A simple and efficient optical interference method for fabricating high quality two- and three-dimensional (2D and 3D) periodic structures is demonstrated. Employing multi-exposure of two-beam interference technique, different types of periodic structures are created depending on the number of exposure and the rotation angle of the sample for each exposure. Square and hexagonal 2D structures are fabricated by a multi-exposure of two-beam interference pattern with a rotation angle of 90° and 60° between two different exposures, respectively. Three-exposure, in particular, results in different kinds of 3D structures, with close lattice constants in transverse and longitudinal directions, which is difficult to be obtained by the commonly used multi-beam interference technique. The experimental results obtained with SU-8 photoresist are well in agreement with the theoretical predictions. Multi-exposure of two-beam interference technique should be very useful for fabrication of photonic crystals.
©2005 Optical Society of America
Recently, there has been considerable interest in the fabrication of two- and three-dimensional (2D and 3D) photonic crystals (PhCs), which consist of periodic dielectric structures [1,2], because they can be utilized as many kinds of optical devices. Various techniques have been used to fabricate templates for PhCs such as self-assembly of colloidal particles [3,4], holographic lithography (HL) [5–13], and direct laser writing [14–17], etc. HL, in particular, is a very promising and inexpensive technique to fabricate large-area and defect-free PhC templates. Multi-beam interference technique is a commonly adopted HL method to fabricate PhC templates. Depending on the number of laser beams and their arrangements, one can fabricate different types of 2D and 3D structures. For example, using interference of three or four beams [5,8,12], 2D hexagonal or square structures can be fabricated, and using interference of three-plus-one or four-plus-one beams [6,9,11,13], one can fabricate 3D hexagonal or square structures. However, since the number of the laser beams used in the multi-beam interference technique is at least three, the experimental setup becomes complicated, in particular for the fabrication of 3D structures. Besides, 3D periodical structures obtained by this technique have very different lattice constants in three dimensions [6,9,11,13]. Furthermore, the polarizations of the laser beams are not exactly parallel in their overlapping region, the modulation of intensity is therefore not 100%, which may influence the quality of the periodic structures [18,19]. In contrast, two-beam interference technique possesses many advantages over the commonly used multi-beam interference technique, such as easy to fabricate different structures (hexagonal or square) using multi-exposure technique, and high contrast between the minimal and maximal intensities of interference pattern due to the identical polarization of two laser beams in the interference area. Recently, several groups have employed this technique to fabricate 2D PhC templates [20–22], and the possibility of fabricating 3D cubic PhC templates was preliminary discussed . However, the feasibility of using this technique to fabricate 3D PhCs still needs to be evaluated. In this work, we demonstrate both theoretically and experimentally the use of multi-exposure two-beam interference as a simple and efficient tool for the fabrication of not only square and hexagonal 2D but also various types of 3D PhCs. In particular, we prove that using this technique one can fabricate 3D periodic structures with close lattice constants in three dimensions, which is difficult to be obtained by multi-beam interference method.
2. Theoretical study of multi-exposure of two-beam interference pattern
Figure 1 shows the experimental setup used to fabricate 2D and 3D periodic structures. A laser beam emitted from a He-Cd or an argon laser was spatially cleaned and extended. A double-iris was used to select two laser beams of the same profile, same polarization, and same intensity. These two laser beams were overlapped in a sample by using two mirrors M1 and M2 to change their directions. These two beams interfered and their total intensity was modulated periodically in one dimension (in x direction). The angle between two laser beams was denoted as 2θ and could be easily controlled by rotation of two mirrors M1 and M2. A sample was fixed in a double rotation stage, which could be rotated around the z-axis by an angle α and around the y-axis by an angle β.
With the introduction of angles α and β, the electric field of each interference beam (called beams 1 and 2) can be written as
where E 10 and E 20 are the amplitudes of electric field of beams 1 and 2, respectively, ω is the angular frequency, k is the wave number, α and β are the rotation angles, and θ is the semi-angle between two laser beams.
The intensity distribution of a two-beam interference pattern in a sample oriented at angles α and β is expressed as
assuming E 01=E 02=E 0.
The period (Λ) of structures can be determined by
where λ is the wavelength of the interference source.
In the case of multi-exposure of two-beam interference pattern at different angles α and β, the exposure dose is accumulated and the total intensity therefore is the sum of intensity of each exposure. It can be expressed as
where i =1, 2, 3,…corresponding to one-exposure, double-exposure, and triple-exposure, etc., at different angles αi and βi.
