Modeling of Backside Power Delivery and Thermal Management in Semiconductor Die Packages

Modern semiconductor packaging faces the dual challenges of efficiently delivering power to numerous transistors and managing heat to prevent hotspots and potential component failure. Backside power delivery (BSPD) distinguishes itself from conventional power delivery methods by delivering power from the backside of the silicon die, using unused space for thicker power lines and thereby reducing resistance loss. Embedded microfluidic cooling strategies have investigated microchannels in the back side of silicon dies to direct coolant over hotspots, effectively dissipating heat for chip temperature management. We propose a synergistic integration of microfluidic channels with power delivery on the backside of semiconductor dies that can potentially offer optimized space utilization to allow balanced power and thermal performance. However, this requires modeling tools that can accurately capture coupled electrical and thermal responses in 3D while resolving the small feature sizes relative to the overall die size that can lead to computational complexity. To address this challenge, we develop a model that employs a homogenization method that allows for sub-grid resolution of microscale features, as well as the transformation of the fully 3D problem into an equivalent set of connected 2D subproblem. This work demonstrates application of this method to numerically study a silicon die with both a backside power delivery network (BSPDN) and manifold liquid cooling microchannels. 3D transport is represented by considering the energy and mass exchange between multiple 2D layers. The homogenized representation treats the domain as a porous composite material with metallic power lines navigating between the flow channels. Homogenized conservation thermofluidic conservation equations for the porous medium that consider electrical Joule heating are used to construct the numerical model. Representative steady-state cases are studied where the silicon die generates uniform heating with local hotspots. Through these case studies, we reveal the potential application advantages of integrating 3D manifold microchannels for cooling in a BSPDN for high-power operations.