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Process variations in nanometer technologies are becoming an important issue for cutting-edge FPGAs with a multi-million gate capacity. Considering both die-to-die and within-die variations in effective channel length, threshold voltage, and gate oxide thickness, we first develop closed-form models of leakage and timing variations at the FPGA chip level. Experiments show that our models are within 3% from Monte Carlo simulation, and the leakage and delay variations can be up to 3× and 1.9×, respectively. We then derive analytical yield models considering both leakage and timing variations, and use such models to evaluate FPGA device and architecture under process variations. Compared to the architecture similar to a commercial FPGA and device setting from ITRS roadmap, device tuning alone improves leakage yield by 39% and architecture and device co-optimization increases leakage yield by 73%. We also show that LUT size 4 gives the highest leakage yield, LUT size 7 gives the highest timing yield, but LUT size 5 achieves the maximum combined leakage and timing yield. To the best of our knowledge, this is the first in-depth study on FPGA device and architecture co-evaluation considering process variations.