The fabrication and characteristics of close-packed lens arrays with a feature size close to the optical diffraction limit are presented in this study. By controlling the size of the submicron nickel rods and the time for reactive dry etching, the hemispherical lens array with a submicron period is made directly on a borosilicate glass. Finite-difference time-domain calculations and optical near-field measurements show that such a lens array can generate a subwavelength optical spot array near the glass surface. Moreover, the spot array periodically appears in the propagation direction. Using this novel optical property, we propose a photolithographic method for the mass-production of multilayer hexagonal structures with a period of 500nm.
© 2007 Optical Society of America
Nanofabrication using a photolithographic method is important in the mass-production of nanometer patterns. To make an optical spot of a size close to half of the wavelength, an objective lens with a large numerical aperture is usually necessary. Using point to point writing and controlling the exposure time to photo resistance, subwavelength patterns have been demonstrated [1, 2]. The writing process makes the fabrication method incapable of sustaining mass-production; however, a parallel process using a close-packed lens array could fulfill this requirement. A lens array simultaneously provides multiple focusing spots from an optical beam and has the capabilities of massive parallelism and micro-miniaturization. To date, most lens arrays are fabricated in the micron scale, for use in fiber bundles, optical switches, charge-coupled device (CCD) cameras and light-emitting diode arrays [3, 4]. They can also be used in biological systems to simulate biomimetic artificial compound eyes . For the mass-fabrication of dense diffraction-limit structures, the lens size needs to be of the submicron scale. Previous results have shown that a close-packed submicron lens array can be produced using a soft-lithography-based method [6, 7]. By templating the surface of a colloidal monolayer, the relief structure can generate PDMS-based hemispherical hexagonal arrays; however, PDMS is a soft material, it causes damage in chemical cleaning and is easily broken down after a long period of use. Therefore, it is difficult to apply in photolithographic processes.
In this paper, a new and simple method for making closed-packed submicron glass lens arrays is presented. We demonstrate the fabrication of the lens array on a borosilicate glass with a period of 500nm. The hard glass lens array is useful for contact photomask lithography. The focusing properties of such submicron lens arrays are studied for the first time in this paper. Differing from the conventional microlens array, which is simply described by ray-optics, the submicron lens array is analyzed using full-wave vector calculations. The calculation results show that such a submicron lens array can generate three-dimensional sub-wavelength focusing spots when the lens diameter is near the incident wavelength. We confirmed the optical field distribution using near-field scanning optical microscopy (NSOM) , and successfully fabricated multilayer hexagonal structures with a period of 500nm using the lens array as a mask in photolithography.
2. Fabrication of the submicron lens array
There are various techniques for fabricating lens arrays on glass substrates , including photothermal expansion, ion exchange, laser irradiation  and reactive ion etching (RIE) . Optical methods, such as the photothermal effect and laser machining, cannot be used to fabricate a submicron lens because the lens profile is below the optical diffraction limit. On the other hand, lens arrays fabricated using the RIE method require a suitable mask for forming the lens profile. A previous method used the thermal reflow effect to form a lens array on a polymer film. If the substrate can be etched only in the depth direction, the lens shape on the polymer film can be directly transferred to the substrate using the RIE method. Fused silica is a good candidate for such unidirectional etching. Figure 1(a) shows the conventional RIE process for forming a lens array. The size of the thermal reflow lens is at the hundred microns scale. A submicron lens is difficult to make due to the large thermal expansion effect of polymers. In this study we propose a different mask design for use in the RIE process. Contrary to the use of a pre-shaped polymer lens as a mask, our method uses a metallic rod array as a hard mask, and the lens array is formed by isotropic etching in the substrate. Figure 1(b) illustrates the evolution of the lens shape. The diameter of each rod is in the submicron scale. At the start of the etching process, the areas beneath the metallic rods are protected. The etching at the rod edges and in unprotected regions form tapers in the substrate. The submicron rod is designed so as the diameter is equal to the etching depth. When lateral etching reaches the center of the rod, a hemispherical lens array is formed due to the isotropic etching effect.
