WO2014112951A1

WO2014112951A1 - Dual mode resonator

Info

Publication number: WO2014112951A1
Application number: PCT/SG2014/000017
Authority: WO
Inventors: Margarita NARDUCCI; Chengliang SUN; Julius Ming Lin Tsai
Original assignee: Agency For Science, Technology And Research
Priority date: 2013-01-15
Filing date: 2014-01-15
Publication date: 2014-07-24

Abstract

A dual mode lamb wave resonator including a piezoelectric layer, first and second electrodes having first and second pluralities of electrode fingers. The first and second pluralities of electrode fingers each have a plurality of first and second electrode patches arranged thereon. The first and second electrode patches have respective first and second sizes which are different from each other, and are arranged according to corresponding first and second two-dimensional lattices on a first surface of the piezoelectric layer. Each of the plurality of second electrode patches arc arranged outside the plurality of first electrode patches. The first lattice is separated from the second lattice at least partially by two or more isolation trenches formed in the piezoelectric layer. Embodiments are directed towards providing real-time self-temperature measurement for robust temperature compensation. Also an microcomputer compensated crystal oscillator (MXCO) and a temperature compensated microelectromechanical system (MEMS) device.

Description

DUAL MODE RESONATOR

PRIORITY CLAIM

[0001] The present application claims priority to Singapore Patent Application No. 201300337-1, filed 15 January, 2013.

FIELD OF THE INVENTION

[0002] The present invention generally relates to lamb wave resonators, and more particularly relates to a lamb wave dual mode resonator for use in a microcomputer compensated crystal oscillator.

BACKGROUND

[0003] In recent years, aluminum nitride (A1N) resonators have been investigated as an alternative to quartz for timing applications. However, the main drawback of A1N resonators is their temperature instability. To overcome this instability, different temperature compensation methods have been implemented. A first approach, passive temperature compensation, can be achieved by either designing the resonator with multilayers of opposite temperature coefficients of frequency (TCF), or with multilayers of opposite p-n doping, or by engineering different device geometries. These methods for passive temperature compensation, however, are limited by non- linearities of the material properties of the resonator. A second approach is to use an external reference device to measure the temperature, the external reference device including readout circuitry to enable the resonator to perform real-time temperature compensation. However, this approach increases the physical size of any device incorporating such sensor. This approach can also introduce undesired effects on the device stack, such as additional stress.

[0004] Thus, what is needed is an efficiently designed self-temperature sensing resonator device which can address the problems of these prior methods and provide real-time self-temperature measurement for robust temperature compensation. Furthermore, other desirable features and characteristics will become apparent from the subsequent detailed description and the appended claims, taken in conjunction with the accompanying drawings and this background of the disclosure.

^■ SUMMARY

[0005] According to the Detailed Description, a dual mode resonator is provided. The dual mode resonator includes a piezoelectric layer, a first electrode ha ing a first plurality of electrode fingers, and a second electrode having a second plurality of electrode fingers. The first plurality of electrode fingers have a first portion of a plurality of first electrode patches and a first portion of a plurality of second electrode patches arranged thereon. The second plurality of fingers have a second portion of the plurality of first electrode patches and a second portion of the plurality of second electrode patches arranged thereon. Each of the plurality of first electrode patches have a first size and are arranged according to a first two-dimensional lattice on a first surface of the piezoelectric layer, and each of the plurality of second electrode patches have a second size different than the first size and are arranged according to a second two-dimensional lattice formed on the first surface of the piezoelectric layer outside the first two-dimensional lattice. The first two-dimensional lattice is separated from the second two-dimensional lattice at least partially by two or more isolation trenches formed in the piezoelectric layer. [0006] In accordance with another aspect, a microcomputer compensated crystal oscillator includes a dual mode resonator generating a first signal having a first frequency with a first temperature coefficient of frequency (TCF) and a second signal having a second frequency with a second TCF different from the first TCF, and a mixer for combining the first signal and the second signal to generate a temperature compensated oscillating output signal having a third frequency. The dual mode resonator includes a piezoelectric layer, a first electrode having a first plurality of electrode fingers, and a second electrode having a second plurality of electrode fingers. The first plurality of electrode fingers have a first portion of a plurality of first electrode patches and a first portion of a plurality of second electrode patches arranged thereon. The second plurality of fingers have a second portion of the plurality of first electrode patches and a second portion of the plurality of second electrode patches arranged thereon. Each of the plurality of first electrode patches have a first size and are arranged according to a first two-dimensional lattice on a first surface of the piezoelectric layer, and each of the plurality of second electrode patches have a second size different than the first size and are arranged according to a second two-dimensional lattice formed on the first surface of the piezoelectric layer outside the first two-dimensional lattice. The first two-dimensional lattice is separated from the second two-dimensional lattice at least partially by two or more isolation trenches formed in the piezoelectric layer.

