Microelectromechanical Devices For Higher Order Passive Temperature Compensation and Methods of Designing Thereof

1 . A MEMS resonator device comprising:

a support structure;

a resonator element doped with at least one of N-type or P-type dopants, wherein a doping concentration of the at least one of N-type or P-type dopants causes a closely temperature-compensated mode in which (i) an absolute value of a first order temperature coefficient of frequency of the resonator element is reduced to a first value that is below a threshold value and (ii) an absolute value of a second order temperature coefficient of frequency of the resonator element is reduced to about zero, and wherein an anchor decoupler region formed on the resonator element causes the absolute value of the first order temperature coefficient of frequency of the resonator element to be further reduced to a second value smaller than the first value; and

at least one anchor coupling the resonator element to the support structure, wherein the anchor decoupler region is formed on the resonator element at least partially surrounding the at least one anchor.

2 . The MEMS resonator device of claim 1 , wherein the anchor decoupler region comprises at least one trench layer comprising one or more trenches etched into the resonator element.

3 . The MEMS resonator device of claim 1 , wherein the threshold value is a first threshold value, and wherein the anchor decoupler region further reduces an amount of energy transferred to the at least one anchor during operation of the MEMS resonator device to satisfy a second threshold value.

4 . The MEMS resonator device of claim 1 , wherein the MEMS resonator device is configured to operate as an oscillator.

5 . The MEMS resonator device of claim 1 , wherein the MEMS resonator device is configured to operate in an in-plane mode of vibration as well as an out-of-plane mode of vibration.

6 . The MEMS resonator device of claim 1 , wherein the MEMS resonator device is configured to operate in a single mode of vibration comprising an in-plane mode of vibration.

7 . The MEMS resonator device of claim 1 , wherein the MEMS resonator device is configured to operate in a single mode of vibration comprising an out-of-plane mode of vibration.

8 . The MEMS resonator device of claim 1 , wherein a geometric modification is applied to the resonator element to, in combination with the anchor decoupler region, cause the absolute value of the first order temperature coefficient of frequency of the resonator element to be further reduced to the second value.

9 . The MEMS resonator device of claim 8 , wherein applying the geometric modification comprises adding one or more additional areas to the resonator element.

10 . The MEMS resonator device of claim 8 , wherein applying the geometric modification comprises subtracting one or more areas from the resonator element.

11 . The MEMS resonator device of claim 8 , wherein applying the geometric modification comprises adding one or more additional areas to the resonator element and subtracting one or more areas from the resonator element.

12 . The MEMS resonator device of claim 1 , wherein an angle of an in-plane rotation of the resonator element, in combination with the anchor decoupler region, causes the absolute value of the first order temperature coefficient of frequency of the resonator element to be further reduced to the second value.

13 . The MEMS resonator device of claim 1 , further comprising:

at least one driving electrode for electrostatic actuation of the resonator element; and

at least one sense electrode for electrostatic sensing of the resonator element.

14 . A method for designing a MEMS resonator device with passive temperature-induced frequency drift compensation, the method comprising:

determining, for a resonator element of the MEMS resonator device, a doping concentration of at least one type of N-type or P-type dopants that causes a closely temperature-compensated mode in which (i) an absolute value of a first order temperature coefficient of frequency of the resonator element is reduced to a first value that is below a threshold value and (ii) an absolute value of a second order temperature coefficient of frequency of the resonator element is reduced to about zero;

doping the resonator element with the at least one type of N-type or P-type dopants at the determined doping concentration;

determining, for the resonator element, an anchor decoupler region to be formed on the resonator element that causes the absolute value of the first order temperature coefficient of frequency of the resonator element to be further reduced to a second value smaller than the first value; and

forming the determined anchor decoupler region on the resonator element at least partially surrounding at least one anchor of the MEMS resonator device coupling the resonator element to a support structure of the MEMS resonator device.

15 . The method of claim 14 , wherein:

determining, for the resonator element, the anchor decoupler region comprises:

determining, for the resonator element, one or more trench layers, wherein each trench layer comprises one or more trenches to be etched into the resonator element; and

forming the determined anchor decoupler region on the resonator element comprises:

etching the one or more trenches of the one or more trench layers into the resonator element.

16 . The method of claim 14 , wherein the threshold value is a first threshold value, and wherein the anchor decoupler region further reduces an amount of energy transferred to the at least one anchor during operation of the MEMS resonator device to satisfy a second threshold value.

17 . The method of claim 14 , wherein the MEMS resonator device is configured to operate as an oscillator.

18 . The method of claim 14 , wherein the MEMS resonator device is configured to operate in an in-plane mode of vibration as well as an out-of-plane mode of vibration.

19 . The method of claim 14 , wherein the MEMS resonator device is configured to operate in a single mode of vibration comprising an in-plane mode of vibration.

20 . The method of claim 14 , wherein the MEMS resonator device is configured to operate in a single mode of vibration comprising an out-of-plane mode of vibration.

21 . The method of claim 14 , further comprising:

determining, for the resonator element, a geometric modification to be applied to the resonator element to, in combination with the anchor decoupler region, cause the absolute value of the first order temperature coefficient of frequency of the resonator element to be further reduced to the second value; and

applying the determined geometric modification to the resonator element.

22 . The method of claim 21 , wherein:

determining, for the resonator element, the geometric modification to be applied to the resonator element comprises:

determining, for the resonator element, one or more additional areas to be added to the resonator element; and

applying the determined geometric modification to the resonator element comprises:

adding the one or more additional areas to the resonator element.

23 . The method of claim 21 , wherein:

determining, for the resonator element, the geometric modification to be applied to the resonator element comprises:

determining, for the resonator element, one or more areas to be subtracted from the resonator element; and

applying the determined geometric modification to the resonator element comprises:

subtracting the one or more areas from the resonator element.

24 . The method of claim 21 , wherein:

determining, for the resonator element, the geometric modification to be applied to the resonator element comprises:

determining, for the resonator element, one or more additional areas to be added to the resonator element; and

determining, for the resonator element, one or more areas to be subtracted from the resonator element; and

applying the determined geometric modification to the resonator element comprises:

adding the one or more additional areas to the resonator element; and

subtracting the one or more areas from the resonator element.

25 . The method of claim 14 , further comprising:

forming at least one driving electrode on the MEMS resonator device for electrostatic actuation of the resonator element; and

forming at least one sense electrode on the MEMS resonator device for electrostatic sensing of the resonator element.