Thermomechanical Modeling and Stress Analysis of Copper Inverse Opal (CIO) Structure for Capillary-Fed Boiling

Recently, a microporous copper inverse opal (CIO) wick material has been utilized in the thermal management of microelectronics as it significantly enhances heat transfer performance with capillary-fed boiling, providing a high critical heat flux of up to ~1100 W/cm2. In this study, we numerically investigate the thermomechanical reliability of the CIO structures with a finite-element method. The mechanical stress of ordered and graded CIO structures is simulated under the conditions of external shear load and boiling-induced thermal expansion. Different geometric parameters, including pore diameter and the neck-to-pore ratio of ordered CIO, and overlap distance and pore gradient of graded CIO, have been parametrically studied. Based on the effective mechanical properties extracted with the representative volume element (RVE) method, the mechanical response of the porous structure can be further understood. The von Mises yield criterion is applied to determine the fracture of the copper (Cu) structure. The reliability of ordered CIOs is assessed by evaluating the maximum von Mises stress and shear stress under the shear load, showing lower stresses with larger pore diameters and smaller pore-to-neck ratios. In contrast, a decrease in thermal stresses is found to appear in ordered CIOs with small pores and large neck-to-pore ratios under boiling conditions. The thermomechanical reliability of graded CIOs is analyzed with different pore gradients and overlap distances. The stress distribution of graded CIO structures in the shear test indicates that a well-coupled CIO interface could improve interfacial reliability and transfers the maximum stress point to pores near the silicon (Si)–Cu interface. The interfaces between the layers of CIOs are found to be more vulnerable under boiling conditions. The graded CIO with a larger gradient tends to be more fragile due to the stress concentration at the CIO interfaces induced by the increased differences in pore diameter.