Contour-mode piezoelectric micromechanical resonators

A contour mode micromechanical piezoelectric resonator, comprising:

• a bottom electrode;
• a top electrode;
• a piezoelectric layer disposed between said bottom electrode and said top electrode, said piezoelectric resonator having a planar surface having a cantilevered periphery, dimensioned to undergo in-plane lateral displacement at said periphery;
• one or more tethers that anchor said piezoelectric resonator to a substrate or other resonators, wherein said tethers have width chosen from a group consisting of about one quarter-wavelength and an odd multiple of about one quarter-wavelength of said fundamental frequency of said resonator;
• and
• means for applying an alternating electric field across the thickness of said piezoelectric resonator, said electric field configured to cause said resonator to have a contour mode in-plane lateral displacement that is substantially in the plane of said planar surface, wherein the fundamental frequency for the displacement of said piezoelectric resonator is set in part lithographically by the planar dimensions of one of said bottom electrode, said top electrode and said piezoelectric layer.