Thermal resistance in superconducting flip-chip assemblies

Cryogenic microsystems that utilize different 3D integration techniques are being actively developed, e.g., for the needs of quantum technologies. 3D integration can introduce opportunities and challenges to the thermal management of low temperature devices. In this work, we investigate sub-1 K inter-chip thermal resistance of a flip-chip bonded assembly, where two silicon chips are interconnected by compression bonding via indium bumps. The total thermal contact area between the chips is 0.306 mm$^2$ and we find that the temperature dependence of the inter-chip thermal resistance follows the power law of $\alpha T^{-3}$, with $\alpha = 7.7-15.4$ K$^4$$\mu$m$^2$/nW. The $T^{-3}$ relation indicates phononic interfacial thermal resistance, which is supported by the vanishing contribution of the electrons to the thermal conduction, due to the superconducting interconnections. Such a thermal resistance value can introduce a thermalization bottleneck in particular at cryogenic temperatures. This can be detrimental for some applications, yet it can also be harnessed. We provide an example of both cases by estimating the parasitic overheating of a cryogenic flip-chip assembly operated under various heat loads as well as simulate the performance of solid-state junction microrefrigerators utilizing the observed thermal isolation.