Microelectromechanical gyroscopes and related apparatus and methods

1. An apparatus, comprising:

a substrate having a first plate and a second plate, the first plate and the second plate collectively having a first mode when excited by a drive signal and having a second mode when excited by a gyroscopic effect, wherein the first and second plates each include a temperature-compensated stack having first and third layers that have a stiffness that increases with increasing temperature over a temperature range with a second layer between the first and third layers, wherein the second layer is formed from a different material than the first and third layers.

2. The apparatus of claim 1 , wherein the first plate and the second plate are configured to be excited in the first mode based on a piezoelectric effect.

3. The apparatus of claim 1 , wherein the first plate and the second plate are configured to be excited in the first mode based on based on an electrostatic excitation.

4. The apparatus of claim 1 , further comprising: a circuit configured to detect the gyroscopic effect when the first plate and the second plate are collectively in the second mode based on a piezoelectric effect.

5. The apparatus of claim 1 , further comprising: a circuit configured to detect capacitively the gyroscopic effect when the first plate and the second plate are collectively in the second mode.

6. The apparatus of claim 1 , wherein the first plate and the second plate flex substantially 180 degrees out of phase from each other when the first plate and the second plate are excited in the first mode.

7. The apparatus of claim 1 , wherein the first plate and the second plate extend substantially 180 degrees out of phase from each other when the first plate and the second plate are excited in the first mode.

8. The apparatus of claim 6 , further comprising a circuit configured to detect an extensional mode associated with the second mode when the first plate and the second plate flex substantially 180 degrees out of phase from each other.

9. The apparatus of claim 7 , further comprising a circuit configured to detect a flexural mode associated with the second mode when the first plate and the second plate extend substantially 180 degrees out of phase from each other.

10. The apparatus of claim 1 , further comprising: a piezoelectric layer included with the first plate and the second plate, the piezoelectric layer being made of at least one of aluminum nitride, zinc oxide, lead zirconate titanate (PZT), lithium niobate (LiNbO3), potassium niobate (KNbO3), lithium tantanate (LiTaO3), quartz, BST (Ba Sr TiO3, barium strontium titanate) or MNT (Mn Nb TiO3, Manganese niobium titanate).

11. The apparatus of claim 1 , wherein the first plate and the second plate is each made of at least one of silicon or silicon oxide.

12. The apparatus of claim 1 , wherein the first plate and the second plate each includes at least one piezoelectric thin film.

13. The apparatus of claim 1 , wherein the first plate and the second plate each includes a first piezoelectric thin film, a second piezoelectric thin film, and an electrode layer disposed between the first piezoelectric thin film and the second piezoelectric thin film.

14. The apparatus of claim 1 , wherein the first plate and the second plate collectively have a shape and are made from a material which when coupled with a voltage source enable excitation in the first mode with a frequency substantially equal to a resonance frequency of the first mode.

15. The apparatus of claim 1 , wherein the first plate and the second plate are collectively configured to be excited in the first mode with a frequency different from a resonance frequency of the first mode when coupled with a voltage source that enables excitation in the first mode at the different frequency.

16. The apparatus of claim 1 , wherein the first plate and the second plate collectively have a shape and are made from a material which when coupled with a voltage source enable excitation in the first mode at a frequency substantially equal to a resonance frequency of the second mode.

17. The apparatus of claim 1 , wherein the first plate and the second plate collectively have a shape and are made from a material which have a shape and are made from a material which when coupled with a voltage source enable excitation in the first mode at a frequency different from a resonant frequency of the mode and different from a resonant frequency of the second mode.

18. The apparatus of claim 1 , wherein the first plate and the second plate have a shape and are made from a material that enable excitation in the first mode differentially when coupled with a voltage source.

19. The apparatus of claim 1 , further comprising: a circuit configured to detect the gyroscopic effect when the first plate and the second plate are collectively in the first mode differentially via a voltage source.

20. The apparatus of claim 1 , wherein the first plate and the second plate are configured to be excited in the first mode based on a piezoelectric effect, the apparatus further comprising: a circuit configured to detect the gyroscopic effect when the first plate and the second plate are collectively in the second mode based on a piezoelectric effect.

21. The apparatus of claim 1 , wherein at least one of the first mode or the second mode is based on a piezoelectric effect and tuned electrostatically to define a mode-matched condition.

22. The apparatus of claim 21 , wherein: the substrate is unpatterned and conductive; and the at least one of the first mode or the second mode is tuned electrostatically by an applied voltage between (1) the substrate and (2) the first plate and the second plate.

