Self-Consistent Electrothermal Modeling of Distributed Vertical Power Delivery Architecture With Substrate-Embedded Microfluidic Cooling

Lateral power delivery (LPD) becomes infeasible for high-performance computing (HPC) processors operating at voltages near 1 V with current densities of 2 A·mm^-2 due to large routing losses and Joule heating. Distributed vertical power delivery (DVPD) with integrated voltage regulators (IVRs) addresses this challenge by placing conversion stages close to the load, while substrate-embedded microfluidic cooling provides effective heat-dissipation pathways for inner tiers in vertically dense stacks. However, frameworks for self-consistent electrothermal modeling of DVPD at the system scale remain underexplored. This work develops such a framework, achieving high physical fidelity and computational efficiency. These attributes are realized by enforcing geometric and power profile consistency between the electrical and thermal models and through automation and optimized meshing. Applied to a 48-to-1 V DVPD architecture delivering 1 kW to a 500 mm² die at 2 A·mm^-2, the framework yields a self-consistent solution near the 85 °C threshold with a total system loss of 231 W and a maximum temperature of 85.7 °C, requiring a mass flow rate of 1.39 g·s^-1 in embedded microchannels. Compared to an uncoupled initial estimate of 200 W with an initial mass flow rate of 1 g·s^-1, the total system loss increases by about 15.8 %, which shows that neglecting electrothermal coupling underestimates both losses and cooling requirements. Additionally, region-specific meshing balances mesh resolution by refining near critical features and coarsening elsewhere, reducing both meshing and per-iteration times by over 30.0 % without loss of prediction accuracy.