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.

A silicon test chip for the thermomechanical analysis of MEMS packagings

“…The first is the analytical way. In the past, many analytical models were developed to describe the behavior of simple and plane geometric structures being compounded of two or three different isotropic materials (Timoshenko and Gere 1961;Nejhad et al 2003). All these theories are not usable for complex three-dimensional structures, which are composed of a large number of different materials on a small spatial extend with partly anisotropic material properties.…”

Analysis of thermal stresses in HfO2/SiO2high reflective optical coatings for high power laser applications

“…In the past decades, many researchers have taken efforts to analyze the thermal stresses by developing some analytical models of thermal stresses in elastic multilayer systems 2,[4][5][6][7] . What's more, with the development of computing technology, more and more researchers are using numerical methods like finite element method (FEM) to model and investigate the thermal stresses in multilayer coatings [8][9][10] . Hence, analytical method and FEM ought to be good ways to investigate thermal stresses in the HfO 2 /SiO 2 multilayer optical coatings since the difficulty to obtain the thermal stress from the experiments.…”

Residual stress modeling of density modulated silicon thin films using finite element analysis

“…Silicon (Si) has been considered to be an attractive candidate anode material for Li-ion batteries because of its high theoretical specific capacity of 3500-4200 mAh/g (for Li 15 Si 4 and Li 22 Si 5 structures, respectively), which is the highest known value among current anode materials. 1 Si thin film anodes are believed to be advantageous over their bulk forms in terms of shorter pathways and faster transportation kinetics in Li-ion batteries besides their better stability and capacity retention.…”

“…[12][13][14] Basically, there are two different types of stress that should be considered in thin film structures. These stresses could be categorized as fabrication stresses 15,16 and operation stresses. 17,18 In the second class, Si film anodes in Li-ion batteries also suffer from high volume expansion/ compression during lithiation/delithiation, which introduces additional stress and can lead to cracking and pulverization of the whole film.…”