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김상현,James G. Boyd IV 대한기계학회 2008 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.22 No.11
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.
Modeling of Mechanical Behavior of Microcantilever due to Intrinsic Strain during Deposition
Kim Sang-Hyun,Mani Sathyanarayanan,Boyd James G. IV The Korean Society of Mechanical Engineers 2006 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.20 No.10
A model of mechanical behavior of microcantilever due to intrinsic strain during deposition of MEMS structures is derived. A linear ordinary differential equation is derived for the beam deflection as a function of the thickness of the deposited layer. Closed-form solutions are not possible, but numerical solutions are plotted for various dimensionless ratios of the beam stiffness, the intrinsic strain, and the elastic moduli of the substrate and deposited layer. This model predicts the deflection of the cantilever as a function of the deposited layer thickness and the residual stress distribution during deposition. The usefulness of these equations is that they are indicative of the real time behavior of the structures, i.e. it predicts the deflection of the beam continuously during deposition process.