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A bulk acoustic wave (BAW) resonator, comprises : a first electrode; a second electrode comprising a plurality of sides. At least one of the sides comprises a cantilevered portion. The bulk acoustic wave (BAW) resonator also comprises a piezoelectric layer disposed between the first and second electrodes. The piezoelectric layer comprises a piezoelectric material doped with a plurality of rare earth elements, and the cantilevered portion extends above the piezoelectric layer. The bulk acoustic wave (BAW) resonator comprises a gap between the cantilevered portion and the piezoelectric layer.