[0007] In accordance with yet another aspect, a temperature compensated microelectromechanical system (MEMS) device is provided. The temperature compensated MEMS device include an oscillator and a dual mode resonator coupled to the oscillator for generating a first signal having a first frequency and a second signal having a second frequency. A third signal resulting from mixing the first signal and the second signal is used for temperature compensation of the MEMS device. The dual mode resonator includes a piezoelectric layer, a first electrode having a first plurality of electrode fingers, and a second electrode having a second plurality of electrode fingers. The first plurality of electrode fingers have a first portion of a plurality of first electrode patches and a first portion of a plurality of second electrode patches arranged thereon. The second plurality of fingers have a second portion of the plurality of first electrode patches and a second portion of the plurality of second electrode patches arranged thereon. Each of the plurality of first electrode patches have a first size and are arranged according to a first two-dimensional lattice on a first surface of the piezoelectric layer, and each of the plurality of second electrode patches have a second size different than the first size and are arranged according to a second two-dimensional lattice formed on the first surface of the piezoelectric layer outside the first two-dimensional lattice. The first two-dimensional lattice is separated from the second two-dimensional lattice at least partially by two or more isolation trenches formed in the piezoelectric layer.

BRIEF DESCRIPTION OF THE DRAWINGS

[0008] The accompanying figures, where like reference numerals refer to identical or functionally similar elements throughout the separate views and which together with the detailed description below are incorporated in and form part of the specification, serve to illustrate various embodiments and to explain various principles and advantages in accordance with a present embodiment.

[0009] FIG. 1, comprising FIGs. 1A and IB, depict diagrams illustrating a conventional lamb wave resonator where FIG. 1A is a cross-sectional planar view of the resonator and FIG. IB is a top planar view of the resonator. [0010] FIG. 2, comprising FIGs. 2A, 2B and 2C, depicts illustrations of a dual mode resonator in accordance with a present embodiment where FIG. 2A is a cross- sectional planar view of the dual mode resonator, FIG. 2B is a top planar view of the dual mode resonator, and FIG. 2C is a graph depicting temperature coefficient of frequency variations for various substrated dual mode resonators in accordance with the present embodiment.

[0011] FIG. 3 depicts a graph of frequency response of the dual mode resonator of FIG. 2 in accordance with the present embodiment.

[0012] FIG. 4 depicts a block diagram of a microcomputer compensated crystal oscillator (MXCO) application of the dual mode resonator of FIG. 2 in accordance with the present embodiment. - [0013] FIG. 5, comprising FIGs. 5A and 5B, depict graphs of conventional dual mode oscillator operation and operation of the MXCO of FIG. 4 in accordance with the present embodiment, wherein FIG. 5A depicts a graph of temperature dependency of the frequencies of conventional dual mode oscillators, and FIG. 5B depicts a graph of temperature dependency of the beat frequency of the MXCO incorporating the dual mode resonator of FIG. 2 in accordance with the present embodiment.

