y. R. Wang, “Interference of three noncoplanar beams: patterns, contrast and polarization optimization,” J. Mod. Opt. 49(10), 1663–1672 (2002). 9. L. Z. Cai, X. L. Yang, and Y. R. Wang, “All fourteen Bravais lattices can be formed by interference of four noncoplanar beams,” Opt. Lett. 27(11), 900–902 (2002). 10. J. de Boor, N. Geyer, U. Gösele, and V. Schmidt, “Three-beam interference lithography: upgrading a Lloyd’s interferometer for single-exposure hexagonal patterning,” Opt. Lett. 34(12), 1783–1785 (2009). 11. L. J. Wu, Y. C. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, “Fabrication of large area two- and threedimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86(24), 241102 (2005). 12. A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney, and M. D. Perry, “Methods for fabricating arrays of holes using interference lithography,” J. Vac. Sci. Technol. B 15(6), 2439–2443 (1997).
#212311 - $15.00 USD (C) 2014 OSA
Received 19 May 2014; revised 10 Jul 2014; accepted 13 Jul 2014; published 25 Jul 2014 28 July 2014 | Vol. 22, No. 15 | DOI:10.1364/OE.22.018778 | OPTICS EXPRESS 18778
13. A. Fernandez and D. W. Phillion, “Effects of phase shifts on four-beam interference patterns,” Appl. Opt. 37(3), 473–478 (1998). 14. M. Ellman, A. Rodriguez, N. Perez, M. Echeverria, Y. K. Verevkin, C. S. Peng, T. Berthou, Z. Wang, S. M. Olaizola, and I. Ayerdi, “High-power laser interference lithography process on photoresist: Effect of laser fluence and polarisation,” Appl. Surf. Sci. 255(10), 5537–5541 (2009). 15. N. D. Lai, W. P. Liang, J. H. Lin, C. C. Hsu, and C. H. Lin, “Fabrication of two- and three-dimensional periodic structures by multi-exposure of two-beam interference technique,” Opt. Express 13(23), 9605–9611 (2005). 16. X. Zhang, M. Theuring, Q. Song, W. D. Mao, M. Begliarbekov, and S. Strauf, “Holographic Control of Motive Shape in Plasmonic Nanogap Arrays,” Nano Lett. 11(7), 2715–2719 (2011). 17. X. Zhang and S. Strauf, “Formation of triplet and quadruplet plasmonic nanoarray templates by holographic lithography,” Appl. Phys. Lett. 102, 093110 (2013). 18. W. D. Mao, G. Q. Liang, H. Zou, and H. Z. Wang, “Controllable fabrication of two-dimensional compound photonic crystals by single-exposure holographic lithography,” Opt. Lett. 31(11), 1708–1710 (2006). 19. A. Rodriguez, M. Echeverria, M. Ellman, N. Perez, Y. K. Verevkin, C. S. Peng, T. Berthou, Z. B. Wang, I. Ayerdi, J. Savall, and S. M. Olaizola, “Laser interference lithography for nanoscale structuring of materials: From laboratory to industry,” Microelectron. Eng. 86(4-6), 937–940 (2009). 20. H. H. Solak, C. David, J. Gobrecht, L. Wang, and F. Cerrina, “Four-wave EUV interference lithography,” Microelectron. Eng. 61–62, 77–82 (2002). 21. H. H. Solak, C. David, J. Gobrecht, L. Wang, and F. Cerrina, “Multiple-beam interference lithography with electron beam written gratings,” J. Vac. Sci. Technol. B 20(6), 2844–2848 (2002). 22. J. L. Stay and T. K. Gaylord, “Contrast in four-beam-interference lithography,” Opt. Lett. 33(13), 1434–1436 (2008). 23. B. Auguie, X. M. Bendana, W. L. Barnes, and F. J. G. de Abajo, “Diffractive arrays of gold nanoparticles near an interface: Critical role of the substrate,” Phys. Rev. B 82(15), 155447 (2010).
