other mechanisms that are not included in the model, including glass shrinkage and development of a depleted zone or initial wafer bow variations. The initial shape of the silicon and Pyrex wafers prior to bonding affects the overall bonded wafer shape and could be considered to further improve modeling accuracy. Furthermore, inaccuracies in the thermal measurement system in the bond systems can result in different anisothermal conditions than expected. Finally, the model assumes that each wafer is held at a constant and uniform temperature. The anodic bonder used in this study requires that the wafers be maintained in close proximity during the heating phase, separated by an air gap of less than 1 millimeter and with thin steel “flags in contact with the both wafers at three points on the outer periphery. As such, it is expected that the wafers will not be at a uniform temperature prior to bonding. The temperatures reported here are those measured at the bonding chuck in contact with the unbounded surface of both the Pyrex and silicon wafer. However, other bonder designs can provide a large gap between the wafers with no direct contact, reducing this concern. Figure 2 displays IR-GFP results from the isothermal and anisothermal bond recipes. It is immediately apparent that significantly different stress states are associated with these features. The residual shear stress patterns at these defects displays an opposite orientation, resulting from the concentration of a tensile stress field in the silicon wafer from isothermal conditions and a compressive residual stress field in the silicon wafer from the anisothermal conditions chosen for this investigation. Figure 2: Representative IR-GFP images of an etched cavity in a bonded wafer pair using the isothermal (left) and anisothermal (right) bond recipes. Note the opposite orientation of the local residual shear stress field indicating that the anisothermal recipe results in a concentrated residual maximum normal stress distribution near the cavity corners. IV. CONCLUSIONS AND FUTURE WORK This study has provided the foundation for a simple method to control the residual stresses and thus resulting wafer bow in anodically bonded structures by controlling the initial bond temperatures of the silicon and Pyrex wafers independently. The process should be capable of inducing a range of residual stresses states including leaving the silicon devices layer in a stress free state or introduction of a residual compressive stress in the silicon wafer that often contained etched features. Finally, it was shown that the stress concentrations associated with etched features are modified through this process such that a highly tensile stress can be eliminated thus 272
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