Abstract
Due to the mismatch between the coefficients of thermal expansion (CTE) of two adjacent films, the residual stress was growing up during thermal cycling. The aim of this work is to extend the Stoney equation for the multilayer thin films with heterostructure (voids filled with gas or other solids) or unsmooth interface. The general theoretical models were built for elastic and elastic-plastic deformation in the multilayer films with void region filled with other solid or gas. The proposed closed solution (CS) was simplified for analyzing the micro/nano devices with the micromachined multilayered multilayer films structure that thin films locate on a much thicker substrate. One model of through silicon via (TSV) has been built and analyzed. Based on the finite element method (FEM) and the initial CS, a modified CS is built up. The influence of the location and thickness of void, CTE and Young’s modulus (YM) on the normal stress of the thin films was analyzed by the simplified CS and FEM. Based on the FEM and CS the linear and coupled relationship has been set up. With the FEM analysis, the equivalent CTE and YM influenced by the void can be described by equation. The difference of critical temperature for the film from elastic deformation to plastic deformation was studied.
Highlights
With the development of microelectro-mechanical system (MEMS), the microelectronic devices are miniaturization and densification
The internal stress affected by the filling process has been analyzed by the Stoney equation with perfect interface assumption.[8]
The following analysis are based on Eq(10a)–(10b) for elastic deformation and Eq(13a)–(13b) for plastic deformation
Summary
With the development of microelectro-mechanical system (MEMS), the microelectronic devices are miniaturization and densification. The thermal mechanical stress of the microstructural devices becomes an important factor to predict the fatigue life and optimize the design.[1] Since thermal mechanical properties[2,3] and the mismatch between the coefficients of thermal expansion of two adjacent films all affect the thermal mechanical stress. The temperature variation could not be avoided during the fabricating,[4] packaging, and operating process.[5] The analytical analysis and numerical analysis are the effective and low-cost ways to evaluate the stress. Stoney equation[6] (Eq(1)) has been used widely to analyze the stress of the microelectronic device with multilayer films, such as TSV7,8 and microcantilever biosensors.[9] σ = Est2s /(6tf r)
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