bow with the silicon concave as is expected due to the mismatch in silicon and Pyrex CTE. The standard isothermal bonding recipe yields a significant wafer bow with a radius of curvature of approximately -8.1 m. This magnitude of wafer bow is similar to that reported in the literature with an isothermal recipe [7-10]. Meanwhile, the wafer pair bonded via the anisothermal recipe shows that a nearly opposite curvature (+6.5 m) can be achieved by reducing the Pyrex wafer temperature by approximately 45oC from the silicon temperature.. Figure 1: Representative local area line scans depicting wafer curvature for wafers bonded with Pyrex and silicon temperatures of (blue) 400oC, 400oC and (red) 388oC, 343oC respectively. With no other change in bond process (in terms of time, power and input requirements), it is possible to completely reverse the wafer bow that results from anodic bonding. This simple modification to the bond recipe does not cause any changes to the processing time or require any addition power input. The only additional control parameter for anisothermal bonding is the independent control of platen temperatures, which can be done in a fairly straightforward manner with modern bonding equipment and control capabilities. The 45 oC temperature differential requirement to change the resultant wafer bow is small enough that it can easily be supported within a bond chamber without requiring special feedback or cooling of either chuck, yet it provides a large enough range that it should be possible to easily define a final curvature based on the anisothermal inputs. As such, structures can be designed to have a larger bow than shown here or to have bow as small as the virgin wafers prior to bonding. As a means of comparison, an ABAQUS finite element model was developed, whereby silicon and Pyrex wafers are joined at their interfacial nodes with each wafer at a uniform, elevated wafer bonding temperature. The wafers then cool to room temperature and the resulting bulk wafer curvature is calculated based on the temperature dependent coefficient of thermal expansion for each wafer. It is assumed that both silicon and Pyrex are at uniform temperature after bonding. As a baseline, an isothermal bond procedure is studied, where both silicon and Pyrex wafers are initially at 400oC. In this case, a resulting wafer radius of curvature is estimated to be roughly -9.1m (silicon “concave” in our geometry). The Pyrex temperature is then reduced until a roughly opposite curvature is predicted by the model. When the silicon wafer is maintained at 400 oC and the Pyrex wafer temperature is reduced to 360 oC, the model predicts a curvature of roughly 8.5 m (silicon “convex” in our geometry). Table 1 provides a comparison between experimental results and the corresponding numerical predictions roughly match the experimental conditions. Model and experiment agree to within approximately 20%, which is quite good for the simplicity of the model. This suggests that the bulk of the residual stress state can be explained by the mismatch in temperature dependent material thermal expansion coefficients. There are several 271
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