Mechanical resonator device

Patent metadata

Field	Value
Publication number	US-11486756-B2
Application number	US-201716322645-A
Country	US
Kind code	B2
Filing date	Aug 1, 2017
Priority date	Aug 1, 2016
Publication date	Nov 1, 2022
Grant date	Nov 1, 2022

Abstract

A mechanical resonator device. The resonator device includes a resonator element made of an elastic material under tensile stress and adapted for sustaining at least one oscillation mode; and a clamping structure supporting the resonator element. The clamping structure has a phononic density of states exhibiting a bandgap or quasi-bandgap such that elastic waves of at least one polarisation and/or frequency are not allowed to propagate through the clamping structure. The resonator element and the clamping structure are configured to match with a soft-clamping condition that elastic waves of polarisation and/or frequency corresponding to the at least one oscillation mode of the resonator penetrate evanescently into the clamping structure in a manner such as to minimize bending throughout the entire resonator device. Thereby, bending related loss may be minimized and the Q-factor of the mechanical resonator may be maximized.

First claim

The invention claimed is:

1. Mechanical resonator device, the resonator device comprising
a resonator element made of an elastic material under tensile stress and adapted for sustaining at least one oscillation mode; and
a clamping structure supporting the resonator element;
wherein the clamping structure has a phononic density of states exhibiting a bandgap or quasi-bandgap such that elastic waves of at least one polarisation and/or frequency are not allowed to propagate through the clamping structure; and
wherein the resonator element and the clamping structure are configured in a manner such that elastic waves of polarisation and/or frequency corresponding to the at least one oscillation mode of the resonator element penetrate evanescently into the clamping structure so as to provide a soft-clamping of the resonator element; wherein configuration of the resonator element and the clamping structure includes integral minimization of bending related loss over tensile energy over the entire resonator device.

2. Resonator device according to claim 1 , wherein an energy-normalized mode shape curvature integral for said oscillation mode of the resonator device is less than an energy-normalized mode shape curvature integral for a corresponding mode with the same frequency of a reference resonator directly suspended from fixed anchoring means on a substrate.

3. Resonator device according to claim 1 , wherein the bandgap or quasi-bandgap is produced in the clamping structure by a periodic pattern with lattice constant a.

4. Resonator device according to claim 1 , wherein the resonator element and the clamping structure are made of the same elastic material under tensile stress.

5. Resonator device according to claim 1 , wherein the resonator element and the clamping structure are formed in a membrane.

6. Resonator device according to claim 1 , wherein the at least one oscillation mode of the resonator element is an out-of-plane oscillation mode.

7. Resonator device according to claim 1 , wherein the elastic material under tensile stress is one of silicon nitride, diamond, quartz, aluminium nitride, silicon carbide, gallium arsenide, indium gallium arsenide, aluminium gallium arsenide, aluminium, gold, graphene, polymer materials, or combinations thereof.

8. Resonator device according to claim 1 , wherein the elastic material under tensile stress is one of dielectrics, metals, semiconductors, metal dichalcogenides, ceramics or piezoelectric materials, or combinations thereof.

9. Resonator device according to claim 1 , wherein an initial stress in the elastic material under tensile stress is between 10 MPa and 50 GPa.

10. Resonator device according to claim 1 , wherein the resonator device comprises at least one further resonator element supported by the clamping structure, wherein
each further resonator element is made of an elastic material under tensile stress and adapted for sustaining at least one respective further oscillation mode; and
wherein each of the further resonator elements is configured with respect to the clamping structure in a manner such that elastic waves of polarisation and frequency corresponding to the at least one further oscillation mode of the at least one further resonator element penetrate evanescently into the clamping structure so as to provide a soft-clamping of the further resonator element.

11. Resonator device according to claim 10 , wherein the resonator element, the at least one further resonator element, and the clamping structure are made of the same elastic material under tensile stress.

12. Resonator device according to claim 1 , wherein a decay length of evanescent elastic waves is in the range of 0.1 to 20 times the wavelength of the elastic waves in the clamp.

13. Method of providing a mechanical resonator device, the resonator device comprising a resonator element and a clamping structure supporting the resonator element, the method comprising the steps of:
determining at least one oscillator mode for the resonator element,
determining a phononic density of states for the clamping structure, the phononic density of states exhibiting a bandgap or quasi-bandgap such that elastic waves of at least one polarisation and/or frequency are not allowed to propagate through the clamping structure; and
matching the resonator element and the clamping structure in a manner such that elastic waves of polarisation and/or frequency corresponding to the at least one oscillation mode of the resonator penetrate evanescently into the clamping structure so as to provide a soft-clamping of the resonator element; wherein matching the resonator element and the clamping structure includes integrally minimizing bending related loss over tensile energy over the entire resonator device.

14. Method according to claim 13 , wherein an energy-normalized mode shape curvature integral for said oscillation mode of the resonator device is less than an energy-normalized mode shape curvature integral for a corresponding mode with the same frequency of a reference resonator directly suspended from fixed anchoring means on a substrate.

15. Method according to claim 13 , wherein matching the resonator element and the clamping structure includes determining a quality factor Q of the resonator device according to the equation:
Q −1 =ΔW /(2π W ),

wherein ΔW is the bending related loss per oscillation cycle of a given mode, and W is the total energy of the mode.

16. Method according to claim 15 , wherein the given mode is an out-of-plane oscillation mode, wherein u(x,y) denotes out-of-plane displacement of the resonator device in a z-direction as a function of a lateral position denoted by lateral position coordinates x and y, and wherein the bending related loss per oscillation cycle ΔW is determined as:

Δ
⁢

⁢
W

≈

∫

π
⁢

E
2

1
-

ν
2

⁢

z
2

⁡

(

∂
2

⁢
u

∂

x
2

+

Assignees

• Schliesser Albert
• Univ Copenhagen

Inventors

• Schliesser Albert
• Tsaturyan Yeghishe
• Polzik Eugene Simon
• Barg Andreas

Classifications

• G01N29/022 Primary

  Fluid sensors based on microsensors, e.g. quartz crystal-microbalance [QCM], surface acoustic wave [SAW] devices, tuning forks, cantilevers, flexural plate wave [FPW] devices (microdevices per se B81B) · CPC title

• G01G3/165 Primary

  Constructional details · CPC title

• G01N2291/014

  Resonance or resonant frequency · CPC title

• G01H13/00

  Measuring resonant frequency · CPC title

• H03H9/2405

  of microelectro-mechanical resonators · CPC title