A Semi-Analytical Thermal Modeling Framework for Liquid-Cooled ICs

While possessing the potential to replace conventional air-cooled heat sinks, inter-tier microchannel liquid cooling of 3D ICs also creates the problem of increased thermal gradients from the fluid inlet to outlet ports [1, 2]. These cooling-induced thermal gradients can be high enough to create undesirable stress in the ICs, undermining the structural reliability and lifetimes. In this paper, we present a novel design-time solution for the thermal gradient problem in liquid-cooled 3D Multi-Processor System-on-Chip (MPSoC) architectures. The proposed method is based on channel width modulation and provides the designers with an additional dimension in the design-space exploration. We formulate the channel width modulation as an optimal control design problem to minimize the temperature gradients in the 3D IC while meeting the design constraints. The proposed thermal balancing technique uses an analytical model for forced convective heat transfer in microchannels, and has been applied to a two tier 3D-MPSoC. The results show that the proposed approach can reduce thermal gradients by up to 31% when applied to realistic 3D-MPSoC architectures, while maintaining pressure drops in the microchannels well below their safe limits of operation.