On the modelling and placement of bonding-pillar holes in multi-wafer, vacuum-packaged MEMS

Reliability considerations in multi-wafer, vacuum- packaged MEMS often require the usage of bonding pillars connecting the top and bottom capping wafers. Such bonding pillars in turn require the etching of holes into the device wafer. Placement constraints sometimes necessitate that these holes be etched through the mechanical element itself, be it the beam, the membrane or the proofmass. In this paper, we use the example of a micro-scale piezoelectric energy harvesting platform to incorporate the effect of bonding-pillar holes of arbitrary shapes and sizes in the electromechanical model of the device. In particular, we develop the corresponding multi-modal equivalent circuit model (ECM) and use a MEMS-CMOS co-simulation environment to obtain the single-mode terminal voltage output under resistive loads. The ECM has been fully validated using 3D Finite Element analysis, and the impact of bonding-pillar holes on device metrics has been compactly parameterised for the first time. This modeling approach is included in a new design framework for device structural integrity whose goal is the optimal placement and sizing of bonding pillars in multi- wafer, vacuum-packaged MEMS.