Die stacking has enabled 2.5D FPGAs by integrating multiple active dice on a passive silicon interposer for improved yield and capacity, and paved the way for 3D architectures that stack active dice directly atop one another. In these multi-die devices, the unique electrical and physical characteristics of the underlying die-stacking technology impose limitations on inter-die connection density and latency, necessitating a bespoke inter-die routing architecture. However, the absence of accurate and versatile modeling tools has left most questions about how to best design the inter-die routing architecture unanswered. To address this gap, we enhance the open-source FPGA CAD tool VTR to flexibly model a wide range of multi-die routing architectures, and augment VPR's placement and routing engines to improve optimization for both 2.5D and 3D FPGAs. We perform HSPICE-based circuit modeling of inter-die connections for active dice using a 7 nm process node and a 45 nm silicon interposer across several die-crossing technologies. Using this enhanced framework, we conduct a detailed design space exploration of inter-die routing architecture in 2.5D and 3D FPGAs, characterizing the impact of die-crossing technology, inter-die connection count, fan-in/fan-out, and interposer wire length on critical path delay (CPD), wirelength, area, and routability. Our results show that with suitable inter-die routing architectures, 2.5D and 3D FPGAs can increase capacity without significant routability or delay penalties. Specifically, 3D FPGAs achieve up to 14% wirelength reduction and 6% CPD improvement over 2D devices, and remain routable even with existing $10\,μ$m pitch technologies, while 2.5D FPGAs incur only a 2% wirelength and 4% CPD overhead at 32% inter-die connectivity. All extensions are open source and integrated with the VTR master branch.

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