Transversely-excited film bulk acoustic resonators with counter chirped interdigital transducers (IDTs) for mechanical and process compensation

A filter device, comprising:

• a piezoelectric layer having first and second surfaces that oppose each other, the second surface facing a substrate, portions of the piezoelectric layer forming a plurality of diaphragms that are over respective cavities in an intermediate layer of the substrate;
• a conductor pattern on at least one of the first and second surfaces, the conductor pattern comprising a plurality of interdigital transducers (IDTs) that each have interleaved fingers on a respective diaphragm of the plurality of diaphragms,
• wherein at least one of a pitch or a mark of the interleaved fingers of each IDT varies over the respective diaphragm,
• wherein the pitch is a center-to-center spacing between adjacent fingers of the interleaved fingers of at least one IDT of the plurality of IDTs, and the mark is a width of at least one finger of the interleaved fingers of the at least one IDT, and
• wherein the at least one of the pitch or the mark of the interleaved fingers of the IDT varies according to p′i=(p′2−hi2)1/2, where i is an integer representing the pitch between the adjacent fingers or the mark of the at least one finger, p′i is a counter pitch or mark variation for the at least one finger, p′ is a length along a direction of a distortion of the at least one finger, and h is a height of the distortion of the at least one finger.