Validation of the porous-medium approach to model interlayer-cooled 3D-chip stacks

Interlayer cooling is the only heat removal concept which scales with the number of active tiers in a vertically integrated chip stack. In this work, we numerically and experimentally characterize the performance of a three tier chip stack with a footprint of 1 cm². The implementation of 100 mum pitch area array interconnect compatible heat transfer structures results in a maximal junction temperature increase of 54.7 K at 1bar pressure drop with water as coolant for 250 W/cm² hot-spot and 50 W/cm² background heat flux. The total power removed was 390 W which corresponds to a 3.9 kW/cm³ volumetric heat flow. An efficient multi-scale modeling approach is proposed to predict the temperature response in the complete chip stack. The experimental validation confirmed an accuracy of +/-10%. Detailed sub-domain modeling with parameter extraction is the base for the system level porous-media calculations with thermal field-coupling between solid fluid and solid solid interfaces. Furthermore, the strength and weakness of microchannel and pin fin heat transfer geometries in 2-port and 4-port fluid architectures is identified. Microchannels efficiently mitigate hot spots by distributing the dissipated heat to multiple cavities due to their low porosity. Pin fins with improved permeability and convective heat dissipation are advantageous at small power map contrast and aligned hot spots on the different tiers. Large stacks of 4 cm² can be cooled sufficiently by the 4-port fluid delivery architecture. The flow rate is improved four times compared to the 2-port fluid manifold. The nonuniformity of the flow in case of the 4-port demands a more careful floor-planning with hot spots placed in the chip stack corners. This is especially true in case of communicating heat transfer geometries such as pin fin structures with zero fluid velocity in the stack center. This large velocity contrast can be reduced by the implementation of - non-communicating microchannels.