MEMS resonator
A MEMS (microelectromechanical system) resonator assembly ( 100 ), comprising a support structure ( 102 ), a resonator element ( 101 ) suspended to the support structure ( 102 ), and an actuator for exciting the resonator element ( 101 ) to a resonance mode. The resonator element ( 101 ) vibrates at resonance frequency f 0 and comprises at least one bulk acoustic resonator ( 110 a, 110 b ). The ESR*A*f 0 values of the resonator assembly ( 100 ) are in the range from 12 Ωmm 2 MHz to 83 Ωmm 2 MHZ.
1 . A MEMS resonator assembly, comprising
a support structure,
a resonator element suspended to the support structure, and
an actuator for exciting the resonator element to a resonance mode
wherein
the resonator element vibrates at resonance frequency f 0 and comprises at least one bulk acoustic resonator, and wherein
ESR*A*f 0 is in the range from 12 Ωmm 2 MHz to 83 Ωmm 2 MHz, where ESR is the equivalent series resistance of the MEMS resonator assembly and A is the area of the resonator element.
2 . The MEMS resonator assembly of claim 1 , wherein the said bulk acoustic resonator is a length-extensional resonator, an assembly of interconnected length-extensional resonators, a width-extensional resonator, a square-extensional resonator, or a Lame resonator, and/or wherein the said bulk acoustic resonator is an in-plane resonator.
3 . The MEMS resonator assembly of claim 1 , wherein ESR*A*f 0 is equal to or larger than 16 Ωmm 2 MHZ.
4 . The MEMS resonator assembly of claim 1 , wherein the area A of the resonator element is in the range from 0.001 mm 2 to 1 mm 2 and/or wherein the ratio of the motional capacitance to the shunt capacitance is smaller than 0.005, and/or wherein the figure of merit is larger than 10.
5 . The MEMS resonator assembly of claim 1 , wherein more than 50% of the mass of the resonator element consists of single-crystalline silicon.
6 . The MEMS resonator assembly of claim 1 , wherein the principal direction of the vibration of the said bulk acoustic resonator is substantially parallel to a <100> crystalline direction of single-crystalline silicon layer within the resonator element and the average phosphorus dopant concentration of the said single-crystalline silicon layer is larger than 2×10 19 cm −3 .
7 . The MEMS resonator assembly of claim 1 , wherein the actuator is a piezoelectric actuator, and/or wherein the resonator element comprises a layer of piezoelectric AlN, Sc-doped AlN, ZnO, LiNbO 3 , or LiTaO 3 and/or wherein the resonator element comprises a layer of piezoelectric material with the thickness in the range from 0.5 μm to 4 μm.
8 . The MEMS resonator assembly of claim 7 , wherein the average phosphorus dopant concentration of single-crystalline silicon within the resonator element is larger than 2×10 19 cm −3 and the ratio of the thickness of the piezoelectric layer to the thickness of the single-crystalline silicon layer or to the sum of respective thicknesses of two single-crystalline silicon layers within the resonator element is larger than 0.07.
9 . The MEMS resonator assembly of claim 1 , wherein the resonance frequency f 0 is in the range from 7 MHz to 160 MHz, and/or wherein the variation of the resonance frequency f 0 in the temperature range from −30° C. to 85° C. is within ±30 parts per million with respect to the said resonance frequency at the temperature 25° C., and/or herein there are two turnover points in the resonance frequency f 0 vs. temperature curve in the temperature range from −30° C. to 85° C.
10 . The MEMS resonator assembly of claim 1 , wherein the number of silicon oxide layers within the resonator element is either zero or one.
11 . The MEMS resonator assembly of claim 1 , wherein the resonator element comprises two bulk acoustic resonators, both vibrating at the resonance frequency f 0 in the same or 180 degrees shifted phase with respect to each other, and a material portion mechanically connecting the said two bulk acoustic resonators.
12 . The MEMS resonator assembly of claim 11 , wherein the material portion which mechanically connects the bulk acoustic resonators is a substantially rigid intercoupling element, or wherein the said material portion which mechanically connects a first of the two bulk acoustic resonators and a second of the two bulk acoustic resonators is a flexural mode resonator.
13 . The MEMS resonator assembly of claim 11 , wherein a first of the two bulk acoustic resonators and a second of the two bulk acoustic resonators are tethered to the same support structure which is formed within the plane of the resonator element along a line which is in the middle of the first and second bulk acoustic resonators, and/or wherein a distance between the two bulk acoustic resonators is 50 μm or less.
14 . The MEMS resonator assembly of claim 11 , wherein the resonance frequency f 0 substantially equals the fundamental or a Nth overtone frequency of the first bulk acoustic resonator and the fundamental or a Nth overtone frequency of the second bulk acoustic resonator, and/or wherein a Nth overtone frequency of the flexural mode resonator substantially equals the resonance frequency f 0 .
15 . The MEMS resonator assembly of claim 11 , wherein the first bulk acoustic resonator and the second bulk acoustic resonator resonate in a direction of vibration, and the flexural resonator is a beam resonator a longest dimension of which being oriented perpendicular to said direction of vibration.
16 . The MEMS resonator assembly of claim 11 , wherein the flexural resonator is an in-plane flexural beam resonator.
17 . The MEMS resonator assembly of claim 11 , wherein the flexural resonator is mechanically connected to the first bulk acoustic resonator and the second bulk acoustic resonator at anti-nodal points of the first and second bulk acoustic resonators, and/or wherein the resonance mode shape of the flexural mode resonator has two types of anti-nodal points wherein anti-nodal point(s) of the first type has/have a positive displacement along an axis of vibration and at least one of them is a connection point for a mechanical connection to a first of the two bulk acoustic resonators, and anti-nodal point(s) of the second type has/have a negative displacement along the said axis of vibration and at least one of them is a connection point for a mechanical connection to a second of the two bulk acoustic resonators.
18 . The MEMS resonator assembly of claim 11 , wherein the flexural resonator is mechanically connected to the first bulk acoustic resonator at one or more connection points on a first side of the flexural resonator and to the second bulk acoustic resonator at one or more connection points on a second, opposite, side of the flexural resonator, or wherein the flexural resonator is mechanically connected to the first bulk acoustic resonator at one or more connection points on one side of the flexural resonator and to the second bulk acoustic resonator at one or more connection points on the same side of the flexural resonator.
19 . The MEMS resonator assembly of claim 11 , wherein the first bulk acoustic resonator resonates in a first direction of vibration and the second bulk acoustic resonator resonates in a second direction of vibration perpendicular to the first direction of vibration.
20 . The MEMS resonator assembly of claim 11 , wherein the flexural mode resonator comprises a material portion which has a form of a rectangular frame.