Recessed frames in thickness mode piezoelectric resonators

A system, comprising:

• a piezoelectric resonator including:
• a first metal layer;
• a second metal layer;
• and
• a piezoelectric material layer between the first and second metal layer along an axis, the piezoelectric material layer including first portions and second portions, each of the second portions having a smaller thickness than the first portions and overlapping both the first and second metal layers;
• and
• a controller coupled to the first metal layer and the second metal layer, the controller configurable to drive the piezoelectric material layer into resonance.

A device, comprising:

• a first metal layer;
• a second metal layer;
• and
• a piezoelectric material layer between the first metal layer and the second metal layer, the piezoelectric material layer having recesses that overlap with the first and second metal layer.