Methods for suppressing spurious modes in microresonators

1. A method of suppressing one or more spurious modes in a microresonator, the method comprising:

providing a coupling-of-modes model of the microresonator, wherein the model comprises a forward acoustic wave and a backward acoustic wave that characterizes the microresonator;

adjusting an acoustic velocity in a transducer domain of the model to provide a minimized spurious response, wherein the transducer domain in the model comprises one or more electrodes;

determining a thickness of a first dielectric layer that corresponds to the acoustic velocity of the minimized spurious response; and

depositing the first dielectric layer on a top surface of the microresonator, wherein the first dielectric layer comprises the thickness from the determining step and the top surface comprises one or more electrodes.

2. The method of claim 1 , wherein the providing step comprises providing a two-dimensional coupling-of-modes model.

3. The method of claim 1 , wherein the model further comprises a detuning parameter δ for each domain of the model.

4. The method of claim 3 , wherein the model comprises a detuning parameter δ t for a transducer domain of the model, a detuning parameter δ b for a buss domain of the model, a detuning parameter δ f for a free space domain of the model, and/or a detuning parameter δ s for a stub domain of the model.

5. The method of claim 4 , wherein each detuning parameter for each domain is associated with an acoustic velocity in each domain.

6. The method of claim 4 , wherein the adjusting step comprises increasing or decreasing an acoustic velocity v t in the transducer domain.

7. The method of claim 6 , wherein the adjusting step comprises an acoustic velocity v t in the transducer domain that is less than an acoustic velocity v b in the buss domain and/or less than an acoustic velocity v f in the free space domain.

8. The method of claim 7 , wherein v t is less v b , which in turn is less than v f .

9. The method of claim 1 , wherein the adjusting step comprises decreasing an acoustic velocity.

10. The method of claim 9 , wherein the adjusting step further comprises determining a transmission measurement of the model.

11. The method of claim 1 , wherein the determining step comprises a transfer matrix method, an iterative method, a finite element method, a finite difference method, or a finite volume method.

12. The method of claim 11 , wherein the depositing step comprises depositing the first dielectric layer on a top surface of the one or more electrodes of the microresonator.

13. The method of claim 1 , wherein the thickness of the first dielectric layer is of from about 0.5 μm to about 1 μm.

14. The method of claim 1 , wherein the one or more spurious modes comprises one or more fine-frequency modes.

15. The method of claim 14 , wherein the one or more fine-frequency modes has a center frequency of from about 450 MHz to about 500 MHz.

16. The method of claim 1 , wherein the microresonator comprises:

a piezoelectric layer comprising a top surface and a bottom surface; and

a top electrode layer disposed on the top surface of the piezoelectric layer, wherein the top electrode layer comprises an input electrode and an output electrode.

17. The method of claim 16 , wherein the input electrode comprises:

a first interconnect buss;

a first plurality of fingers that extend orthogonally from the first interconnect buss, each finger in the first plurality of fingers having a first length; and

a first plurality of stubs that extend orthogonally from the first interconnect buss, each stub in the first plurality of stubs having a second length, the second length being less than the first length.

18. The method of claim 17 , wherein the output electrode comprises:

a second interconnect buss in parallel with the first interconnect buss, wherein the first plurality of fingers extend from the first interconnect buss towards the second interconnect buss;

a second plurality of fingers that extend orthogonally from the second interconnect buss towards the first interconnect buss, each finger in the second plurality of fingers having the first length; and

a second plurality of stubs that extend orthogonally from the second interconnect buss towards the first interconnect buss, each stub in the second plurality of stubs having the second length.

19. The method of claim 16 , wherein the microresonator further comprises:

the first dielectric layer disposed on a top surface of the top electrode layer.

20. The method of claim 16 , wherein the microresonator further comprises:

a bottom electrode layer disposed on the bottom surface of the piezoelectric layer.

21. The method of claim 20 , wherein the microresonator further comprises:

a second dielectric layer disposed on a bottom surface of the bottom electrode layer.

22. The method of claim 1 , wherein the microresonator comprises a size of less than 500 μm in length, 150 μm in width, and/or 10 μm in thickness.

23. A method of suppressing one or more spurious modes in a microresonator, the method comprising:

providing the microresonator comprising a piezoelectric layer comprising a top surface and a bottom surface; and a top electrode layer disposed on the top surface of the piezoelectric layer, wherein the top electrode layer comprises an input electrode and an output electrode;

providing a coupling-of-modes model of the microresonator, wherein the model comprises a forward acoustic wave and a backward acoustic wave that characterizes the microresonator;

adjusting an acoustic velocity in a transducer domain of the model to provide a minimized spurious response, wherein the transducer domain in the model comprises one or more electrodes;

determining a thickness of a first dielectric layer that corresponds to the acoustic velocity of the minimized spurious response; and

depositing the first dielectric layer on the top surface of the piezoelectric layer of the microresonator, wherein the first dielectric layer comprises the thickness from the determining step.