For this study, we used borosilicate glasses (GoldSeal, No.3010) as the substrates. The borosilicate glass contains large amounts of metallic ions that make the glass difficult to etch along the depth direction. We found that there is substantial lateral etching in the borosilicate glass when using SF6, CHF3 and argon as the etching gases. A submicron-scale Ni rod array was used as a hard mask, prepared using an electron beam lithographic method. First, a 300nm-thick poly(methyl methacrylate) (PMMA) film was spin-coated onto a glass. Using an electron beam writer, a hexagonal rod array with a period of 500nm was then written onto the PMMA, which is a positive electron resist and can be developed by an IPA:MBIK (3:1 by volume) solution after writing. A 150nm-thick Ni film was deposited on the patterned PMMA. After lift-off, the 500nm-period hexagonal Ni rod array was formed on the glass substrate, as shown in Fig. 2(a). It is noted that there is substantial size non-uniformity of the rods. The origin of the non-uniformity is probably due to residual PMMA during lift-off process. These PMMA residues have no effect on the following etching process. The sample was sent into an RIE machine (Oxford Plasmalab 80 plus). A gas mixture of SF6 (24sccm), CHF3 (12sccm) and argon (12sccm), at a total pressure of 10mtorr, was used to etch the glass . There was a comparable lateral etching beneath the Ni film. The process resulted in different shapes being formed at different etching times. Figures 2(b), 2(c), and 2(e) show the RIE results after 30, 60 and 90 minutes of etching, respectively. After 30 minutes of dry etching, only part of the glass beneath the Ni rod array was etched, forming a cone array with flat top surfaces. When the etching time was 60 minutes, the lateral etching arrived at the center of the Ni rod, resulting in a hexagonal array consisting of hemispherical lenses. The height of lens was ~250nm and the diameter at the bottom surface was ~500nm. The surface is smooth, with some small rings near bottom area. After 90 minutes of etching, the etched shape became a pyramid, with a rough surface on the glass substrate.
It should be noted that the substrate material is of great importance in forming the hemispherical lens. For example, Fig. 2(f) shows the etching result using fused silica. The etching time was 60 minutes and the mask was the same Ni rod array as previously described. As the etching is highly anisotropic, the Ni pattern resulted in a high-aspect-ratio rod array in the silica substrate. In addition to the substrate effect, the shape of lens is also controlled by the initial size of the metallic rod. We have tested different diameters of Ni rods and found that the best condition for forming a hemispherical lens is an Ni rod of a diameter of one half of the period. We have also tested RIE conditions at different etching times, from 30 to 90 minutes with 10 minutes interval, to get different shapes. From the SEM images, we found that the hemispherical profile can be well controlled at about 60 minutes etching time.
3. Calculations of the Focusing Properties
To our knowledge, there have been no studies related to the submicron lens array. The widely-used ray-optics cannot be used to calculate the focusing properties because the lens size is very close to the wavelength; therefore, we applied the finite-difference time-domain (FDTD) method  to calculate the distribution of light through the submicron lens array. The FDTD calculations were performed using a commercial product (BeamPro, FullWave 3.0), and the layout for the calculations is plotted in Fig. 3(a). The lens array was composed of hemispherical glass with a 250nm radius and a 500nm period. The refractive index of the glass was 1.5 and the incident wavelength was 442nm, simulating a He–Cd laser passing through the array. Figure 3(b) shows the calculated optical field distribution at the XZ plane. It is obvious that such a lens array generates a focusing spot array near the lens surface. The spot has a diameter ~250nm, close to one half of the wavelength; the depth of the spot is ~400nm, and the aspect ratio of the spot is ~1.6. It was noted that the spot array appears alternatively in the z-direction; the period is ~1μm, twice that of the period of the lens array. Figure 3(c) shows the optical field distributions at the XY plane at different z positions, and it can be seen that the focusing spots form a 3D hexagonal array. The maximum intensity in the focal spot is twice as large as the intensity in the non-focal region. The large optical intensity contrast indicates that a photoresist pattern can be easily made using the optical spot array in a photolithographic process. It is noted that transparent periodic structures illuminated with a highly spatially coherent plane wave produce self-images and self-image-like field distributions in certain planes behind the grating structures. The lens-like imaging produced solely by free-space propagation of a diffracted field is known as the Talbot effect.. The 3D hexagonal array generated by the submicron lens array can be understood by this Talbott effect.
It was found that the above focusing property is altered when the period of the submicron lens array is changed. Figure 4 shows the XZ plots of the optical distributions for different periods of the lens arrays. Figure 4(a) was a 300nm-period array. The curvature of lens is too large, such that most of the light is confined in the lens. No focusing spots are formed in the air region. Figure 4(b) shows the result for a 700nm-period array. The focusing behavior is similar to that of the 500nm-period array, but with a longer focusing period in the z direction. Figure 4(c) shows the result for a 900nm-period array. The curvature of the lens is too small to form a tight spot, and the optical pattern is complicated due the interference of diffraction beams from the grating structures. We performed a series of FDTD calculations and found that a suitable period for the hemispherical lens array is between once and twice the size of the wavelength.