[0014] And FIG. 6 depicts a block diagram of a micro-electromechanical system (MEMS) oscillator incorporating the MXCO of FIG. 5 with the dual mode resonator of FIG. 2 in accordance with the present embodiment.

[0015] Skilled artisans will appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily been depicted to scale. For example, the dimensions of some of the elements in the block diagrams or flowcharts may be exaggerated in respect to other elements to help to improve understanding of the present embodiments. DETAILED DESCRIPTION

[0016] The following detailed description is merely exemplary in nature and is not intended to limit the invention or the application and uses of the invention. Furthermore, there is no intention to be bound by any theory presented in the preceding background of the invention or the following detailed description. It is the intent of this invention to present self-temperature sensing for implementation in a microcomputer compensated crystal oscillator (MCXO) by using a dual mode lamb wave resonator which produces temperature-dependent beat frequencies inherent to the lamb wave resonator, thereby eliminating any spatial or thermal lag associated with an external temperature sensor.

[0017] Referring to FIG. 1 A, a planar cross-section view 100 of a conventional lamb wave resonator 102 includes a substrate 104 having a bottom electrode 106 thereon. Top electrodes including electrode plates 108 are separated from the bottom electrode 106 by a piezoelectric layer 110. Referring to FIG. IB, a top planar view 150 depicts a checkerboard patterned array 152 of the electrode plates 108 connected to a positive electrode 154 and a negative electrode 156, the positive and negative electrodes 154, 156 having interdigitated positive electrode fingers 158 and negative electrode fingers 160. Using this array 152 of checkerboard patterned electrode plates 108, a longitudinal acoustic wave can be excited in the piezoelectric layer 110 as shown by arrows 112 in FIG. 1A by lateral field excitation (LFE) when the bottom electrode 106 is set to a ground potential and an electric field is applied between the positive electrode 154 and the negative electrode 156.

[0018] The electrode plates 108 are quadrilaterals (e.g., squares) and a length of one side of each electrode plate 108 parallel to the positive and negative electrode fingers 158, 160 and the distance along the electrode fingers 158, 160 separating an electrode plate 108 from an adjoining electrode plate 108 is the distance λ in FIG. IB. The frequency of the acoustic wave generated by LFE can be adjusted by changing λ (e.g., by changing the size of electrode plates 108 or the distance between the electrode plates) as shown in Table 1. In addition, the impedance level can be adjusted by changing the number of electrode plates 108 as it would change the total size of the resonator as shown in Table 2.

TABLE 1

TABLE 2 [0019] Referring to FIGs. 2A and 2B, a dual mode lamb wave resonator 202 in accordance with a present embodiment is depicted. FIG. 2A illustrates a cross- sectional planar view 200 of the dual mode resonator 202 and FIG. 2B illustrates a top planar view 240 of the dual mode resonator 202. The dual mode resonator 202 includes a piezoelectric layer 204 with first electrode patches 206 and second electrode patches 208 on one side and a bottom electrode 210 on an opposite side, the bottom electrode 210 formed on a semiconductor substrate 212. The first electrode patches 206 are a different size than the second electrode patches 208 (e.g., in FIGs. 2A and 2B, first electrode patches 206 are smaller than the second electrode patches 208). As seen in FIG. 2B, the first electrode patches 206 are formed in a first two- dimensional lattice structure 214 having a checkerboard pattern, where the positive ones are connected to a first portion of first electrode fingers connected to a positive electrode and the negative ones are connected to a first portion of second electrode fingers connected to a negative electrode and interdigitated with the first portion of the first electrode fingers (while not shown in FIG. 2B, the electrode fingers and positive and negative electrodes are formed in a manner similar to that shown in FIG. IB).

