We report a simple method for forming surface corrugation of microlenses based on a volume growth effect of sol-gel glass. The volume growth effect was fully calibrated with a high-energy beam-sensitive grayscale mask, where the amount of growth was determined as a function of electron-beam-induced optical densities in the mask. This technique provides an excellent surface smoothness compared with other development based fabrication techniques. For example, a refractive microlens with a diameter of 140 µm and a sag height of 2.13 µm was demonstrated.
© 2003 Optical Society of America
Recently, micro-optical elements have been found to be useful in many applications, and various microfabrication techniques have been explored. In early conventional microelectronics fabrication processes, the fabrication of micro-optical elements and/or diffractive optical elements was based on two lithographic steps; i.e., the structures were first patterned and developed by UV or electron-beam lithography and then transferred onto the substrate by an etching process. The drawback of this method is that the final surface profile will be significantly determined by fidelity control in both lithographic and etching processes. In many cases, it could be a tremendous effort to implement the etching process precisely. An alternative lithographic technique for fabrication of micro-optical elements is based on solgel glass. Compared with a two-step fabrication technique, single-step lithography without etching in photosensitive SiO2/ZrO2 and SiO2/TiO2 sol-gel materials has been reported and studied extensively for guided wave and free-space optics [1–8]. In the single-step lithographic technique, the solgel material that is used as a negative-tone photosensitive resist is first cured by UV or e-beam exposure to cross link the material in the exposed areas. To complete the lithography, it is necessary to remove the unexposed areas in the sol-gel material through a development process. Finally, permanent microstructures are built into the silica-based sol-gel glass followed by a postbake at a low temperature, for example, 160°C as reported in Refs. 7 and 8.
It is noted, however, that in the single-step fabrication of micro-optical elements in sol-gel glass described above, the surface profile and the surface roughness are fully dominated by the development process. Since it is a chemical process, the surface quality of the permanent microstructures in the sol-gel glass was limited by chemical reactions during its development. To improve the surface smoothness during sol-gel fabrication, a reflowing technique for negative-tone sol-gel material was developed . The reflowing technique has been widely used for patterning simple structures in positive photoresist materials . It is a low-cost and simple fabrication technique; however, because of the reflowing mechanism it is difficult to control the surface profile precisely.
In this paper, we demonstrate that the fabrication of micro-optical elements in sol-gel glass can be realized by a self-volume growth effect; that is, surface corrugation is formed without the need for a separate development process. To further precisely control the surface relief profile, we employed a high-energy beam-sensitive (HEBS) gray-scale mask to determine the profile height. The HEBS gray scale mask had previously been used for fabrication of multilevel and continuous structures in both conventional photoresist and sol-gel materials [7,11]. To the best of our knowledge, this is the first time that the volume growth effect in sol-gel materials has been explored by use of a HEBS gray-scale mask. The volume growth was fully calibrated as a function of electron-beam-induced optical densities in the HEBS glass. For example, a refractive microlens was fabricated with a user-defined mask.
2. Fabrication and discussion
The hybrid sol-gel material was prepared by hydrolysis of 3-(trimethoxysilyl) propyl methacrylate in isopropanol and acidified water with a molar ratio of 0.04 ml:0.048 ml:0.053 ml; then 0.01 mol of titanium propoxide [Ti (OCH)4] was hydrolyzed in 0.04 mol of acetylacetone in a nitrogen environment. After 30 min, the two solutions were mixed at a molar ratio of 4:1 (Si:Ti). After 24-h aging at room temperature, 3% (by weight) of photoinitiator [bis(2,4,6-trimethylbenzoyl)-phenylphosphineoxide] was added to the homogeneous sol solution to make it photosensitive. After another 30 min of aging, the sol solution was distilled in vacuum to make the sol solution sufficiently viscous. Then the sol solution was spincoated onto a fused-silica substrate. A 40µm-thick film in one layer was obtained with 3500-rpm spinning speed. The refractive index of this material measured by a prism coupler was 1.50. Before being exposed to a laser beam, the film was prebaked at 90°C for 10 min so that the excessive solvent could be removed.
It is known that HEBS glass, which is a patented product and is commercially available from Cayon Materials, Inc., is sensitive to electron-beam exposure because it contains alkali. The gray scales can be produced as a result of ion exchange in the exposed areas during electron-beam radiation. As we will use the gray-scale mask to fabricate a microlens, first it is necessary to establish a relationship between the amount of volume growth in the solgel glass and the optical density of the gray scales required on the HEBS mask. For this purpose, we divided the calibration sample into 21 gray-scale levels; each subsampling area had dimensions of 10 µm×300 µm. The gray-scale levels were generated by electron-beam exposure with a fixed beam current of 93 pA and an accelerating voltage of 25 keV for different exposure times. The electron-beam dosage was generated from 20 to 640 µC/cm2 and was nonlinearly distributed in the 21 levels. The nth level is given by 20×1.19(n-1) (µC/cm2), where n is the gray-level number. It is noted that the higher the e-beam dosage, the darker the gray level and the smaller the growth of the volume.
