We present a quantitative study on the fabrication of microlenses using a low-cost polymer dispending technique. Our method is based on the use of a silicon micro-cantilever robotized spotter system. We first give a detailed description of the technique. In a second part, the fabricated microlenses are fully characterized by means of SEM (Scanning Electron Microscope), AFM (Atomic Force Microscopy) non contact optical profilometry and Mach-Zehnder interferometry. Diameters in the range [25–130μm] are obtained with an average surface roughness of 2.02nm. Curvature radii, focal lengths as well as aberrations are also measured for the first time: the fabricated microlenses present focal lengths in the range [55–181μm] and exhibit high optical quality only limited by diffraction behaviour with RMS aberration lower than λ/14.
©2007 Optical Society of America
Refractive microlenses arrays have been studied extensively in recent years  and various technological approaches have been proposed [2–12]. Among them, fabrication methods using polymers are of great interest because of their easy and low-cost use. The authors have recently proposed an alternative deposition method to fabricate polymer microlenses in view of VCSEL beam collimation . The principle of this original technique consists in monomer droplets deposition using a robotized silicon-cantilever-based microsystem. The ability of this technique to deposit polymer droplets in the dimension range required for integration on VCSELs has been experimentally demonstrated . In this paper, we present additional results on the influence of the contact time on the final droplet volume, demonstrating the possibility of controlling accurately lens dimensions at a micrometer scale. The geometrical and the optical characteristics of the microlenses have been also characterized, demonstrating the suitability of this deposition technique for micro-optics applications.
2. The microlens fabrication process
2.1 Spotter description
The principle of this microlens fabrication technique relies on the deposition of droplets using an automatized array of silicon microcantilevers. The microsystem-based spotting tool, consisting of a cantilever array fixed on a three-stage automated spotter [Fig. 1(a)], was initially developed for picoliter biological sample deposition . The microcantilevers are realized using conventional microfabrication techniques on a silicon-on-insulator wafer. The two major steps of the fabrication process are the reactive ion etching of the front side and the back side of the wafer to create the cantilever shape and to release them, respectively. The cantilevers, shown in Fig. 1(b), are 2 mm long, 210 μm wide and 5 μm thick. A reservoir and a slit are incorporated in the bulk silicon for liquid storage and deposition. The section of the slit is 5 μm × 5 μm, and drop formation is due to a liquid transfer between the tip of the cantilevers and the surface to be patterned upon direct contact.
2.2 Spotting procedure
The microcantilever array is spatially moved owing to a computer-controlled three-axis translation stage. First, the cantilever deflection that occurs when touching the substrate allows determining the surface contact point. The vertical position of the cantilevers at this contact point is stored in the PC used to control the displacement of the array. The experimental deposition protocol starts by loading the cantilever with the polymer to be deposited. This loading step is achieved by dipping the cantilevers during a few seconds in a drop of liquid polymer, the slit being filled via capillary forces. The cantilever array is then moved on top of the deposition area using the XYZ motion control system. Liquid droplet deposition is finally achieved by putting the cantilevers in contact with the substrate surface. To ensure a good contact between the cantilever tip and the surface, thus allowing a proper liquid transfer, the cantilevers are moved down 10 μm after the detected surface contact point.
The material used in this study is a thermocurable polymer with a very low viscosity  which allows efficient and reproducible loading and deposition processes. Chemical formulation of the pre-polymer used in this study is as follows: a siloxane chain: bis(dimethylsiloxane)epoxypropoxypropyl terminated (DMS-DGE), is functionalised with epoxy groups, this molecule is polymerized with a diamine:1.3bis(aminomethyl) cyclohexane (BAC). All components used in this study are liquid and present a viscosity lower than 9mPa.s at 20°C. The amine (BAC) was supplied by Sigma-Aldrich and DMS-DGE by ABCR. During the deposition process, the sample is kept at a constant temperature of around 40°C to avoid polymer demixing, owing to the use of a heating plate. After deposition, droplets are in situ polymerised at 120°C.
2.4 Influence of the contact time on the droplet size
Using the spotter described above with a single cantilever, liquid drops were formed on an SU-8 layer deposited on a glass substrate. The contact angle of the considered thermocurable polymer after deposition and polymerization on an SU-8 surface has been first measured on a millimiter-scale with a GBX Digidrop surface tension analyser and found to be equal to (40±2)°. For this given value, rows of droplets were realized by incrementing contact times from 200 ms to 60s in order to investigate the influence of the contact time on the size of the printed spots [see example on Fig. 2(a)]. Following the deposition step, the droplet sizes were measured by optical microscopy. The diameters were found to range between 20 μm and 130 μm. As seen in Fig. 2(b), the droplet diameter increases rapidly with the contact time but an asymptotic value is reached after 30 seconds. This phenomenon has been already observed when depositing water-glycerol drops using cantilevers that exhibit smaller fluidic slits . A steady state seems to occur when the equilibrium between the pressure of the deposited drop and the pressure of the liquid in the channel is established. The maximal value of the spot size and thus the microlens diameter is consequently set by three key parameters: the size of the fluidic channel, the surface tension of the liquid and the wettability of the surface. To fabricate larger microlenses, larger fluidic channels should then be used; deposition on more hydrophilic surfaces and the use of more wettable polymers could be also investigated.