1. Introduction Periodic nanostructures play an important role in numerous fields of research including optics, plasmonics, and microelectronics with applications such as photonic crystals [1], optical metamaterials [2], substrates for plasmonic sensing [3] or surface enhanced Raman scattering [4], 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 [7]. 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 [8] or four [9] non-coplanar beams. Several arrangements of three-beam IL, including those utilizing an extended Lloyd’s mirror [10] or a special optical prism [11], 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 [14]. 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 #212311 - $15.00 USD (C) 2014 OSA
Received 19 May 2014; revised 10 Jul 2014; accepted 13 Jul 2014; published 25 Jul 2014 28 July 2014 | Vol. 22, No. 15 | DOI:10.1364/OE.22.018778 | OPTICS EXPRESS 18779
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 rightangled 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. 2. Theory 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: E n = En en exp ( ikn ⋅ r + φn ) ,
(1)
where En is a real amplitude of the electric field, en is a unit vector of polarization, kn is a wave vector ( kn = kn0 2π / λ , kn0 is a unit vector in the direction of kn and λ is a wavelength), and φ n is the initial phase. In our case, where four coherent waves are all present at some point r, the total intensity given by the interference of these four waves can be written as: 4
4
I ( r ) = Em2 + 2 Em En Vmn cos ( km − kn ) ⋅ r + φm − φn , m =1
(2)
m=2 n0.93 for geometries in Fig. 2(a)-(c).
Fig. 2. Calculated interference patterns for λ = 325 nm and different angles of incidence and declinations of the polarization plane νpol of the incoming beam: a) θ = 5°, φ = 0, νpol = 5°, b) θ = 5°, φ = 25°, νpol = 0, c) θ = 75°, φ = 0, νpol = 0, d) θ = 30°, φ = 0, νpol = 0, e) θ = 30°, φ = 0, νpol = 21°. Interference pattern obtained by superimposition of two, two-beam interference patterns (angle between coherent beams in each of two-beam interference is 90°) perpendicular to each other (f).
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 #212311 - $15.00 USD (C) 2014 OSA
Received 19 May 2014; revised 10 Jul 2014; accepted 13 Jul 2014; published 25 Jul 2014 28 July 2014 | Vol. 22, No. 15 | DOI:10.1364/OE.22.018778 | OPTICS EXPRESS 18782
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 [15]. 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.
Fig. 3. a) Layout of the 4-beam interferometer based on right-angle corner reflector-like interferometer made of two mirrors and base plate with the photoresist-coated substrate. b) Photograph of the corner reflector-like interferometer with two rotation axes.
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
#212311 - $15.00 USD (C) 2014 OSA
Received 19 May 2014; revised 10 Jul 2014; accepted 13 Jul 2014; published 25 Jul 2014 28 July 2014 | Vol. 22, No. 15 | DOI:10.1364/OE.22.018778 | OPTICS EXPRESS 18783
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.
Fig. 4. a) Modulation of the interference pattern as a consequence of the misalignment of the mirrors by γdev = 2 deg. b) Scheme of the optical adjustment of the perpendicularity of the interferometer mirrors using a shear plate (transparent plate with the front and back surface oriented to form a slight wedge).
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 spincoater (SCS G3, Specialty coating systems, USA). After spin-coating, the samples were softbaked 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.
#212311 - $15.00 USD (C) 2014 OSA
Received 19 May 2014; revised 10 Jul 2014; accepted 13 Jul 2014; published 25 Jul 2014 28 July 2014 | Vol. 22, No. 15 | DOI:10.1364/OE.22.018778 | OPTICS EXPRESS 18784
Fig. 5. Scheme of the fabrication procedure used herein: 4-beam interferometric exposure (1), wet development (2), optional deposition of a contact mask (3), deposition of plasmonic metal (4), and lift-off of the sacrificial layers with or without the contact mask (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°
