Bulk acoustic wave accelerometers

1. An accelerometer, comprising:

a resonator element configured to vibrate along a first axis in a bulk acoustic wave mode at a resonant frequency, the resonator element being suspended in air by a suspension member and having a mechanical spring constant that is a substantially fixed and a variable electrical spring constant that depends on a size of a capacitive gap between the resonator element and at least one electrode, a polarization voltage being applied between the resonator element and the at least one electrode;

the suspension member having a dimension substantially different than that of the resonator element;

the at least one electrode capacitively coupled to the resonator element configured to sense a change in a parameter value tied to a change in the electrical spring constant and to provide an output signal therefor; and

an acceleration determination module configured to determine an amount of external acceleration applied to the accelerometer based on the output signal provided by the at least one electrode.

2. The accelerometer of claim 1 , wherein the parameter value tied to a change in the electrical spring constant comprises a change in the resonant frequency of the resonator element, the change in the resonant frequency being caused by a change in the electrical spring constant.

3. The accelerometer of claim 1 , wherein the at least one electrode comprises a drive electrode displaced from the resonator element by less than 200 nm.

4. The accelerometer of claim 1 , wherein the change in a parameter value is a change in the resonant frequency of the resonator element.

5. The accelerometer of claim 1 , wherein the change in a parameter value is a phase shift in the resonant frequency of the resonator element.

6. The accelerometer of claim 1 , wherein the resonance mode is a bulk acoustic wave mode.

7. The accelerometer of claim 1 , wherein the resonator element having a resonant frequency of at least about 1 MHz.

8. An accelerometer, comprising:

a resonator element having a resonant frequency of at least about 1 MHz, the resonator element being configured to vibrate along a first axis, the resonator element being suspended in air by a suspension member and having a variable electrical spring constant that depends on a size of a capacitive gap between the resonator element and a first electrode, a polarization voltage being applied between the resonator element and the first electrode;

the suspension member having a dimension substantially different than that of the resonator element;

the first electrode capacitively coupled to the resonator element configured to sense a change in a parameter value tied to a change in the electrical spring constant and provide an output signal therefor; and

an acceleration determination module configured to determine an amount of external acceleration applied to the accelerometer based on the output signal provided by the first electrode.

9. The accelerometer of claim 8 , wherein the parameter value tied to a change in the electrical spring constant comprises the resonant frequency being caused by a change in the electrical spring constant.

10. The accelerometer of claim 8 , wherein the resonator element has a mechanical spring constant that is a substantially fixed.

11. The accelerometer of claim 8 , wherein the first electrode is displaced from the mechanical resonator element by less than about 200 nm.

12. The accelerometer of claim 8 , having a quality factor of at least 1,000.

13. An accelerometer, comprising:

a resonator element comprising a proof mass suspended relative to a substrate by at least one suspension member attached thereto and configured to allow motion of the proof mass, the proof mass configured to vibrate along a first axis in a bulk acoustic resonance mode at a resonant frequency and the suspension member configured to vibrate in a flexural mode at a frequency different than the resonant frequency, the resonator element having a variable electrical spring constant that depends on a size of a capacitive gap between the resonator element and a first electrode, a polarization voltage being applied between the resonator element and the first electrode; and

a parameter sensing electrode configured to sense a change in a parameter value tied to a change in the electrical spring constant and provide an acceleration determination signal.

14. The accelerometer of claim 13 wherein the resonant frequency is greater than the frequency at which the suspension member vibrates.

15. The accelerometer of claim 13 wherein the resonant frequency is an order of magnitude greater than the frequency at which the suspension member vibrates.

16. An accelerometer, comprising:

a drive electrode;

a resonator element comprising a proof mass suspended relative to a substrate by at least one suspension member attached thereto and configured to allow the proof mass to be separated from the drive electrode by a capacitive gap and driven by the drive electrode to vibrate along a first axis in a bulk acoustic resonance mode at a resonant frequency, the suspension member having dimensions substantially different than the proof mass and configured to vibrate in a flexural mode, the resonator element having a variable electrical spring constant that depends on a size of a capacitive gap between the resonator element and a first electrode, a polarization voltage being applied between the resonator element and the first electrode; and

a parameter sensing electrode configured to sense a change in a parameter value tied to a change in the electrical spring constant and provide an acceleration determination signal.

17. The accelerometer of claim 16 , wherein the change in a parameter value is a change in the resonant frequency of the resonator element.

18. The accelerometer of claim 16 , wherein the change in a parameter value is a phase shift in the resonant frequency of the resonator element.

19. The accelerometer of claim 16 wherein the resonator element comprises a pair of suspension members.