Acoustic wave resonators with doped piezoelectric material and frame members

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A bulk acoustic wave (BAW) resonator includes a first electrode; a second electrode; and a piezoelectric layer disposed between the first and second electrodes. The piezoelectric layer includes a piezoelectric material doped with at least one rare earth element. In an embodiment, the BAW resonator includes a recessed frame element disposed over a surface of at least one of the first and second electrodes. In another embodiment, the BAW resonator includes a raised frame element disposed over a surface of at least one of the first and second electrodes. In yet another embodiment, the BAW resonator includes both the raised and recessed frame elements.