Calculation and selection of silicon to glass anodic bonding modes based on the criterion of minimum residual stress

TL;DR

This paper develops a scientifically justified method for selecting anodic bonding parameters between silicon and glass to minimize residual stresses, enhancing MEMS device reliability through theoretical modeling and experimental validation.

Contribution

It introduces a new technique for minimizing residual stresses in silicon-glass anodic bonding by analyzing thermal expansion and optimizing material thickness ratios.

Findings

Thermal expansion coefficients of glass vary with temperature from -100°C to 500°C.

Optimal silicon-to-glass thickness ratio reduces residual stress.

A practical technique for residual stress minimization in device design.

Abstract

The goal of this work is a scientifically justified choice of efficient technological parameters of anodic bonding of silicon to glass, ensuring a minimum level of residual stresses. The relevance of this dissertation is determined by the continuous efforts to reduce the negative effects of the joint use of dissimilar materials in electronic devices. Theoretical and practical results: the temperature dependence of the true values of the coefficient of thermal expansion of popular glass brands in the temperature range from minus 100 \deg C to 500 \deg C were obtained; the ratio of thicknesses of silicon and glass that minimizes residual stress on the silicon surface was calculated; the technique of minimizing the residual stresses in silicon anodically bonded to glass was developed. Results of this research are applicable to MEMS devices design and simulations. The first chapter provides the analysis of the current state of research in the field of anodic bonding technology application. The second chapter is devoted to the experimental study of temperature dependence of the linear thermal expansion coefficient of the glass. Thermomechanical properties and composition of the following glass brands: LK5, Schott Borofloat 33, Corning 7740, Hoya SD-2 were measured. The third chapter describes the existing models of estimating the residual stresses in the silicon-glass bonds. Two models based on a theory of strength of materials and the classical lamination theory with an additional temperature dependence of coefficients of thermal expansion are proposed for further use. Residual stresses in silicon-glass bonds are estimated with these models and data from the preceding chapter. The fourth chapter describes the experiments carried out to confirm claims from the previous chapters. The proposed technique of minimizing residual stresses is described as steps for a device designer.