[0020] The second electrode patches 208 are formed in a second two-dimensional lattice structure 216 in the same plane as the first two-dimensional lattice structure 214. The second two-dimensional lattice structure 216 also has a checkerboard pattern formed outside the area of the first two-dimensional lattice structure 214 with positive ones of the second electrode patches 208 connected to a second portion of the first electrode fingers connected to the positive electrode and the negative ones of the second electrode patches 208 connected to a second portion of the second electrode fingers connected to the negative electrode and interdigitated with the second portion of the first electrode fingers outside the checkerboard pattern of the first two- dimensional lattice structure 214.

[0021] Isolation trenches 218 formed in the piezoelectric layer 204, the bottom electrode 210 and the substrate 212 separate the first two-dimensional lattice structure 214 from the second two-dimensional lattice structure 216 except in areas of trench- breaks 220. The trench-breaks 220 allow interconnection of the positive electrode to the first portion of the first electrode fingers in the first two-dimensional lattice structure 214 and the second portion of the first electrode fingers in the second two- dimensional lattice structure 216, as well as allowing interconnection of the negative electrode to the first portion of the second electrode fingers in the first two- dimensional lattice structure 214 and the second portion of the second electrode fingers in me second two-dimensional lattice structure 216.

[0022] The piezoelectric layer 204 is formed from piezoelectric materials such as aluminum nitride (AIN), zinc oxide (ZnO), or lithium niobate (LiNb0₃). The first and second electrode patches 206, 208, the first and second electrode fingers, and the bottom electrode 210 are formed from a conductive material such as gold (Au), aluminum (Al), molybdenum (Mo), tungsten (W), platinum (Pt), or titanium (Ti).

[0023] The semiconductor substrate 212 is formed from a semiconductive material such as silicon (Si), doped silicon, silicon dioxide (Si0₂), or'any combination thereof. Referring to FIG. 2C, a graph 250 of simulation results depicts temperature coefficients of frequency variations for various substrated dual mode resonators in accordance with the present embodiment. Temperature is plotted along the x-axis 252 in degrees Centigrade and frequency variations in parts per million is plotted along the y-axis 254. A first trace 256 shows frequency variations changing as temperature increases when the semiconductor substrate 212 is formed from a combination of silicon and silicon dioxide. A second trace 258 shows that frequency variations change less as temperature increases when the semiconductor substrate 212 is formed from a combination of doped silicon and silicon dioxide. And a third trace 260 shows that frequency variations change even less as temperature increases when the semiconductor substrate 212 is formed from a combination of doped silicon and silicon dioxide and a second semiconductor substrate of silicon dioxide is formed above the first and second electrode patches 206, 208 (not shown in FIG. 2A).

[0024] Thus, the dual mode acoustic wave resonator 202 with two checkerboard patterned lattice structures 214, 216 of electrode plates 206, 208 simultaneously excites a first shape mode at two different frequencies for real-time self-temperature measurement. The two different frequencies are determined by λι and λ₂ in FIG. 2B, where the electrode plates 206, 208 are quadrilaterals (e.g., squares) and λ_\ is a length of one side of each electrode plate 208 parallel to the positive and negative electrode fingers plus the distance along the electrode fingers separating one electrode plate 208 from an adjoining electrode plate 208. Likewise, λ₂ is a length of one side of each electrode plate 206 parallel to the positive and negative electrode fingers plus the distance along the electrode fingers separating one electrode plate 206 from an adjoining electrode plate 206.

[0025] Applying the electric field between adjacent electrodes (LFE) and setting the bottom electrode as ground generates two acoustic lamb waves by LFE. The two intersecting acoustic waves (one traveling along X direction and the other along Y direction) are simultaneously excited. The resonance frequency of these waves can be adjusted by changing the size of the electrode plates 206, 208 and the distance in between them, as seen in Equation (1):

where E is Young's modulus, p . is density and is the wavelength of the checkerboard pattern.

