Mechanical Stresses Estimation in Silicon and Glass Bonded at Elevated Temperature

TL;DR

This paper evaluates thermal mismatch stresses in silicon-glass bonds formed at high temperatures, proposing models to optimize bonding parameters and minimize internal stresses caused by thermal expansion differences.

Contribution

It introduces mathematical models for assessing and reducing thermal mismatch stresses in silicon-glass bonds, considering nonlinear thermal expansion coefficients and multilayered assemblies.

Findings

Varying glass thickness can minimize stress at specific depths.

Models enable optimization of bonding parameters to reduce residual stresses.

Assessment of different glass types and bonding temperatures.

Abstract

During electrostatic bonding, also known as anodic bonding, silicon is bonded to glass by applying an external voltage and simultaneous heating to temperatures of 200...450 $\deg$C. While cooling to working temperature after bonding happened pieces are mutually deformed. Due to linear thermal expansion coefficients mismatch of anodically bonded glass and silicon samples an internal stress state is generated. Such stresses are called thermal mismatch stresses. The aim of this paper is a determination of technological and design solutions to achieve minimal thermal mismatch stresses in resulting bond. The nonlinear dependence of linear thermal expansion coefficients of bonded samples' materials on temperature makes it difficult to minimize thermal mismatch stresses by chosing materials with close average thermal expansion coefficients in particular temperature range. To assess means of lowering thermal mismatch stress in this paper two different ways to describe assembly are used: two thin bonded layers and multilayered composite material. Based on properties of two brands of glass (LK5, Borofloat 33) and silicon used with described mathematical models thermal mismatch stresses at temperature $T_w$ in samples bonded at several different temperatures $T_b$ are evaluated. Bonded silicon surface stress dependence of glass to silicon wafer thickness ratio is evaluated. Based on such evaluations one can say that by varying thickness of glass bonded to silicon one can obtain zero thermal mismatch stress at a particular depth of material or obtain stress of some defined value at this depth. Models of assembly description used in this paper can be used to optimize anodic bonding process parameters. Such usage aimed to minimize thermal mismatch stresses at device working temperatures is presented in this paper.