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We propose a novel digital switch, the piezoelectronic transistor or PET. Based on properties of known materials, we predict that a nanometer-scale PET can operate at low voltages and relatively high speeds, exceeding the capabilities of any conventional field effect transistor (FET). Depending on the degree to which these attributes can be simultaneously achieved, the device has a broad array of potential applications in digital logic. The PET is a 3-terminal switch in which a gate voltage is applied to a piezoelectric (PE), resulting in expansion compressing a piezoresistive (PR) material comprising the channel, which then undergoes a continuous, reversible insulator-metal transition. The channel becomes conducting in response to the gate voltage. A high piezoelectric coefficient PE, e.g., a relaxor piezoelectric, leads to low voltage operation. Suitable channel materials manifesting a pressure-induced metal-insulator transition can be found amongst rare earth chalcogenides, transition metal oxides, and among others. Mechanical requirements include a high PE/PR area ratio to step up pressure, a rigid surround material to constrain the PE and PR external boundaries normal to the strain axis, and a void space to enable free motion of the component side walls. Using static mechanical modeling and dynamic electro-acoustic simulations, we optimize device structure and materials and predict performance.