[0026] In accordance with the present embodiment, to generate a first shape mode simultaneously in two different frequencies within the same piezoelectric layer 204, two distinct electrode plate sizes isolated by the isolation trenches 218 in the piezoelectric layer 204 is preferable to reduce or eliminate interference between the two tonal frequencies.

[0027] A analysis of the resonance modes, frequencies and dependence with temperature was carried out using the finite element method software ANSYS. Referring to FIG. 3, a graph 300 of frequency response of a dual mode resonator 202 with λ = 38μιη and λ₂ = 19μπι in accordance with the present embodiment is illustrated. Frequency is plotted along the x-axis 302 and impedance is plotted along the y-axis 304. As can be seen from a trace 306 on the graph 300, the first tone 308 (corresponding with λι = 38μπι) is at ~210MHz and the second tone 310 (corresponding with λ₂ = 19μιη) is at ~425MHz. Both tones exhibit negative frequency shift as temperature rises, where the first tone has TCF1= -24ppm/degC° and the second tone has the TCF2= -14ppm/degC°.

[0028] Referring to FIG. 4, a block diagram 400 of a microcomputer compensated crystal oscillator (MXCO) 402 of the dual mode resonator 202 in accordance with the present embodiment is depicted. The lamb wave dual mode resonator 202 acts as an input for the oscillator 403 for active temperature compensation. The oscillator 403 includes circuitry for filtering the signals from the dual mode resonator 202 and circuitry for providing feedback to the dual mode resonator for maintaining oscillation of the resonator 202 for generating two signals 404, 406 having the two tonal frequencies f\ and i, the two signals 404, 406 generated simultaneously by excitation of a first resonance mode, in two different frequencies, as described above. The oscillator outputs the signals 404, 406 to a mixer 408 which combines the two signals 404, 406 to generate a beat frequency 410 t«- ⁼J2— fi), the beat frequency 410 filtered by a low pass filter 412 is then used for temperature sensing and/or active temperature compensation.

[0029] The two frequencies, /_! and/i, are mixed by the mixer 408 to form the beat frequency fi,. The temperature dependence of f_\, fi and can be expressed as 2(D = /2(r₀) (3) fb (J) = fb(T₀) (a_t— ο₂)ΔΓ τ - (4) where a and b are constants, T₀ is a reference temperature and Δ. ^' = T— 7 . Only taking into account the first order terms, the fractional change in beat frequency is given as

fh(T) _ (α, - α^ΔΤ

fb(Ta) K¾ (5) .

[0030] As it can be seen from Equation 5, the beat frequency would be more sensitive to temperature changes, allowing in this way advantageous self-temperature sensing. Referring to FIGs. 5A and 5B, graphs 500, 550 illustrate comparison of temperature dependency of conventional dual mode oscillators to temperaturedependency of the beat frequency of the MXCO 402, where the temperature dependency of the output frequencies of conventional dual mode oscillators is shown in the graph 500 and temperature dependency of the beat frequency of the MXCO 402 in accordance with the present embodiment is shown in the graph 550. The change in temperature (ΔΤ) is plotted along the x-axes 502, 552 and the change in frequency (A fj is plotted along the y-axes 504, 554.

[0031] Referring to the graph 500, a conventional dual mode oscillator uses a base frequency fl 506 and a third overtone of that frequency £3 508 for temperature sensing. As seen from the graph 550, temperature sensing in accordance with the present embodiment using the beat frequency, , 556 can realize improved temperature sensing and, consequently more accurate temperature compensation. Furthermore, the two frequencies,/_! and/, used to generate the beat frequency,/ are individually determined in response to the structure of each of the electrode plates, 206, 208, in the two checkerboard two-dimensional lattice structures 214, 216. In this manner, design of dual mode resonators in accordance with the present embodiment is more flexible than previous designs where the second frequency is an overtone (i.e., determined in response to) of the first frequency such as the conventional design used for the simulation results of FIG. 5 A where the frequency f3 is an overtone of the frequency fl as shown in the graph 500. This also enables dual mode resonators designed in accordance with the present embodiment to be more robust and more energy efficient than previous dual mode resonators as the resonator can generate a larger variety of frequencies in the first mode rather than prior art dual mode resonators that are restricted to a base frequency and its overtones.

