662 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 22, NO. 3, JUNE 2013 Effect of Fluid Viscosity on Dynamics of Self-Assembly at Air–Water–Solid Interface Kwang Soon Park, Ji Hao Hoo, Rajashree Baskaran, and Karl F. Böhringer Abstract—This paper details the effect of fluid viscosity on previously presented self-assembly at an air–water–solid interface through experimental and analytical approaches. The assembly method is subdivided into three process steps (approach, rotation, and pull-up), and their viscosity dependence is investigated. The motion of a moving part is described using a derived model- ing equation. The assembly proceeds row-by-row as an assem- bly substrate is pulled up through an air–water–solid interface. High yields at different viscosities are demonstrated using thin square parts (2000 × 2000 × 100 μm 3 ). Near 100% yield can be achieved by adding visual feedback control for the application of Faraday waves. The combined effect of the application time and the fluid viscosity is analyzed. [2012-0255] Index Terms—Directed self-assembly, fluidic self-assembly (FSA), orientation specific, packaging, self-assembly, viscosity. I. I NTRODUCTION D UE TO the increasing demand for cost-effective and value-added systems with small form factors [1], minia- turization for functional densification is being done with smaller and thinner parts. However, thin parts with low aspect ratios are particularly fragile when exposed to high accelera- tions and point forces in the assembly process [2]. For assem- bly with large numbers of small and thin parts, conventional pick-and-place becomes costly, and self-assembly is a viable alternative. Self-assembled structures in nature have inspired modern research in engineered self-assembly at the nano-to-millimeter scale [3], [4] to replace traditional manufacturing methods. Industry and research groups have developed self-assembly strategies, which employ various driving forces such as gravity [5], surface tension [6]–[8], and electrostatic [9] or magnetic force [10], [11], and often require adhesives, liquid solder, shape-matching structures, or two different liquids [12]. For ex- ample, Alien Technology (Morgan Hill, CA) has commercial- Manuscript received August 28, 2012; revised December 16, 2012; accepted December 26, 2012. Date of publication February 15, 2013; date of current version May 29, 2013. This work was supported by the Defense Advanced Research Projects Agency N/MEMS S&T Fundamentals program under Grant N66001-10-1-4004 issued by the Space and Naval Warfare Systems Center Pacific. Part of this work was conducted at the University of Washington Microfabrication/Nanotechnology User Facility, a member of the NSF National Nanotechnology Infrastructure Network. Subject Editor C.-J. Kim. K. S. Park, J. H. Hoo, and K. F. Böhringer are with the Department of Electrical Engineering, University of Washington, Seattle, WA 98195 USA (e-mail: gomgom75@uw.edu; jhoo@uw.edu; karlb@u.washington.edu). R. Baskaran is with the Department of Electrical Engineering, University of Washington, Seattle, WA 98195 USA, and also with Intel Corporation, Hillsboro, OR 97124 USA (e-mail: rajashree.baskaran@intel.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JMEMS.2013.2239257 ized fluidic self-assembly (FSA) to assemble radio frequency chips across large plastic substrates based on shape matching [13], [14]. Jacobs et al. introduced a method for self-assembling small parts at a liquid–liquid–solid interface [12], which assem- ble parts in unique orientation and does not use Faraday waves [15], [16] for one-to-one part-to-binding site registration. In [17], we introduced a novel FSA of millimeter-scale thin square parts (2000 × 2000 × 100 μm 3 ) at the air–water–solid interface utilizing an interfacial capillary force. High yield assembly using temporary Faraday waves was demonstrated with a comprehensive model and experimental support. In [18], our FSA method was improved to assemble thin parts in unique orientations by adding a Ni pattern on parts and magnets underneath each binding site. The detailed motion of objects suspended in fluids with different viscosities has been extensively studied by many groups [19]–[21]. For FSA, velocity change of moving parts [14] and the effect of viscosity are briefly mentioned in [13] and [22]. However, to our knowledge, detailed studies on the effect of viscosity on self-assembly processes or yields have not been undertaken. Here, we investigate in detail the effects of viscosity on the assembly processes, assembly speed, and yield of our FSA using a newly derived modeling equation, experimental results, and analysis. II. FSA STRATEGY A. FSA System Setup The orientation-specific FSA system in Fig. 1 consists of a water container set on a linear electromagnetic vertical vibra- tion table (Brüel & Kjær Type 4809), an assembly substrate, and Ni-patterned parts floating at an air–water–solid interface, and a stepper motor (Soyo, SY42STH38-0406A) with a con- troller (Phidgets, 1062) to pull up the assembly substrate. The acceleration uniformity over the vibration table is ±10 mg or 0.72% as measured using a laser vibrometer (Polytec OFV-534 laser unit and OFV-2500 vibrometer controller) when driven at 80 Hz/1.5 g (1 g =9.8 m/s 2 ). The substrate is tilted at a 45 ◦ angle with respect to the water surface and is vertically pulled up by the stepper motor at a speed of 0.415 mm/s. Accurate magnet-binding site alignment is achieved using a photolithographically patterned “magnet template.” The mag- nets are placed in the 100-μm-deep trenches on the template. Then, the magnet template is aligned with the assembly sub- strate (40 × 40 mm 2 ). The assembly substrate is fabricated from a silicon wafer coated with Cr/Au (10/100 nm) by electron beam evaporation. 1057-7157/$31.00 © 2013 IEEE