3. Characterization of the microlenses
3.1 Lens shape characterization
With the method described above, single microlenses as well as arrays of microlenses can be deposited successively with a single cantilever, as shown in Fig. 3.
The deposited droplet arrays have been characterized by Scanning Electron Microscopy (SEM) and present a well-defined hemispherical shape. This has been confirmed using a Wyko NT2000 non-contact optical profiler in the VSI mode . A cross section of the lens profile is shown as an example on Fig. 4. Corresponding data are provided in Table 1. Dx and Dy are the diameter along the horizontal and vertical direction respectively. h represents the lens height or sag and is determined as the height difference between the lens vertex and the substrate level; measured sags are in the range [3–20μm] for diameters between 20 and 110 μm. The vertical resolution on the measurements is 3nm while the lateral resolution is 0.4μm. From these measurements, the curvature radius R of the lenses can be inferred using the following equation:
The obtained data are in good agreement with curvature radii deduced from circular fits directly performed on the experimental profiles (see Table 1).
After this geometrical analysis, we can conclude that all microlenses have a spherical footprint. In addition, the contact angle can be determined by the relation:
We found a value of 38±1.5°, which is in quite good agreement with the expected values, namely 40°. Moreover, we have tested the deposition of 25 successive identical droplets and have measured a standard deviation of 2.7% on the diameter (29.03±0.79μm) and of 2% on the curvature radius (25.64±0.52μm). This variation can be correlated to the SU-8 surface topography variation and the deposition uniformity could be therefore improved by using integrated force sensors .
3.2 Surface roughness
AFM characterization achieved on top of the microlenses reveals that the surface presents an average roughness (Ra) of 2.02 nm, to be compared to 0.3nm on the initial surface, for a randomly selected area of 500nm×500nm (Fig. 5). These measurements confirm that the surface morphology of the microlenses fabricated by our spotter seems to be as good as that obtained by ink-jet printing or other dispensing methods. This can be accounted for by the fact that for all these techniques the lens formation is based on surface tension of the liquid polymer droplet.
3.3 Optical properties of the microlenses
We have first evaluated the optical properties of the microlenses by focusing an optical microscope on their surface. Once this first position was recorded, the microscope objective was moved down to the focal plane by forming an image through the lens. The difference between the two positions provides the lens focal length . The obtained values are plotted in Fig. 6.
Lenses were also characterized with a transmission Mach-Zehnder interferometer . With this method, the imaging suffers from diffraction for lenses with diameters smaller than 50μm. Therefore only measurement results for larger lenses can be considered as reliable. Values of both methods are in good agreement in the common available range (Fig. 6). From this figure we can observe that the evolution of the focal length as function of the lens diameter is linear which means the numerical aperture is quite constant whatever the size: NA≈0.33 (f/# ≈1.51). Therefore, this deposition method is suitable for fabricating small f-numbered microlenses. The wave aberrations of the refractive microlenses have been evaluated using a transmission Mach-Zehnder interferometer with a spherical wavefront illumination. The measurement of the wave aberrations is carried out by using a phase shifting interferometry (PSI) algorithm. From the data the software calculates the unwrapped phase distribution and, by subtracting the tilt and the defocus, the deviation from an ideal wavefront (phase/lambda) can be found. Fitting this deviation to a 4th degree Zernike polynomial then gives the aberrations (phase/lambda). Results are reported in Fig. 7 and in Table 2. We can conclude that microlenses with diameters consistent with the available measurement range exhibit a diffraction-limited behaviour with RMS aberrations lower than λ/14 . These results show the interest of the present fabrication technique for low-cost fabrication of micro-optical elements.
4. Discussion and conclusions
The ability of our cantilever-based spotter technique to fabricate spherical microlenses with good optical quality has been demonstrated with a home-made thermocurable epoxy polymer. With regard to other techniques, this fabrication method is well suited for custom-made lens prototyping rather than for high speed mass production and its main advantages lie on its simplicity and its low cost. In addition, since the absolute position of the cantilevers is realtime optically controlled and it is a contact method, the drops can be positioned accurately with a micrometric resolution. In this work, diameters in the range [25–130μm] with corresponding focal lengths in the range [60–105μm] and f-numbers around 1.5 have been achieved. There is no technical limitation to fabricate microlenses with larger sizes providing the use of larger cantilevers. To allow for parallel deposition of microlens arrays and to improve size uniformity at a nanometric scale, the use of integrated force sensors could be also investigated. In addition, this technique could be tested with commercial UV-curable polymers, allowing a room temperature process and thus increasing post-processing compatibility. Finally, this technique makes possible the individual adjustment of the size -and thus of the focal length- of each microlens of an array in function of the corresponding light source to correct. This advantage will be exploited in microlenses fabrication for VCSEL arrays collimation.
This work is supported by an internal project of the LAAS-CNRS laboratory. The authors would like to thank Chantal Fontaine, Jean-Bernard Pourciel and Liviu Nicu for fruitful discussions as well as the partners of the Optonanogen IST STREP project for initiating the study. Optical characterizations were in part supported by the Fund for Scientific Research in Flanders FWO, the Flemish Large Scale Infrastructure and the Network of Excellence on Micro-Optics (NEMO). Heidi Ottevaere is indebted to FWO for her research funding.
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