Lamb wave resonator

1. A lamb wave resonator comprising:

at least one piezoelectric layer; and

a first electrode against a first face of said at least one piezoelectric layer and comprising a pattern parallel to a plane of the first face, the pattern comprising a plurality of fingers and a contact arm, each finger comprising a first side in contact with said contact arm and two other sides parallel to one another, and said plurality of fingers being spaced apart from one another by a distance W calculated according to the following equation:

W

=

n

·

va

lateral

f

,

with

⁢

⁢

n

∈

N

where,

va lateral is an acoustic propagation speed of Lamb waves,

n is an order of a resonance mode of the Lamb waves,

f is a resonance frequency of the Lamb wave resonator, and

said at least one piezoelectric layer having at least one recess between said plurality of fingers of said first electrode.

2. The lamb wave resonator according to claim 1 , wherein the at least one recess is formed based on a pattern including a plurality of holes.

3. The lamb wave resonator according to claim 1 , wherein the at least one recess extends through the at least one piezoelectric layer between said plurality of fingers.

4. The lamb wave resonator according to claim 1 , wherein said at least one piezoelectric layer has a second face opposite the first face, and wherein the at least one recess extends through the first face to the second face.

5. The lamb wave resonator according to claim 1 , wherein said at least one piezoelectric layer has a second face opposite the first face, and further comprising a second electrode against the second face.

6. The lamb wave resonator according to claim 5 , wherein said second electrode comprises, in a plane parallel to the plane of the first face of said at least one piezoelectric layer, a second pattern comprising a plurality of second fingers and a second contact arm, in which a surface of said plurality of second fingers is similar and superimposed on the surface formed by said plurality of fingers of said first electrode in the same plane.

7. The lamb wave resonator according to claim 6 , wherein the second pattern of said second electrode is similar to the pattern of said first electrode in the same plane, and a surface of said second contact arm of said second electrode is not superimposed on a surface of said contact arm of said first electrode in the same plane.

8. The lamb wave resonator according to claim 1 , wherein a surface of said plurality of fingers of said first electrode is included in a surface formed by said second electrode in the same plane.

9. The lamb wave resonator according to claim 1 , wherein each finger of said first electrode is substantially rectangular shaped.

10. The lamb wave resonator according to claim 1 , wherein a number of said plurality of fingers of said first electrode is between 2 and 100.

11. The lamb wave resonator according to claim 1 , wherein said contact arm of said first electrode is substantially rectangular shaped.

12. The lamb wave resonator according to claim 11 , wherein a line parallel to the two sides of each finger of said first electrode, spaced apart from one another by a distance W, is substantially perpendicular to a line passing through a side of said contact arm of said first electrode to which said finger is connected.

13. The resonator according to claim 1 , wherein said plurality of fingers of said first electrode are connected to at least one of the following of said contact arm of said first electrode: a single side thereof, two opposite sides thereof, and three sides thereof.

14. The resonator according to claim 1 , wherein said contact arm of said first electrode is substantially circular shaped, and wherein said plurality of fingers of said first electrode are connected thereto.

15. A resonator comprising:

at least one piezoelectric layer; and

a first electrode against a first face of said at least one piezoelectric layer and comprising a plurality of fingers and a contact arm, each finger comprising a first side in contact with said contact arm and two other sides parallel to one another, and said plurality of fingers being spaced apart from one another by a distance W calculated according to the following equation:

W

=

n

·

va

lateral

f

,

with

⁢

⁢

n

∈

N

where,

va lateral is an acoustic propagation speed of Lamb waves,

n is an order of a resonance mode of the Lamb waves,

f is a resonance frequency of the resonator, and

said at least one piezoelectric layer having at least one recess between said plurality of fingers of said first electrode.

16. The resonator according to claim 15 , wherein the at least one recess is formed based on a pattern including a plurality of holes.

17. The resonator according to claim 15 , wherein the at least one recess extends through the at least one piezoelectric layer between said plurality of fingers.

18. The resonator according to claim 15 , wherein said at least one piezoelectric layer has a second face opposite the first face, and wherein the at least one recess extends through the first face to the second face.

19. The resonator according to claim 15 , wherein said at least one piezoelectric layer has a second face opposite the first face, and further comprising a second electrode against the second face.

20. The resonator according to claim 19 , wherein a surface of said plurality of fingers of said first electrode is included in a surface formed by said second electrode in the same plane.

21. The resonator according to claim 19 , wherein said second electrode comprises a second pattern comprising a plurality of second fingers and a second contact arm, in which a surface of said plurality of second fingers is similar and superimposed on a surface formed by said plurality of fingers of said first electrode in the same plane.

22. The resonator according to claim 21 , wherein the second pattern of said second electrode is similar to the pattern of said first electrode in the same plane, and a surface of said second contact arm of said second electrode is not superimposed on a surface of said contact arm of said first electrode in the same plane.

23. A method for producing a Lamb wave resonator comprising:

forming at least one piezoelectric layer;

forming a first electrode against a first face of the at least one piezoelectric layer, the first electrode comprising a pattern parallel to a plane of the first face, the pattern comprising a plurality of fingers and a contact arm, each finger comprising a first side in contact with the contact arm and two other sides parallel to one another, and the plurality of fingers being spaced apart from one another by a distance W calculated according to the following equation:

W

=

n

·

va

lateral

f

,

with

⁢

⁢

n

∈

N

where,

va lateral is an acoustic propagation speed of Lamb waves,

n is an order of a resonance mode of the Lamb waves,

f is a resonance frequency of the resonator; and

etching at least one recess in the at least one piezoelectric layer between the plurality of fingers of the first electrode.

24. The method according to claim 23 , wherein the at least one piezoelectric layer is at least partially etched according to a pattern including a plurality of holes.

25. The method according to claim 23 , wherein the at least one piezoelectric layer is entirely etched.

26. The method according to claim 23 , wherein the at least one piezoelectric layer has a second face opposite the first face, and wherein the portions of the at least one piezoelectric layer are etched through the first face to the second face.

27. The method according to claim 23 , wherein the at least one piezoelectric layer has a second face opposite the first face, and further comprising forming a second electrode against the second face.

28. The method according to claim 27 , wherein a surface of the plurality of fingers of the first electrode is included in a surface formed by the second electrode in the same plane.

29. The method according to claim 27 , wherein the second electrode comprises, in a plane parallel to the plane of the first face of the at least one piezoelectric layer, a second pattern comprising a plurality of second fingers and a second contact arm, in which a surface of the plurality of second fingers is similar and superimposed on the surface formed by the plurality of fingers of the first electrode in the same plane.

30. The method according to claim 29 , wherein the second pattern of the second electrode is similar to the pattern of the first electrode in the same plane, and a surface of the second contact arm of the second electrode is not superimposed on a surface of the contact arm of the first electrode in the same plane.