4. Optical near-field measurements
From the FDTD calculations, it was found that the focusing spots of the submicron lens array are close to one half the size of the wavelength. This focusing property cannot be measured by a conventional optical microscope. In order to obtain a resolution of greater than 100nm, we applied NSOM to measure the optical distribution near the lens surface, the NSOM measurement operating in a collection mode  as shown in Fig. 5(a). A 473nm laser was incident from the glass substrate, and a tapered fiber probe collected light near the sample surface. Due to the small aperture of the tapered tip, of ~80nm, a super-resolution image was obtained. Figures 5(b)–5(d) shows the NSOM measurement results. Figure 5(b) is a topographic image of a submicron lens array; the period was 500nm. The topographic image shows that the hemispherical lens was smooth and had a good uniformity. Figure 5(c) shows the corresponding optical near-field distribution. The spot array confirmed the existence of the focusing effect. Compared with the topographic image, the focusing spots exist at the topographic higher regions.
The FDTD calculations indicate that the submicron lens array not only forms a spot array in the horizontal plane, but also has periodically focused light in the longitudinal direction, meaning that the focusing array will appear alternatively in the z direction. To verify this distribution, we scanned the fiber probe in the XZ plane to measure the optical distribution along the propagation direction; the result is shown in Fig. 5(d), from which it can be seen that the submicron lens array does indeed have alternative focusing beams in the z direction.
5. Photolithographic results
From above investigations, the submicron lens array exhibits different optical properties to conventional micron lens arrays. First, the focusing spots occur very near to the lens surface; second, the focusing spots periodically appear in the propagation direction. Hence, the submicron lens array is not suitable for multiple imaging. However, such focusing properties are very useful in contact photomask lithography, to make 2D and 3D periodic patterns with a resolution below the incident wavelength. To demonstrate this capability, we experimentally fabricated array patterns using the submicron lens array as a photomask. Figure 6(a) shows the optical setup for photomask lithography. The photoresist (PR) used in this study was the AZ-351 (Clariant, 20cP). It was spin-coated on a glass substrate and placed in an oven at 80°C for one hour. The PR surface was in direct contact with the submicron lens array. After exposure to a 30mW, 442nm-wavelength He–Cd laser (Melles Griot Laser) for 30 seconds, the PR was developed with AZ-350MIF (Clariant), rinsed with water, and dried with nitrogen. Figure 6(b) shows the developed pattern in the PR sample. The AZ-1500 is a positive photoresist; hence it formed an air-hole array in the PR film. From the SEM image, the diameter of the hole was ~250nm and the period was 500nm, the same as that of the lens array mask. The cross-section of the hexagonal hole array, viewed at a tile angle of 45°, is also shown in Fig. 6(b). The depth of the hole was ~500nm, and the aspect ratio was ~2, consistent with the FDTD calculations. It is noticeable that conventional hexagonal patterns are made by using multiple beams interference method. The profile made by interference beams has a squared sinusoidal shape. From Fig. 6(b), it can be seen that pattern profile fabricated by using the submicron lens array is non-sinusoidal. The developed hole array has sharper edge than patterns made by the interference method.
Those periodically-focusing spots are not limited to making 2D structures. From the distribution of the optical pattern, it is possible to fabricate a 3D PR pattern. We have proved this concept by using a similar photolithographic process with a longer exposure time. In the sample preparation, the thickness of AZ-1500 was increased to 2μm. The PR was in direct contact with the submicron lens array. The exposure time was extended to 60 seconds, twice as long as that used for the fabrication of a 2D structure. Figures 7(a) and 7(b) show the PR results; Figure 7(a) is a SEM image viewed from the top surface, Fig. 7(b) is the cross-section image, viewed at a tile angle of 45°. It is found that there are two alternative layers in the photoresist, and the alternative distribution is just the same as the prediction made from the FDTD simulations. In principle, the patterns can be extended to many layers to form a 3D structure; however, due to over-exposure at the initial layer, our single-photon photolithographic process can only be used to prepare up to 2~3 layers. It is suggested that two-photon polymerization  may overcome the problem of over-exposure of the initial layer. The creation of 3D patterns is of great interest, as it can be used as a template for forming 3D photonic bandgap structures [17, 18].
We present a method of fabricating submicron lens arrays on borosilicate glasses. By controlling the reactive ion etching time and the diameter of the Ni rod patterns, a hemispherical lens array can be directly formed on a glass surface. The FDTD calculations and NSOM measurements confirm the existence of subwavelength focusing spots near the submicron lens array. Moreover, the focusing array periodically appears in the propagation direction, resulting in a three-dimensional periodic pattern. Such properties makes the submicron lens array very useful for generating 2D and 3D periodic patterns with a feature size smaller than the incident wavelength. We successfully employed these properties to make both one- and two-layer hexagonal air-hole arrays with a 500nm period in the photoresist.
This research is supported by the National Science Council, Taiwan (Grant No. NSC 95-2215-E-001-001) and the Nano Program of Academia Sinica, Taiwan.
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