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Microelectromechanical relays have recently been proposed for ultra-low-power digital logic because their nearly ideal switching behavior can potentially enable reductions in supply voltage (Vdd) and, hence, energy per operation beyond the limits of MOSFETs. Using a calibrated analytical model, a sensitivity-based energy-delay optimization approach is developed in order to establish simple relay design guidelines. It is found that, at the optimal design point, every 2 X energy increase can be traded off for a ~1.5x reduction in relay delay. A contact-gap-to-actuation-gap thickness ratio of 0.7-0.8 is shown to result in the most energy-efficient relay operation, implying that pull-in operation is preferred for an energy-efficient relay design. Based on the analytical model and design guidelines, a scaling theory for relays is presented. A scaled relay technology is projected to provide >; 10 X energy savings over an equivalent MOSFET technology, for circuits operating at clock frequencies up to ~100 MHz.