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  1. Energy efficiency in digital circuits is limited by the subthreshold swing (SS), which defines how abruptly a transistor switches between its on and off-states. The SS is particularly important for circuits targeting minimum-energy computation which operate in the subthreshold region between the on and off-states of the transistor. The SS of MOSFET devices is fundamentally limited by thermionic emission, which has inspired a search for new devices whose SS can reach below the Boltzmann thermal limit. Tunnel field-effect transistors (TFETs) have emerged as a post-CMOS candidate with low (steep) SS and have been investigated using an evolving selection of geometries and materials that yield continuously improving device performance and circuit performance estimates. To unify previous works and guide future TFET iterations, this paper provides a comprehensive theory on minimum-energy operation in the subthreshold region for steep-SS devices. We show that the optimal supply voltage for energy minimization and minimum obtainable energy are both proportional to the SS, and that a fundamental limit exists for the required Ion/Ioff to achieve operation at the minimum-energy point. We explore how device knobs affect the optimization space for minimum-energy operation, and analyze how common TFET non-idealities affect the potential for minimum-energy operation.