[0032] Referring to FIG. 6, a block diagram 600 depicts a micro-electromechanical system (MEMS) oscillator incorporating the MXCO 402 with the dual mode resonator 202 in accordance with the present embodiment. The dual mode resonator 202 provides input signals to a dual mode oscillator 403. The output signals are combined by the mixer 408 to generate the beat frequency which is converted to a digital temperature sensing signal by a time-to-digital converter 604. The digital temperature sensing signal from the time-to-digital converter 604 is utilized by temperature compensation logic 606 to produce a temperature compensation signal. The temperature compensation signal is provided to a fractional-N phase lock loop 608 which also receives the signal f_\ from the dual mode resonator 202. As can be seen from inset graph 610, the signal f_\ varies with temperature. The output of temperature compensation logic 612 also varies with temperature, but the variations cancel each other out such that the signal output from the fractional-N phase lock loop 608 is temperature stable as seen in inset graph 614.

[0033] Thus, in accordance with the present embodiment, an efficiently designed self-temperature sensing resonator device which provides real-time self-temperature measurement for robust temperature compensation has been provided. A high- sensitivity self-temperature sensing system based on the dual mode resonator 202 has also been presented. A single shape mode (also called the SO mode or cero order symmetric mode) can excite two frequencies having different temperature of coefficients (TCFs) in the dual mode resonator 202. Temperature compensation using the beat frequency thermometer technique in accordance with the present embodiment offers advantages over other methods by enabling the extraction of the beat frequency using only one resonator exciting two tones. Also utilization of the dual-mode resonator 202 in accordance with the present embodiment eliminates the spatial, temporal and thermal lag of conventional devices because the temperature sensing signal comes directly from the resonator 202. In this manner temperature compensation is improved using the thermometric beat frequency, _>· The present embodiment describes using the dual resonator 202 with the MCXO 402 for high frequency stability over varying temperature. While exemplary embodiments have been presented in the foregoing detailed description of the invention, it should be appreciated that a vast number of variations exist. For example, those skilled in the art will realize from the teachings herein that the present technology may also be applied to design filters.

[0034] It should further be appreciated that the exemplary embodiments are only examples, and are not intended to limit the scope, applicability, operation, or configuration of the invention in any way. Rather, the foregoing detailed description will provide those skilled in the art with a convenient road map for implementing an exemplary embodiment of the invention, it being understood that various changes may be made in the function and arrangement of elements and method of operation described in an exemplary embodiment without departing from the scope of the invention as set forth in the appended claims.

Claims

CLAIMS What is claimed is:

1. A dual mode resonator comprising:

a piezoelectric layer;

a first electrode comprising a first plurality of electrode fingers; and a second electrode comprising a second plurality of electrode fingers, wherein the first plurality of electrode fingers have a first portion of a plurality of first electrode patches and a first portion of a plurality of second electrode patches arranged therealong, and wherein the second plurality of fingers have a second portion of the plurality of first electrode patches and a second portion of the plurality of second electrode patches arranged therealong, and wherein each of the plurality of first electrode patches have a first size and are arranged according to a first two- dimensional lattice on a first surface of the piezoelectric layer, and wherein each of the plurality of second electrode patches have a second size different than the first size and are arranged according to a second two-dimensional lattice formed on the first surface of the piezoelectric layer outside the first two-dimensional lattice and in a same plane as the first two-dimensional lattice, and wherein the first two-dimensional lattice is separated from the second two-dimensional lattice at least partially by two or more isolation trenches formed in the piezoelectric layer.

