Deformation Analysis of Center-Anchored Square Plate Induced by Residual Gradient Stress

For optical MEMS or Micro-Electro-Mechanical-Optical System (MEMOS) devices, as depositing metal on the structure plate, the mismatch of thermal expansion coefficients between the metal layer and structure layer will induce residual gradient stress after release. Therefore, the residual gradient stress will deform the structure layer. The deformation could be used as profile of micro focusing mirror due to its parabolic-like shape. In this work, the effect of structure sizes and material properties on residual stress for center-anchored square plate focusing mirror is investigated. The center-anchored circular plate focusing mirror is designed and analyzed. In numerical analysis using finite element method, it is found that the deformation is circular shape in axial direction and parabolic-like profile in the radial direction, even the mirror being square shape. And the radial shape determines the focal length. In general, the thinner plate and the thicker metal layer will cause larger deformation. The larger square sizes will cause larger deformation. However, it is found that the effect of anchor sizes on deformation could be neglected. Only in the anchor near region, the deformation would be affected. And the depositing temperature will have obvious effect on deformation. It is also found in literature review, the deformation would be unsymmetrical and called warpage. Warpage is a serious problem to destroy the devices. Therefore, the warpage is also discussed. The thicker structure layer and thinner metal layer need higher temperature to cause warpage phenomena. The warpage temperature increases nonlinearly as the structure layer increasing. However, in thinner structure layer condition, the warpage temperature decreases first and increases following. In general, from the results it could be considered that as the ratio of structure and depositing metal layer thickness increasing, the deformation will reach to a limit value due to the saturation of stress gradient.