Microelectromechanical gyroscopes and related apparatus and methods

1. A microelectromechanical resonant structure, comprising:

a plate comprising a crystalline support and a piezoelectric thin film coupled to the crystalline support, the plate defining a plane when the resonant structure is not excited and the crystalline support exhibiting in-plane anisotropy within the plane;

a drive electrode configured to excite the plate in a first in-plane mode having a first resonance frequency; and

a sense electrode configured to sense motion of the plate in a second in-plane mode having a second resonance frequency and produce a signal in response to rotation of the resonant structure about an axis substantially orthogonal to the plane defined by the plate when the resonant structure is not excited,

wherein the drive electrode and the sense electrode are arranged on the plate relative to a crystalline direction of the crystalline support such that the first resonance frequency and second resonance frequency are substantially equal.

2. The microelectromechanical resonant structure of claim 1 , wherein the plate is configured to oscillate in the second in-plane mode upon rotation about the axis.

3. The microelectromechanical resonant structure of claim 2 , wherein each of the first in-plane mode and the second in-plane mode is one of an elliptical mode or a flexural mode.

4. The microelectromechanical resonant structure of claim 2 , wherein the first in-plane mode and the second in-plane mode are spatially rotated with respect to each other.

5. The microelectromechanical resonant structure of claim 4 , wherein the first in-plane mode and the second in-plane mode are rotated relative to each other by approximately 45 degrees.

6. The microelectromechanical resonant structure of claim 2 , wherein the drive electrode is configured to excite the plate in the first in-plane mode at a frequency corresponding to the second resonance frequency.

7. The microelectromechanical resonant structure of claim 1 , wherein the plate includes at least one of a disk, a ring, a proof mass, or a double mass plate.

8. The microelectromechanical resonant structure of claim 1 , further comprising:

a substrate, the plate being suspended and coupled to the substrate by a plurality of anchors.

9. The microelectromechanical resonant structure of claim 8 , wherein at least one anchor from the plurality of anchors is a multi-element anchor.

10. The microelectromechanical resonant structure of claim 1 , further comprising a temperature compensation stack coupled to the piezoelectric thin film.

11. The microelectromechanical resonant structure of claim 1 , wherein the piezoelectric thin film is a disk-shaped piezoelectric thin film.

12. The microelectromechanical resonant structure of claim 1 , wherein the piezoelectric thin film is coupled to a conductive layer.

13. The microelectromechanical resonant structure of claim 1 , wherein the crystalline support is silicon.

14. The microelectromechanical resonant structure of claim 1 , wherein the drive electrode is a first drive electrode, and wherein the microelectromechanical resonant structure includes a plurality of drive electrodes including the first drive electrode, wherein the plurality of drive electrodes are configured to excite the plate differentially.

15. The microelectromechanical resonant structure of claim 1 , wherein the sense electrode is a first sense electrode, and wherein the microelectromechanical resonant structure includes a plurality of sense electrodes including the first sense electrode, wherein the plurality of sense electrodes are configured to sense motion of the plate differentially.

16. The microelectromechanical resonant structure of claim 1 , further comprising:

a microelectromechanical system (MEMS) accelerometer, the MEMS accelerometer and the plate being integrated on a common chip.

17. The microelectromechanical resonant structure of claim 1 , further comprising:

a microelectromechanical system (MEMS) timing oscillator, the MEMS timing oscillator and the plate being integrated on a common chip.

18. The microelectromechanical resonant structure of claim 1 , wherein the plate is a first plate, and wherein the microelectromechanical resonant structure further comprises a second plate integrated on a common chip with the first plate and comprising a piezoelectric thin film and a crystalline support.

19. A microelectromechanical resonant structure, comprising:

a drive electrode configured to excite a plate of the microelectromechanical resonant structure in a first in-plane mode having a first resonance frequency, the plate configured to oscillate in a second in-plane mode having a second resonance frequency when excited by the drive electrode and upon rotation of the microelectromechanical resonant structure about an axis substantially orthogonal to a plane defined by the plate when the microelectromechanical resonant structure is not excited, wherein the plate comprises a crystalline support, exhibiting in-plane anisotropy within the plane, and a piezoelectric thin film coupled to the crystalline support; and

a sense electrode configured to sense the oscillation of the plate in the second in-plane mode,

wherein the drive electrode and the sense electrode are arranged relative to a crystalline direction of the crystalline support such that the first resonance frequency and second resonance frequency are substantially equal.

20. A method, comprising:

exciting, by a drive electrode, a plate of a resonant structure in a first in-plane mode having a first resonance frequency, the plate comprising a crystalline support, exhibiting in-plane anisotropy within a plane in which the plate lies, and a piezoelectric thin film coupled to the crystalline support; and

measuring, by a sense electrode, an oscillation of the plate in a second in-plane mode having a second resonance frequency upon rotation of the resonant structure and after exciting the plate,

wherein the drive electrode and the sense electrode are arranged on the plate relative to a crystalline direction of the crystalline support such that the first resonance frequency and second resonance frequency are substantially equal.

21. The method of claim 20 , wherein:

measuring the oscillation includes measuring the oscillation of the plate upon rotation of the resonant structure about an axis substantially orthogonal to the plane.