With the user-defined gray-scale calibration mask, the sol-gel film was fabricated to reveal the volume growth response to the optical densities. This step was implemented on a Q 2001CT UV-mask contact aligner (Quintel Corporation) with a peak emission at a 365-nm wavelength and an irradiance of 15 mW/cm2. Figure 1 shows a schematic diagram of the experimental setup. After UV exposure, it is seen that the HEBS mask with the user-defined optical densities has converted and built the corresponding surface relief heights into permanent sol-gel glass. Based on the findings of the volume growth response, we need to further clarify the relationship between the volume growth and the electron-beam dosage that was used to generate the optical densities. It is noted that, because of such a relationship, it is necessary only to find the electron-beam dosages for a gray-scale mask; tedious measurement of the optical densities at micrometer resolution was not required at all. Figure 2 shows the relationship between the electron-beam dosage and the relative surface relief thickness, which indicates the volume growth difference from the area with the highest UV illumination. Because the HEBS mask was designed as light-field mask, i.e., the optical densities were generated only with the shape of the testing pattern, the measured surface relief thickness represents the height differences between the areas patterned with the gray levels and the outskirts without gray levels. It is shown in Fig. 2 that the maximum surface relief thickness can be as big as 3.6 µm.
To achieve an arbitrary surface profile, one has to define the electron-beam dosage exposure of the HEBS glass for each pixel. For design convenience, the calibration curve is fitted and expressed as the following polynomial:
Y=-26.38119+307.34829×X-46.1826×X2+3.55569×X3, where Y and X represent the electron-beam dosage and the surface relief thickness, respectively. Based on this experimental curve, a gray-scale mask for a microlens was designed and fabricated in HEBS glass by electron-beam lithography.
Figure 3 demonstrates a three-dimensional profile of the microlens fabricated in the self-developed photosensitive hybrid sol-gel glass. The UV exposure time was 8 min. The surface profile was measured by a laser interferometer (WYKO NT 2000). This microlens has a diameter of 140µm and a sag height of 2.13µm. It can be seen from the figure that the microlens is sunk into a circular well in the sol-gel film; this is so because the volume growth in the outskirts was maximized by UV exposure without going through gray levels. Figure 4 illustrates a comparison of the fabricated two-dimensional microlens surface profile and the ideal original shape. It can be clearly seen that there is excellent agreement between the profiles in the central areas. However, it is noted that there is a larger deviation in the outer area of the microlens, which could produce spherical aberration. Further detailed analysis of spherical aberration was implemented with CodeV software (Optical Research Associates), and the calculated results show that the spherical aberration of the fabricated microlens is approximately two times larger than that of a perfect spherical microlens with the same diameter and sag height. We believe that there are two chief reasons why the fabricated surface profile deviated from the theoretical values. The first reason is imperfect fitting of the calibration curve in the lower dose area, as shown in Fig. 2. The thickness in this area is less than 500 nm, and it affects the focusing property of light waves largely through the outer ring zone. The other reason is shrinkage of the film owing to further condensation during postbaking. All these disadvantages can be overcome if we can optimize the various fabrication parameters as a single parameter.
Surface quality is a very important parameter for an optical element. Figure 5 shows the surface roughness property measured by an atomic-force microscope in a 500 nm×500 nm area on the top surface of the fabricated microlens. The root-mean-square value is 1.183 nm, which is just larger than the 1-nm limit that corresponds to 4% reflectance. Thus the resultant microlens surface shows good optical smoothness.
Rantala et al. reported the volume growth phenomenon in hybrid sol-gel materials . It is noted that the volume growth effect can be explained on the basis of monomer diffusion theory. In as much as exposure light interacts with the photoinitiator and produces free radicals that result in photopolymerization of the 3-(trimethoxysilyl) propyl methacrylate monomers, the photoreactive monomer molecules are consumed in the exposed areas. This leads to the migration of the monomers from the unexposed areas into the illuminated regions as a result of concentration and density gradients. In the case of a gray-scale mask, the monomers could be moved away from the areas illuminated with higher optical densities to the regions with lower optical densities. Consequently, following the HEBS mask design, we observed that the controllable volume growth effect formed a microlens.
In summary, we have demonstrated the fabrication of a microlens in self-developed photosensitive hybrid sol-gel glass by using a user-defined gray-scale high-energy beam-sensitive mask. The surface relief thickness of the sol-gel film is related to electron-beam dosages that induced optical densities in a HEBS gray scale mask. With the calibrated result, a gray-scale mask for a microlens was fabricated and a microlens with a 140-µmdiameter and a 2.13µm sag height was obtained. The measured surface profile was found to be in good agreement with the desired profile. This method possesses a great potential to produce high-quality micro-optical elements with good surface smoothness.
References and links
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