MEMS resonators having resonator bodies therein with concave-shaped sides that support high quality factor and low temperature coefficient of resonant frequency
A microelectromechanical (MEMs) resonator includes a concave bulk acoustic resonator (CBAR). One embodiment of a CBAR includes a substrate and a resonator body suspended over the substrate by a pair of fixed supports that attach to first and second opposing ends of the resonator body. The resonator body has a first concave-shaped side extending between the first and second ends of the resonator body and a second concave-shaped side extending opposite the first concave-shaped side. The resonator body may be configured to have a minimum spacing of λ/2 between the first and second concave-shaped sides, where λ is a wavelength associated with a resonant frequency of said resonator body.
1. A concave bulk acoustic resonator (CBAR), comprising:
a substrate; and
a resonator body suspended over the substrate by a pair of fixed supports that attach to first and second opposing ends of said resonator body, said resonator body having a first concave-shaped side extending between the first and second ends of said resonator body, a second concave-shaped side extending opposite the first concave-shaped side and configured to have a minimum spacing of λ/2 between the first and second concave-shaped sides, where λ is a wavelength associated with a resonant frequency of said resonator body.
2. The CBAR of claim 1 , wherein said substrate comprises a drive electrode extending adjacent the first concave-shaped side and a sense electrode extending adjacent the second concave-shaped side.
3. The CBAR of claim 1 , wherein a width of said resonator body at the first end thereof is about 3λ/4.
4. A concave bulk acoustic resonator (CBAR), comprising:
a substrate; and
a resonator body suspended over the substrate by a pair of fixed supports that attach to first and second opposing ends of said resonator body, said resonator body having a first concave-shaped side extending between the first and second ends of said resonator body, a second concave-shaped side extending opposite the first concave-shaped side and configured to have a spacing of λ/2 between the first and second concave-shaped sides at a point midway between the first and second ends of said resonator body, where λ is a wavelength associated with a resonant frequency of said resonator body.
5. The CBAR of claim 4 , wherein a width of said resonator body at the first end thereof is about 3λ/4.
6. A concave bulk acoustic resonator (CBAR), comprising:
a substrate:
a resonator body suspended over the substrate by a pair of fixed supports that attach to first and second opposing ends of said resonator body, said resonator body having a first concave-shaped side extending between the first and second ends of said resonator body and a second concave-shaped side extending opposite the first concave-shaped side;
a drive electrode extending adjacent the first concave-shaped side; and
a sense electrode extending adjacent the second concave-shaped side;
wherein a width of the drive electrode as measured along the first concave-shaped side is less than a spacing between the first and second ends of said resonator body.
7. The CBAR of claim 6 , wherein the width of the drive electrode as measured along the first concave-shaped side is less than one-half a spacing between the first and second ends of said resonator body.
8. The CBAR of claim 6 , wherein the width of the drive electrode as measured along the first concave-shaped side is less than one-third a spacing between the first and second ends of said resonator body.
9. The CBAR of claim 6 , wherein a width of said resonator body at the first end thereof is about 3λ/4.
10. A concave bulk acoustic resonator (CBAR), comprising:
a substrate;
a resonator body suspended over the substrate by a pair of fixed supports that attach to first and second opposing ends of said resonator body, said resonator body having a first concave-shaped side extending between the first and second ends of said resonator body and a second concave-shaped side extending opposite the first concave-shaped side;
a piezoelectric layer on said resonator body;
a first electrode extending across a first of the pair of fixed supports and onto said piezoelectric layer; and
a second electrode extending across a second of the pair of fixed supports and onto said piezoelectric layer.
11. The CBAR of claim 10 , wherein the first and second electrodes comprise interdigitated fingers.
12. The CBAR of claim 11 , wherein said resonator body is configured to have a minimum spacing of λ/2 between the first and second concave-shaped sides, where λ is a wavelength associated with a resonant frequency of said resonator body.
13. The CBAR of claim 10 , wherein said resonator body is configured to have a minimum spacing of λ/2 between the first and second concave-shaped sides, where λ is a wavelength associated with a resonant frequency of said resonator body.
14. The CBAR of claim 13 , wherein a width of said resonator body at the first end thereof is about 3λ/4.