In order to provide a resonator structure (100) in particular a bulk-acoustic-wave (BAW) resonator, such as a film BAW resonator (FBAR) or a solidly-mounted BAW resonator (SBAR), comprising at least one substrate (10); at least one reflector layer (20) applied or deposited on the substrate (10); at least one bottom electrode layer (30), in particular bottom electrode, applied or deposited on the reflector layer (20); at least one piezoelectric layer (40), in particular C-axis normal piezoelectric layer, applied or deposited on the bottom electrode layer (30); at least one top electrode layer (50), in particular top electrode, applied or deposited on the bottom electrode layer (30) and/or on the piezoelectric layer (40) such that the piezoelectric layer (40) is in between the bottom electrode layer (30) and the top electrode layer (50), it is proposed that at least one dielectric layer (63, 65) applied or deposited in and/or on at least one space in at least one region of non-overlap between the bottom electrode layer (30) and the top electrode layer (50). The invention is also concerned with a method of making such resonator structure a its use.