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Microlens arrays were self-assembled from microballs using dielectrophoretic energy wells. Energy wells defined by patterned dielectric were used to produce microlens arrays with array patterns of desire. Microballs of 25μm in diameter were measured to have numerical aperture of 0.8 and focal length of 15.5μm. The optical resolution was found to be 0.4μm. Both the numerical aperture and the focal length were further adjusted to 0.66 and 19.0μm by a post-assembly heat treatment at 190°C for 5 minutes.
©2006 Optical Society of America
1. Introduction
Microlens arrays (MLAs) with lens diameters of a few to several hundred micrometers are extensively used in many optical systems such as image sensors, diffusers and displays. The conventional MLA fabrication techniques reported include microcompress molding [1,2], inkjet [3], laser irradiation [4], laser ablation [5], thermal reflow of photoresist [6–9], plasma etching [10], microporous polymer films with micromolding [11], etc. The techniques mentioned above produce MLAs with numerical aperture (NA) of less than 0.6, typically 0.1-0.3. Low NA values are attributable to the surface profiles and the refractive index of the microlenses; the surface profiles are restricted by the fabrication technologies. Table 1 summarizes MLA fabrication methods for MLA manufacture.
Table 1. Comparison of different MLA fabrication methods.
High NA values are demanded for MLA applications that require high signal to noise (S/N) ratio, including optical interconnects, two-dimensional (2D) high density optical sensor arrays, laser protection goggle [12], 2D optical data recording and projection systems. To achieve high NA, microlenses should have small radius of curvature; thus, a microball lens is one of the best candidates. Microball lens arrays, however, are still unable to be manufactured by the conventional methods mentioned above. Self-assembly methods, including two-dimensional (2D) self-assembly lattice [13] and capillary self-assembly method [14], were proposed to assemble MLAs from individual microball lenses based on surface tension of water. In the 2D self-assembly lattice method, evaporation shrinks a water droplet so that the microballs in the water droplet are pushed toward the center of the droplet. The highest-density packing of the microballs is hexagonal; thus the array pattern is limited to closely-packed hexagonal. The capillary self-assembly utilizes surface tension of water in two parallel plates. When water surface moves, the microballs nearby the water surface are guided and fall into the holes of an array template. These two methods rely on surface tension of water and motions of water surface; thus, the fabrication yield is extremely sensitive to assembly environment. An appropriate density of microballs in water is also required to prevent excessive microballs, vacancies in MLAs, multiple layers of microballs and distortion of arrays. Once the defects exist, no measures can be taken to rectify. Further, the two self-assembly techniques showed no optical results.
To overcome the constraint on array patterns and to enable a measure to rectify the array defects, we proposed a self-assembly method to fabricate MLAs using dielectrophoretic (DEP) energy wells. The method proposed generates DEP energy wells to position one electrically polarizeable microball per energy well. The array patterns of desire can be achieved by patterning dielectric layers. Spatially patterned dielectric under ac voltages distorts uniform electric fields (in between two conductive parallel plates), forming energy wells. To redistribute excessive microballs and to fill up the vacancies in arrays, optically induced DEP energy gradient (i.e. DEP force) [15, 16] is applied. Once microball lens arrays are formed and transferred onto flexible polyimide substrates, the optical properties of microball lenses can be further adjusted by post-assembly heat treatment.
2. Self assembly process
The DEP energy wells, induced by patterned dielectric, are applied to self-assemble MLAs from polystyrene (PS) microballs in water in this study. The DEP force is determined by:
where a is the diameter of microball; εm is the permittivity of the surrounding medium; E is the electric field strength; K*(ω) is Clausius-Mossotti (CM) factor at ac frequency ω (e.g. CM factor ranging from -1/2 to 1). The CM factor of the PS microballs in water is negative at ac signals of 30kHz; the resulting negative DEP force pushes the PS microballs toward the weaker electric fields.
Figure 1 depicts the device used to self-assemble microballs as MLAs. Figure 2 shows the schematic diagram of the DEP energy profile during the self-assembly process. First, ac signal of 5V is applied in between two conductive ITO layers. Dielectric AZ4620 of thickness of 5.5μm is photolithographically produced so that DEP energy wells can be generated according to MLA array of desire [see Fig. 2(a)]. Additional DEP energy gradients that are optically induced are applied to rectify array defects, such as vacancies and excessive microballs. Optical intensity of 5 W/cm2 from a LCD projector (Epson EMP-S1) increases the conductivity of amorphous silicon layer at the region of desire, raising DEP energy level [see Fig. 2(b)]. When the optical power sweeps from one side to the other side, excessive PS microballs are relocated and vacancies are filled [see Fig. 2(c)]. Finally, the PS microball arrays are transferred from self-assembly device onto transparent flexible substrates as MLAs.
