Surface acoustic wave resonator having multilayer piezoelectric substrate with gap regions having reduced permittivity or piezoelectricity for reduced nonlinear response

A method of forming a surface acoustic wave resonator, the method comprising:

• providing a multilayer piezoelectric substrate including an upper layer of a piezoelectric material including first regions of piezoelectric material having a first permittivity and/or piezoelectricity and second regions of piezoelectric material having a second permittivity and/or piezoelectricity, the second permittivity and/or piezoelectricity being less than the first permittivity and/or piezoelectricity;
• and
• forming interdigital transducer (IDT) electrodes on the layer of piezoelectric material, the IDT electrodes including a first bus bar, a second bus bar, a first plurality of electrode fingers extending from the first bus bar toward the second bus bar, and a second plurality of electrode fingers extending from the second bus bar toward the first bus bar and interleaved with the first plurality of electrode fingers in a central region of the resonator, gap regions defined between tips of the first plurality of electrode fingers and the second bus bar and between tips of the second plurality of electrode fingers and the first bus bar, the gap regions being defined over at least portions of the second regions of piezoelectric material.