Abstract
A relation is derived between the mismatch strain, the film thickness, and the displacement of a linear elastic structure under external loading during material deposition. If any two of these variables can be experimentally determined, then the remaining variable can be determined. The method allows one to experimentally determine the mismatch strain by measuring the film thickness and the displacement of a point on the structure that is not undergoing deposition. The intrinsic stresses can be used to self-assemble microstructures during material deposition. Assembly of two components is considered: one component is subjected to deposition and is modeled as an Euler-Bernoulli beam, and the other component is not subjected to deposition and is modeled as a linear spring. For the purposes of this paper, the definition of assembly requires that the beam do work on the spring. The analysis is experimentally verified by electroplating nickel onto an AFM cantilever beam in contact with a second AFM beam (serving as the spring) that does not undergo deposition.
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References
M. Ataka, A. Omodaka, N. Takeshima and H. Fujita, Fabrication and operation of polyimide bimorph actuators for a ciliary motion system, Journal of Microelectromechanical Systems 2 (1993) 146–150.
Y.-P. Ho, M. Wu, H.-Y. Lin and W. Fang, A robust and reliable stress-induced self-assembly mechanism for optical devices, IEEE/LEOS Int. Conf. on Optical MEMS, Lugano, Switzerland, (2002) Paper WP38.
H. Xie, Y. Pan and G. K. Fedder, A CMOS-MEMS mirror with curled-hinge comb, Journal of Microelectromechanical Systems 12 (2003) 450–457.
V. Y. Prinz, D. Grutzmacher, A. Beyer, C. David, B. Ketterer and E. Deckardt, A new technique for fabricating three-dimensional micro-and nanostructures of various shapes, Nanotechnology 12 (2001) 399–402.
B. Mi, D. A. Smith, H. Khan, F. L. Merat, A. H. Heuer and S. M. Phillips, Static and electrically actuated shaped MEMS mirrors, Journal of Microelectromechanical Systems, 14 (2005) 29–36.
P. O. Vaccaro, K. Kubota and T. Aida, Straindriven self-positioning of micromachined structures, Applied Physics Letters 78 (2001) 2852–2854.
J. M. Z. Ocampa, P. O. Vaccaro, K. Kubota, T. Fleischmann, T.-S. Wang, T. Aida, T. Ohnishi, A. Sugimura, R. Izumoto, M. Hosoda and S. Nashima, Characterization of GaAs-based micro-origami mirrors by optical actuation, Microelectronic Engineering 73–74 (2004) 429–434.
P. O. Vaccaro, K. Kubota, T. Fleischmann, S. Saravann and T. Aida, Valley fold and mountain-fold in the micro-origami technique, Microelectronics Journals 34 (2003) 447–449.
A. Vorob’ev, P. O. Vaccaro, K. Kubota, T. Aida, T. Tokuda, T. Hayashi, Y. Sakano, J. Ohta and M. Nunoshita, SiGe/Si microtubes fabricated on a silicon- on-insulator substrate, Journal of Physics D: Applied Physics 36 (2003) L71–L73.
M. W. Judy, Y.-H. Cho, R. T. Howe and A. P. Pisano, Self-adjusting microstructures (SAMS), Tech. Digest, IEEE Micro Electro Mechanical Systems Workshop, Nara, Japan, (1991) 51–56.
G. G. Stoney, The tension of metallic films deposited by electrolysis, Proceedings of the Royal Society of London A82 (1909) 172–175.
L. B. Freund, Some elementary connections between curvature and mismatch strain in compositionally graded thin films, Journal of the Mechanics and Physics of Solids 44 (1996) 723–736.
A. Ni, D. Sherman, R. Ballarini, H. Khan, B. Mi, S. M. Phillips and A. H. Heuer, Optimal design of multilayered polysilicon films for prescribed curvature, Journal of Materials Science 38 (2003) 4169–4173.
S.-H. Kim and J. G. Boyd, Modeling of mechanical behavior of microcantilever due to intrinsic strain during deposition,” Journal of Mechanical Science and Technology 20 (2006) 1646–1652.
S.-H. Kim and J. G. Boyd, Analytical and Experimental Study of Mismatch Strain-Induced Microcantilever Behavior during Deposition,” Journal of Mechanical Science and Technology 21 (2007) 415–420.
J. E. Sader, Calibration of rectangular atomic force microscope cantilever, Review of Scientific Instruments 70 (1999) 3967–3969.
W. N. Sharpe, MEMS Handbook: Chapter 3 — Mechanical Properties of MEMS Material, CRC Press, Boca Raton, (2002).
M. Schlesinger and M. Paunovic, Modern Electroplating, John Wiley & Sons, New York, (2000).
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This paper was recommended for publication in revised form by Associate Editor Maenghyo Cho
Sang-Hyun Kim obtained his B. S. (1993) and M.S. (1995) degrees in Aerospace Engineering from Pusan Nation University and Ph.D. (2005) in Aerospace Engineering from Texas A&M University. After getting Ph.D., he joined Micro Systems Lab. at Samsung Advanced Institute of Technology (SAIT) and worked in the field of MEMS designs, especially microsensors, microactuator and inkjet print head. He is currently working as a faculty member in Mechanical Systems Engineering at Hansung University. His research interest lies in design, fabrication and test of MEMS/NEMS. He is also interested in the development of design platform of multi-physics and multiscale phenomena.
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Kim, SH., Boyd, J.G. Intrinsic stress, mismatch strain, and self-assembly during deposition of thin films subjected to an externally applied force. J Mech Sci Technol 22, 2048–2055 (2008). https://doi.org/10.1007/s12206-008-0806-x
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DOI: https://doi.org/10.1007/s12206-008-0806-x