2. The dual mode resonator in accordance with Claim 1 further comprising a third electrode formed on a second surface of the piezoelectric layer, the second surface opposite to the first surface of the piezoelectric layer thereby forming a dual mode lamb wave resonator.

3. The dual mode resonator in accordance with Claim 1 or Claim 2 wherein the first size is a quadrilateral having one side parallel to the plurality of first electrode fingers with a first predetermined length, and wherein the first lattice structure is a checkerboard pattern of the plurality of first electrode patches, each of the plurality of first electrode patches separated along the first plurality of electrode fingers and the second plurality of electrode fingers by a second predetermined length.

4. The dual mode resonator in accordance with any of the preceding claims wherein the second size is a quadrilateral having one side parallel to the plurality of first electrode fingers with a third predetermined length greater than the first predetermined length, and wherein the second lattice structure is an outer portion of a checkerboard pattern of the plurality of second electrode patches, each of the plurality of second electrode patches separated along the first plurality of electrode fingers and the second plurality of electrode fingers by a fourth predetermined length.

5. The dual mode resonator in accordance with either Claim 3 or Claim 4 wherein a first tone having a first frequency with a first temperature coefficient of frequency (TCF) is excited within the dual mode resonator, the first frequency determined in response to a sum of the first and second predetermined lengths.

6. The dual mode resonator in accordance with either Claim 4 or Claim 5 wherein a second tone having a second frequency with a second TCF different than the first TCF is excited within the dual mode resonator, the second frequency determined in response to a sum of the third and fourth predetermined lengths.

7. The dual mode resonator in accordance with Claim 6 wherein the first tone and the second tone are simultaneously excited within the dual mode resonator utilizing a single shape mode, the two or more isolation trenches formed in the piezoelectric layer preventing interference between the first and second tones, and wherein a beat frequency generated in response to the first frequency and the second frequency is utilized for temperature sensing and/or temperature compensation.

8. The dual mode resonator in accordance with any of the preceding claims wherein the two or more isolation trenches formed in the piezoelectric layer have one or more trench-breaks located between each of the two or more isolation trenches, and wherein the first portion of the first plurality of electrode fingers is connected to the second portion of the first plurality of electrode fingers through the one or more trench-breaks, and wherein the first portion of the second plurality of electrode fingers is also connected to the second portion of the second plurality f electrode fingers through the one or more trench-breaks.

9. The dual mode resonator in accordance with any of Claims 2 to 8 wherein the piezoelectric layer is formed on a semiconductor substrate, the third electrode formed between the piezoelectric layer and the semiconductor substrate.

10. The dual mode resonator in accordance with Claim 9 wherein the substrate is formed from a semiconductive material selected from the group comprising silicon (Si), doped silicon, silicon dioxide (Si0₂) and any combination thereof.

11. The dual mode resonator in accordance with any of the preceding claims wherein the piezoelectric layer is formed from a piezoelectric material selected from the group comprising aluminum nitride (AIN), zinc oxide (ZnO) and lithium niobate (LiNb0₃).

12. The dual mode resonator in accordance with any of the preceding claims wherein the first, second or third electrodes are formed from a conductive material selected from the group comprising gold (Au), aluminum (Al), molybdenum (Mo), tungsten (W), platinum (Pt) and titanium (Ti).

13. A microcomputer compensated crystal oscillator (MXCO) comprising: a dual mode resonator generating a first signal having a first frequency with a first temperature coefficient of frequency (TCF) and a second signal having a second frequency with a second TCF, the second TCF different than the first TCF; and

a mixer for combining the first signal and the second signal to generate a temperature compensated oscillating output signal having a third frequency, wherein the dual mode resonator comprises:

a piezoelectric layer;

