Study of Adhesion, Residual Stress, and Squeeze Film Effect in Plates of Microstructures

• Main Authors: Meng-Ju Lin, 林孟儒
• Other Authors: Rongshun Chen
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/24315812166439899131

博士 === 國立清華大學 === 動力機械工程學系 === 90 === Microelectronmechanical systems (MEMS) become one of the most promising research areas, and have gradually earned the respect in industry, by the advantages of tiny mass and size, fast dynamic response, wide usage in many regimes, and batch fabrication. However, some physical phenomena ignored in macroscale such as adhesion, deformation caused by residual stress, and effect of squeezed gas film, may become very important in microscale. Plates have been widely used as the structure layer in MEMS. The physical properties of plates often determine the success of a sensor or an actuator. Therefore, if a plate is used as a structure layer, the physical properties between a plate and its underlying substrate should be most concerned. In the analysis of plate deformation, theory of beams is frequently applied in the current literatures due to simplicity. However, the mechanical behavior of plates is much more complex than beam, in general. Consequently, if a beam is utilized to model a plate, the predicted errors may be significant. Therefore, in this thesis, the theory of plates-and-shells is introduced to estimate the deflection of the plate caused by capillary force or residual stress. In this thesis, the adhesion, due to the capillary force, between a center-anchored plate, a circular plate or a sector plate, and its underlying substrate is investigated. Then the effect of residual stress caused by thermal treatment processes is studied for both plates considered above. Finally, the effect of squeezed gas film for a rectangular plate and the substrate is examined. The adhesion affected by the factors: thickness of plate, surface tension of liquid, and two material properties: Young’s modulus and Poisson’s ratio, are thoroughly investigated for the considered plates. Two critical gaps, and , are derived for circular plates. When , the plate adheres to substrate, while , it is free from sticking. Furthermore, by using catastrophe theory, a nondimensional elastocapillary number is derived and is employed as the first approximation to determine if the circular plate will pin on the substrate or not. Theoretically, when , the center-anchored circular plate will restore to its desired position, while , it will attach to substrate. Moreover, by the experimental results, a novel criterion is defined to examine the adhesion effect for the proposed devices. For > 0.9903, the plate will be free, while for < 0.9903, it will stick to the substrate. The circular plates have been successfully fabricated through surface micromachining to examine the feasibility of the proposed nondimensional numbers. The experimental results showed that only 8.87% error if = 0.9903 is employed. From theoretical analysis, two critical gaps are derived to judge the adhesion for center-anchored sector plates. However, residual stress is also included here. As in the center-anchored circular plates and by using these two critical gaps, three regions are located to decide the adhesive conditions between the sector plate and its underlying substrate. From theory of plates-and-shells, a mathematical model of residual stress is derived. Using surface micromachining, the sector plates are fabricated to verify the theoretical analysis. It is concluded that residual stress is one of the major factors in sticking. It is also demonstrated that deformation in the tip of the sector plate is larger than in the centerline, and the phenomenon is more obvious if the angles of sector increase. In the deposition of metal, the mismatch of thermal expansion coefficients between the metal layer and structure layer will induce residual stress after release, and thus deform the structure layer and lower the yield ratio of the devices. By theory of plates-and-shells, the deformation caused by residual stress from thermal treatment is investigated. It is shown that the theoretical predictions agree with the measured results. In general, the thinner plate of structure layer and the thicker metal layer will cause larger deformation. The surrounding gas due to the pumping action significantly influences the motion of microstructure, especially as the size of the microstructure is reduced. The effect of squeezed gas film is important in dynamic response when two plates or a plate and its underlying substrate with narrow gap, move normal to each other. A novel model is derived by using Navier-Stokes equation with pulsating flow between parallel surfaces to discuss the effect of squeezed gas film when devices are actuated in one atmosphere pressure. The relationship between spring force caused by squeezed film effect and gaps is found. By experiments, it is proved that the proposed model is fea