Fig. 1. The device for self assembly of microballs as high NA MLAs. Two ITO glasses are sandwiched by a 70μm thick spacer. The bottom ITO glass is first coated with a layer of amorphous silicon followed by insulating silicon dioxide coating. A patterned photoresist is formed on the surface of silicon dioxide using photolithography.
Fig. 2. Schematic diagram of DEP energy over three adjacent energy wells: (a) patterned DEP, (b) illumination near the first energy well, and (c) illumination swept to second energy well. The patterned DEP denotes the DEP energy produced by patterned dielectric and the optical DEP denotes the energy induced by illumination. (d) Movie of self-assembly sequence (618 KB version).
3. Experimental results
Physical arrangement, optical performance and post-assembly heat treatment of the MLA produced using DEP energy wells were investigated. The MLAs assembled from PS microballs of 25μm in diameter were demonstrated in square arrays and hexagonal arrays. Figures 3(a) and 3(b) show the scanning electronic microscope (SEM) and optical microscope (OM) pictures of the self-assembled MLAs on flexible substrates, respectively. Figure 4(a) shows the OM image of the letter “F” on a transparency that is projected through the MLA in square array. Figure 4(b) shows the interference pattern of the MLA in hexagonal array. Figure 4(c) shows the interference images of a MLA on the image planes at continuously changed locations. The experimental setup is shown in Fig. 4(d) [17, 18].
Fig. 3. MLA: (a) SEM picture of a MLA on a flexible substrate. (b) OM picture of a flexible MLA curved at radius of 3mm. (The linty edge is caused by cutting the flexible polyimide substrate with scissors).
Fig. 4. Optical micrograph of projected images through the MLA self-assembled from microball lenses of 25μm in diameter and NA of 0.80: (a) image of lenses arranged in square pattern; (b) interference pattern of lenses arranged in hexagonal pattern; (c) movie of interference image captured by OM (1.05MB version); (d) the experimental setup of movie 4(c).
Parameters of the physical arrangement, including pitch variation and microlens diameter variation, were characterized based on the SEM pictures of the MLAs in square arrays. The pitch variation was measured to be less than 0.2μm (i.e. 0.5% of the pitch of 42μm). Such variation resulted primarily from the process step that self-assembled microball arrays are transferred onto the flexible substrates. The standard deviation of the microball diameter was found to be 0.4%; it is smaller than 10% for microlens of 750μm in diameter by micropressing method [3] and 1% for microlens of 30μm in diameter by ink-jet method [4].
Focal length, NA, image resolution and uniformity in the MLAs were investigated. The initial focal length of the microball lenses was measured to be 15.5μm, corresponding to NA of 0.80. The focal length variation of the MLA was found to be below 0.8μm [see Fig. 4(b)], indicating a good optical uniformity throughout the MLA. The resolution of the microballs in the MLA was measured to be 0.4μm using the United State Air Force (USAF) test target located at 3cm in front of the MLAs. Such resolution is close to the diffraction limit of green light of 0.3 μm that is estimated from the NA value of 0.8. The difference between the measured resolution and the diffraction limit is caused by spherical aberration of the microball lenses.
Both focal length and NA of the MLAs can be further adjusted using post-assembly heat treatment to satisfy specific requirements of optical systems. At the temperatures over the glass transition temperature Tg of 90°C, PS microballs reflow partially or entirely and their geometries change. Directional heating through flexible substrates was applied to impose more heat on the bottom semi-hemispheres of the PS microballs than the other. Hence, the bottom semi-hemispheres of the PS microballs have significant shape change while the top semi-hemispheres almost remain intact. The small alteration of the top semi-hemispheres during heat treatment yields little change at the focal lengths of the MLAs since incident light was projected onto the top semi-hemispheres. Given the post-assembly heat treatments of 91°C for 5 minutes, 120°C for 5 minutes and 190°C for 5 minutes, the corresponding focal lengths increased from initially 15.5μm to 16.0μm, 17.0μm and 19.0μm, respectively. The corresponding NA values for the three heat treatments were evaluated to be 0.78, 0.74 and 0.66, respectively (see Fig. 5). Microballs heated at higher temperatures have longer focal lengths and lower NA values because of larger lateral elongation. Comparing with the MLAs in Table 1, the MLAs self-assembled from microballs have higher NA values.
Fig. 5. Focal length and numerical aperture change for different post heat treatments. The heat-treatment temperatures are 91°C, 120°C and 190°C on a hot plate for 5 minutes. PS microball has glass transition temperature Tg of 90°C. Tr and Tg denote the room temperature and glass transition temperature. (“▪” and “•” denote the focal length and numerical aperture, resnectively.)
4. Conclusions
We concluded to demonstrate MLAs in square or hexagonal arrays that were fabricated using self-assembly method based on DEP energy wells. The array defects in the process of self assembly can be rectified using optically induced DEP. The physical arrangement, optical performance and post-assembly heat treatment of the MLA were characterized. The NA values of the MLAs manufactured using DEP energy wells are higher than that fabricated by conventional methods.
References and links
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