MEMS resonator
A bulk-acoustic-mode MEMS resonator has a first portion with a first physical layout, and a layout modification feature. The resonant frequency is a function of the physical layout, which is designed such that the frequency variation is less than 150 ppm for a variation in edge position of the resonator shape edges of 50 nm. This design combines at least two different layout features in such a way that small edge position variations (resulting from uncontrollable process variation) have negligible effect on the resonant frequency.
1. A bulk-acoustic-mode MEMS resonator having a principal vibration direction, comprising:
a resonator body having a first portion with a first physical layout, a layout modification feature having a second physical layout, wherein, along the principal vibration direction, a first part of the resonator has a first gap pattern and a first lateral cross-section and a second part of the resonator has a second gap pattern and a second lateral cross-section and the respective gap patterns and lateral cross-sections are different from each other, a reflection interface between the first portion and the layout modification feature, the first physical layout differs from a first design layout by a first geometric offset in response to process variations during fabrication of the resonator, the second physical layout differs from a second design layout by a second geometric offset in response to the process variations, and a resonant frequency of the bulk resonator is a function of a relationship between the first geometric offset and the second geometric offset.
2. The resonator as claimed in claim 1 , wherein a first derivative of frequency with respect to an edge position variation is substantially zero.
3. The resonator as claimed in claim 1 , wherein the layout modification feature comprises holes or slits within the first portion.
4. The resonator as claimed in claim 3 , wherein the holes or slits have a dimension smaller than the acoustic wavelength.
5. The resonator as claimed in claim 1 , wherein the resonant vibration is in a one-directional or two-directional mode.
6. The resonator as claimed in claim 1 , further comprising:
external suspension springs.
7. The resonator as claimed in claim 1 , wherein the physical layouts are designed such that a frequency variation is less than 100 ppm for a variation in edge position of resonator shape edges of 50 nm.
8. The resonator as claimed in claim 1 , wherein the physical layouts are designed such that a frequency variation is less than 150 ppm for a variation in edge position of resonator shape edges of 100 nm.
9. The resonator as claimed in claim 1 , further comprising:
an actuation arrangement, which uses electrostatic actuation or thermal actuation.
10. The resonator as claimed in claim 1 , further comprising:
a readout arrangement, which uses capacitive readout, piezoresistive readout, or piezoelectric readout.
11. A method of designing a bulk-acoustic-mode MEMS resonator having a principal vibration direction, comprising;
designing a resonator body having a first portion with a first physical layout, and a layout modification feature having a second physical layout;
modeling a resonant frequency, taking into account the first physical layout and the second physical layout, wherein the first physical layout differs from a first design layout by a first geometric offset in response to fabrication of the resonator, and the second physical layout differs from a second design layout by a second geometric offset in response to the fabrication of the resonator;
selecting the physical layouts such that a resonant frequency variation of the bulk resonator is less than a first threshold for the geometric offsets in edge position of resonator shape edges of a second threshold, wherein along a principal vibration direction a first part of the resonator has a first gap pattern and a first lateral cross-section and a second part of the resonator has a second gap pattern and a second lateral cross-section and the respective gap patterns and lateral cross-sections are different from each other, a reflection interface between the first portion and the layout modification feature, and the modeling takes into account the lateral cross-sections and dimensions of the first portion and the layout modification feature, and any suspension system for the resonator body.
12. The method as claimed in claim 11 , wherein the first threshold is 150 ppm and the second threshold is 50 nm.
13. The method as claimed in claim 12 , wherein the modeling is carried out using finite element analysis.
14. The method as claimed in claim 11 , wherein the layout modification feature comprises holes or slits within the first portion, and the modeling takes into account dimensions and positions of the holes or slits, the first portion dimensions, and any suspension system for the resonator body.
15. The resonator of claim 1 , wherein the different lateral cross-sections include different widths.
16. The resonator of claim 1 , wherein the different lateral cross-sections include different thicknesses.
17. The resonator of claim 1 , wherein the first gap pattern is a plurality of holes and the second gap pattern is a slot.
18. The resonator of claim 17 , wherein a wider part of the resonator has the plurality of holes while a narrower part of the resonator has the slot.