To fabricate 2D periodic structures, the angle β is chosen to be 0° (sample is perpendicular to z-axis), and the angle α is varied. Square or hexagonal periodic 2D structure is then obtained by a double- or triple-exposure with an appropriate rotation angle α. If the angle β is chosen to be different to 0° for at least one exposure, our calculation predicts that 3D periodic structures can be obtained by this multi-exposure two-beam interference method. Figure 2 shows the theoretical calculation results of iso-intensity distribution of two-beam interference obtained with only three exposures. Various kinds of 3D periodic structures can effectively be obtained. Figure 2(a) shows a 3D periodic rectangular-square structure obtained by choosing angles (α,β)= (90°, 0°), (0°, 45°), and (180°, 45°), for three exposures. If angles (α, β) are chosen to be (90°, 0°), (0°, 30°), and (180°, 30°), for three exposures, a 3D periodic rectangular-hexagonal structure, as shown in Fig. 2(b), is obtained. And if angles (α,β) are chosen to be (60°, 0°), (0°, 30°), and (180°, 30°), for three exposures, a 3D periodic hexagonal-hexagonal structures, as shown in Fig. 2(c), is obtained. In particular, the lattice constants of the 3D structures obtained by this method are close in three dimensions for any value of angle θ, which is difficult to be obtained by the commonly used one exposure of multi-beam interference (for that, the period in z direction is several times larger than that in x or y direction). Multi-exposure two-beam interference method is therefore very useful for the fabrication of 3D PhCs. Note that if the exposure number is extended to four or five, the simulation results show that other types of 3D periodic structures (Woodpile, bcc, etc.) can be obtained.
3. Experimental results and discussions
Experimentally, we first used SU-8 photoresist (Micro. Chem. Corp.) to fabricate 2D periodic structures by choosing the angle β=0° and changing the angle α(Fig. 1). Since the wavelength of the irradiation source (He-Cd laser at 325 nm) is close to the peak absorption of the photoresist, no high power of irradiation is needed to fabricate large-area periodic structures. The sample film of 2μm thickness was spin-coated into a glass substrate and baked at 65°C for 2 minutes and then 95°C for 3 minutes to remove the solvent. After exposed for fabrication of 2D structures, the sample was post-baked at 70°C for 2 minutes and then 100°C for 3 minutes to improve the cross-linking of the polymerized resin. The sample finally was developed for 3 minutes in SU-8 developer and rinsed by ethanol.
Figure 3(a) shows the experimental result of a 2D square periodic structure obtained with a double-exposure (exposure time of each exposure was 1 second and exposure power was 1mW) of two-beam interference pattern at α= 0° and 90°. The structure (Λ= 1μm, agreeing with the result calculated from the Eq. (3) by choosing angle θ= 9.35°) is quite uniform in a very large area (6mm × 6mm, corresponding to the size of the iris). Moreover, using this multi-exposure two-beam interference we can fabricate either square or hexagonal structures by choosing appropriate rotation angles. The hexagonal structure shown in Fig. 3(b) containing with non-circle holes was obtained by a double-exposure at α= 0°, and 60°. In contrast, the shape of dots (holes) of the hexagonal structure in Fig. 3(c) becomes circle as predicted by theoretical calculation when we made a triple-exposure at α= -60°, 0°, and 60°.
In particular, by controlling the exposure-dose, i.e. exposure-time or exposure-power, we were able to fabricate 2D periodic structures with either material-cylinders or air-holes .
To fabricate 3D periodic structures, we varied both α and β for different exposures. Note that it is not suitable to use 325nm as the irradiation wavelength and pure SU-8 as the photoresist to fabricate 3D structures, because the strong absorption of pure SU-8 photoresist at 325 nm limits the exposure thickness of the sample. To solve this problem, we have added a new photoinitiator H-Nu-470 (Spectra Group Limited) into pure SU-8 photoresist. This new mixing photoresist resulted in high absorption in UV range and low absorption in visible range. An argon laser at 514nm was used as the irradiation source for the fabrication of 3D periodic structures. The preparation of the sample and developing process are the same as those of 2D structures. The thickness of the sample was about 20μm. The total power of two laser beams was fixed at about 1W and the exposure-time was 15 second for one exposure. Two configurations of 3D structures were adopted to fabricate: rectangular-square and hexagonal-hexagonal (Figs. 2(a) and 2(c)). For that, we used only three exposures with the following angles arrangements (α,β) = (90°, 0°), (0°, 45°), and (180°, 45°) for rectangular-square, and (α,β) = (90°, 0°), (0°, 30°), and (180°, 30°) for hexagonal-hexagonal. The angle θ was chosen to be 7.38°, which resulted in the period Λ = 2μm, according to Eq. (3). Figure 4 shows the SEM pictures of these periodic 3D structures. The experimental results show that 3D structures are uniform in large area and in well agreement with the simulation results. Moreover, comparing the lattice constants in top view and side view of 3D structures, we confirm that they are close in three dimensions as predicted by theory, which is not true when it is fabricated by four- or five-beam interference.
In conclusion, we have demonstrated both theoretically and experimentally that using multi-exposure two-beam interference technique one can easily and efficiently fabricate large-size two- and three-dimensional periodic structures with various configurations, square, hexagonal, rectangular, etc. The periodic structures are very uniform in large area (6mm × 6mm). In particular, the lattice constants of 3D structures are close in three dimensions, which is difficult to be obtained by using the commonly used multi-beam interference method. The experimental results obtained are in agreement with the simulations using the theory for multi-exposure of two-beam interference. This technique should be very useful for photonic crystal fabrications.
We gratefully acknowledge the financial support from the National Science Council, Taiwan under grant Nos. NSC 94-2120-M194-006 and NSC 94-2112-M194-003. N. D. Lai acknowledges the support of postdoctoral fellowship from National Science Council, Taiwan.
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