A piezoelectric MEMS microphone comprising a multi-layer sensor that includes at least one piezoelectric layer between two electrode layers, with the sensor being dimensioned such that it provides a near maximized ratio of output energy to sensor area, as determined by an optimization parameter that accounts for input pressure, bandwidth, and characteristics of the piezoelectric and electrode materials. The sensor can be formed from single or stacked cantilevered beams separated from each other by a small gap, or can be a stress-relieved diaphragm that is formed by deposition onto a silicon substrate, with the diaphragm then being stress relieved by substantial detachment of the diaphragm from the substrate, and then followed by reattachment of the now stress relieved diaphragm.