23. An apparatus, comprising:

a substrate;

a member moveably coupled to the substrate at a first anchor and a second anchor, the member being in a first mode when excited by a drive signal and being in a second mode when excited by a gyroscopic effect, wherein the member includes a temperature-compensated stack having first and third layers that have a stiffness that increases with increasing temperature over a temperature range with a second layer between the first and third layers, wherein the second layer is formed from a different material than the first and third layers; and

a circuit coupled to the member and configured to detect the gyroscopic effect.

24. The apparatus of claim 23 , wherein the member is configured to be excited in the first mode based on a piezoelectric effect.

25. The apparatus of claim 23 , wherein the member is configured to be excited in the first mode based on an electrostatic excitation.

26. The apparatus of claim 23 , wherein the circuit is configured to detect the gyroscopic effect when the member is in the second mode based on a piezoelectric effect.

27. The apparatus of claim 23 , wherein the circuit configured to detect capacitively the gyroscopic effect when the member is in the second mode.

28. The apparatus of claim 23 , wherein the member is configured to be excited in a torsional mode.

29. The apparatus of claim 23 , wherein the member is configured to be excited in an extensional mode.

30. The apparatus of claim 23 , wherein the circuit is configured to detect an extensional mode of the member when the member is excited in the extensional mode by the gyroscopic effect.

31. The apparatus of claim 23 , wherein the circuit is configured to detect a torsional mode of the member when the member is excited in the torsional mode by the gyroscopic effect.

32. The apparatus of claim 23 , further comprising: a piezoelectric layer included with the member, the piezoelectric layer being made of at least one of aluminum nitride, zinc oxide, lead zirconate titanate (PZT), lithium niobate (LiNbO3), potassium niobate (KNbO3), lithium tantanate (LiTaO3), quartz, BST (Ba Sr TiO3, barium strontium titanate) or MNT (Mn Nb TiO3, Manganese niobium titanate).

33. The apparatus of claim 23 , wherein the member is made of at least one of silicon or silicon oxide.

34. The apparatus of claim 23 , wherein the member includes at least one piezoelectric thin film.

35. The apparatus of claim 23 , wherein the member includes a first piezoelectric thin film, a second piezoelectric thin film, and an electrode layer disposed between the first piezoelectric thin film and the second piezoelectric thin film.

36. The apparatus of claim 23 , wherein the member has a shape and is made from a material which when coupled with a voltage source enable excitation in the first mode with a frequency substantially equal to a resonance frequency of the first mode.

37. The apparatus of claim 23 , wherein the member has a shape and is made from a material which when coupled with a voltage source enable excitation in the first mode with a frequency different from a resonance frequency of the first mode.

38. The apparatus of claim 23 , wherein the member has a shape and is made from a material which when coupled with a voltage source enable excitation in the first mode at a frequency substantially equal to a resonance frequency of the second mode.

39. The apparatus of claim 23 , wherein the member has a shape and is made from a material which when coupled with a voltage source enable excitation in the first mode at a frequency different from a resonant frequency of the mode and different from a resonant frequency of the second mode.

40. An apparatus, comprising:

a micromechanical gyroscope configured to be excited in a first mode by a drive signal, the micromechanical gyroscope configured to be excited in a second mode by a gyroscopic effect, wherein the micromechanical gyroscope includes a temperature-compensated stack having a first layer of first material that has a stiffness that increases with increasing temperature over a temperature range and a second layer of second material that is different from the first material; and

a circuit coupled to the micromechanical gyroscope and configured to detect the gyroscopic effect when the micromechanical gyroscope is in the second mode.

41. The apparatus of claim 40 , wherein the second material has lower acoustical loss characteristics than the first material and further comprising: a circuit electrically coupled to the micromechanical gyroscope, the circuit defining a positive gain feedback loop when the drive signal is applied to the micromechanical gyroscope such that the drive signal has a frequency substantially corresponding to a natural resonance frequency of the first mode.

42. The apparatus of claim 40 , wherein the first material comprises silicone dioxide, wherein the second material comprises silicon, diamond, silicon carbide, sapphire, quartz, germanium, aluminum nitride, or gallium arsenide, and further comprising: a mixer coupled to the micromechanical gyroscope; and a low-pass filter coupled to the mixer, the low-pass filter configured to output an output voltage when the drive signal is applied to the micromechanical gyroscope such that the output voltage is substantially proportional to an angular rate of the micromechanical gyroscope and associated with the gyroscopic effect.