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Exponential increase in leakage power has emerged as a major barrier to technology scaling. Existing circuit techniques for leakage reduction either suffer from reduced effectiveness at nanometer technologies or affect performance and gate-oxide reliability. In this paper, we propose application of a specific carbon nanotube (CNT)-based nano-electromechanical switch as a leakage-control structure in logic and memory circuits. In case of memory circuits, we demonstrate that the proposed hybridization can be employed to reduce both cell leakage and bitline leakage, thereby improving the read noise margin as well. Due to the unique electromechanical properties of CNTs, these switches have high current-carrying capacity, extremely low leakage current, and low operating voltages. Moreover, they can act as nonvolatile memory elements, which can be exploited for data retention of important registers and latches during power down. Simulation results for a set of benchmark circuits show that we can obtain several orders of magnitude improvement in leakage saving in logic circuits at iso-performance compared to existing multi-threshold CMOS technique. In memory circuits, simulations show reduction in standby leakage and reduction in bitline leakage compared with the best existing techniques.