Coefficient of Thermal Expansion Mismatch Induced Stress Calculation for Field Assisted Bonding of Silicon to Glass

TL;DR

This paper analyzes the residual stresses caused by thermal expansion mismatch in silicon-glass assemblies, providing calculation methods and experimental validation relevant for electronic packaging and MEMS device reliability.

Contribution

It introduces a stress calculation approach based on lamination theory and presents experimental validation for bonded silicon-glass structures.

Findings

Stress distribution varies with material thicknesses

Bonded silicon surface stress depends on glass-to-silicon thickness ratio

Experimental birefringence measurements confirm stress calculations

Abstract

The residual stress induced in assembly is a common concern in electronic packaging. The mismatch in coefficient of thermal expansion between borosilicate glass and silicon, upon temperature variation, generates an internal stress state. This affects important characteristics of microelectromechanical devices or constituent elements. Such as self frequence or stiffness. Stresses caused by thermal expansion coefficients mismatch of anodically bonded glass and silicon samples are studied in this paper. Stress calculation based on lamination theory is presented. Usage examples of such calculations are described. For bonded silicon and LK-5 glass several results of calculations are presented. Stress distribution in bonded silicon and glass of several thicknesses is evaluated. Stress distribution in bonded glass-silicon-glass structure is evaluated. Bonded silicon surface stress dependence of glass to silicon wafer thickness ratio is evaluated. Experimental study of thermal mismatch stress in glass based on birefringence phenomenon was conducted. It's results are presented in this paper. Keywords: anodic bonding, field assisted bonding, thermal expansion, stress.