Linear thermal expansion coefficient (at temperatures from 130 to 800 K) of borosilicate glasses applicable for coupling with silicon in microelectronics

TL;DR

This study measures the linear thermal expansion coefficients of two borosilicate glasses over 130 to 800 K, providing data crucial for microelectronics device modeling and silicon-glass bonding optimization.

Contribution

It offers new precise measurements and polynomial models of thermal expansion for LK5 and Borofloat 33 glasses across a wide temperature range.

Findings

Thermal expansion coefficients determined with less than ±5% and ±3% imprecision.

Polynomial equations modeling temperature dependence provided.

Results aid in device modeling and bonding process optimization.

Abstract

Processing results of measurements of linear thermal expansion coefficients and linear thermal expansion of two brands of borosilicate glasses --- LK5 and Borofloat 33 --- are presented. The linear thermal expansion of glass samples have been determined in the temperature range 130 to 800 K (minus 143 to 526 $\deg$C) using thermomechanical analyzer TMA7100. Relative imprecision of indirectly measured linear thermal expansion coefficients and linear thermal expansion of both glass brands is less than $\pm$5 % and $\pm$3 % respectively. Polynomial equations, approximating temperature dependence of obtained measurements, are presented. The results will facilitate the modeling of the characteristics of the devices which are used in microsystems engineering and fabricated by anodic bonding of silicon to glass, they can also be used to optimize the temperature regime of silicon to glass bonding process. Keywords: linear expansion, thermal expansion coefficient, thermomechanical analysis, borosilicate glass.