Intrinsic Strain Modeling and Residual Stress Analysis for Thin-Film Processing of Layered Structures

Abstract

Residual stresses develop due to intrinsic and extrinsic strains that form during the processing. Extrinsic strains can be determined using coefficient of thermal expansion, material properties, and processing conditions. An “Equivalent Reference Temperature (ERT)” technique is described and used to model and evaluate the intrinsic strains. piezoelectric microelectromechanical systems (P-MEMS) are considered in this work. Laminate theory with three-dimensional state of stress and strain is used to evaluate residual stresses using the ERT model. In finite element analysis (FEA), the residual stresses and strains of multi-layer P-MEMS structures deposited layer-by-layer during processing, are simulated using the “element birth-and-death” approach. The evaluated residual stresses for a simplified geometry using ANSYS three-dimensional FEA and analytical analysis employing three-dimensional laminate theory are presented along with their corresponding experimental results. A user-friendly software based on the 3-D laminate theory is developed and installed on the Internet. The “equivalent reference temperature” as well as residual stresses and strains can be determined using this software. The level of residual stresses and strains of P-MEMS depend upon various factors such as geometrical design, material selection, and process conditions.