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The concept and the simulated device characteristics of ultralow-power and high-performance band-to-band tunneling field-effect transistors employing stepped broken-gap heterobarriers, HetTFETs, are presented. Abrupt switching is defined by the onset of a band overlap. High on-state currents are provided by narrow tunnel barriers defined by crystal growth rather than electrostatics. Sentaurus Device simulations exhibit current roll-offs by approximately 106 over ranges of ~ 15 meV down to a few millielectronvolts, depending on the prototype device structure, and approximately constant above-threshold transconductance values approaching current CMOS-like values.