Reducing thermal mismatch stress in anodically bonded silicon–glass wafers: theoretical estimation

This paper reports the theoretical study and estimations of thermal mismatch stress reduction in anodically bonded silicon–glass stacks by justifiable selection of bonding temperature and glass thickness. This can be done only after prior thorough study of temperature dependence of the linear thermal expansion coefficient of the glass and silicon to be used. We show by analyzing such a dependence of several glass brands that the usual idea of decreasing the bonding process temperature as a solution to the thermal mismatch stress problem can be a failure. Interchanging glass brands during device design is shown to produce very contrasting changes in residual stresses. These results are in good agreement with finite-element modeling. This paper reports there is proportion between glass and silicon wafer thicknesses minimizing thermal mismatch stress at unbonded side of the silicon independently of the bonding or working temperatures chosen.