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Nanoelectromechanical (NEM) relays are promising candidates for programmable routing in Field-Programmable-Gate Arrays (FPGAs). This is due to their zero leakage and potentially low on-resistance. Moreover, NEM relays can be fabricated using a low-temperature process and, hence, may be monolithically integrated on top of CMOS circuits. Hysteresis characteristics of NEM relays can be utilized for designing programmable routing switches in FPGAs without requiring corresponding routing SRAM cells. Our simulation results demonstrate that the use of NEM relays for programmable routing in FPGAs can simultaneously provide 43.6% footprint area reduction, 37% leakage power reduction, and up to 28% critical path delay reduction compared to traditional SRAM-based CMOS FPGAs at the 22nm technology node.