A reliability of silicon-crystalline quartz bonding through reducing of the residual stresses

In this work, a new additional opportunity to reduce the residual stresses when bonding a pair of dissimilar materials such as silicon and crystalline quartz has been revealed as a result of theoretical calculations. In parallel with a traditional method, based on lowering of bonding temperature, additional reduction of the residual stresses becomes possible owing to difference in elastic properties of dissimilar materials of the pair. In the case of coupled plates, with different coefficients of thermal expansion, the residual stresses can be reduced if the following two conditions hold simultaneously: E ₁/(1-v ₁)< E ₂/(1-v ₂) and h ₁<h ₂. Here E _i- the Young's modulus, v _i- the Poisson ratio, and hi- the thickness of the first (i=1) and the second (i=2) bonded plates respectively. For the quartz/silicon pair, the residual stresses at the interface will be approximately 20% lower if h ₁/h ₂ =0.2 as compared the case when both wafers are of equal in thickness.