a first electrode comprising a first plurality of electrode fingers; and a second electrode comprising a second plurality of electrode fingers, wherein the first plurality of electrode fingers have a first portion of a plurality of first electrode patches and a first portion of a plurality of second electrode patches arranged therealong, and wherein the second plurality of fingers have a second portion of the plurality of first electrode patches and a second portion of the plurality of second electrode patches arranged therealong, and wherein each of the plurality of first electrode patches have a first size and are arranged according to a first two-dimensional lattice on a first surface of the piezoelectric layer, and wherein each of the plurality of second electrode patches have a second size different than the first size and are arranged according to a second two-dimensional lattice formed on the first surface of the piezoelectric layer outside the first two-dimensional lattice, and wherein the first two-dimensional lattice is separated from the second two-dimensional lattice at least partially by two or more isolation trenches formed in the piezoelectric layer.

14. The MXCO in accordance with Claim 13 further comprising a third electrode formed on a second surface of the piezoelectric layer, the second surface opposite to the first surface of the piezoelectric layer thereby forming a dual mode lamb wave resonator.

15. The MXCO in accordance with Claim 13 or Claim 14 wherein the first size is a square having a first predetermined length, and wherein the first lattice structure is a checkerboard pattern of the plurality of first electrode patches, each of the plurality of first electrode patches separated along the first plurality of electrode fingers and the second plurality of electrode fingers by a second predetermined length.

16. The MXCO in accordance with any of Claims 13 to 15 wherein the second size is a square having a third predetermined length greater than the first predetermined length, and wherein the second lattice structure is an outer portion of a checkerboard pattern of the plurality of second electrode patches, each of the plurality of second electrode patches separated along the first plurality of electrode fingers and the second plurality of electrode fingers by a fourth predetermined length.

17. The MXCO in accordance with Claim 16 wherein the first signal having the first frequency is excited within the dual mode resonator, the first frequency determined in response to a sum of the first and second predetermined lengths, and wherein the second signal having the second frequency is excited within the dual mode resonator, the second frequency determined in response to a sum of the third and fourth predetermined lengths.

18. The MXCO in accordance with Claim 17 wherein the first signal and the second signal are simultaneously excited within the dual mode resonator utilizing a single shape mode, the two or more isolation trenches formed in the piezoelectric layer to prevent interference between the first and second signals, and wherein a beat frequency generated in response to the first frequency and the second frequency is utilized for generating the temperature compensated oscillating output signal.

19. A temperature compensated microelectromechanical system (MEMS) device comprising:

an oscillator; and

a dual mode resonator coupled to the oscillator for generating a first signal having a first frequency with a first temperature coefficient of frequency (TCF) and a second signal having a second frequency with a second TCF different than the first TCF, wherein a third signal having a beat frequency resulting from mixing the first signal with the first frequency and the second signal with the second frequency is used for temperature compensation of the MEMS device, the dual mode resonator comprising:

a piezoelectric layer;

a first electrode comprising a first plurality of electrode fingers; and a second electrode comprising a second plurality of electrode fingers, wherein the first plurality of electrode fingers have a first portion of a plurality of first electrode patches and a first portion of a plurality of second electrode patches arranged therealong, and wherein the second plurality of fingers have a second portion of the plurality of first electrode patches and a second portion of the plurality of second electrode patches arranged therealong, and wherein each of the plurality of first electrode patches have a first size and are arranged according to a first two-dimensional lattice on a first surface of the piezoelectric layer, and wherein each of the plurality of second electrode patches have a second size different than the first size and are arranged according to a second two-dimensional lattice formed on the first surface of the piezoelectric layer outside the first two-dimensional lattice, and wherein the first two-dim ensional lattice is separated from the second two-dimensional lattice at least partially by two or more isolation trenches formed in the piezoelectric layer.

20. The temperature compensated MEMS device in accordance with Claim 19 further comprising a third electrode formed on a second surface of the piezoelectric layer of the dual mode resonator, the second surface opposite to the first surface of the piezoelectric layer thereby forming a dual mode lamb wave resonator, wherein the first signal and the second signal are simultaneously excited within the dual mode resonator utilizing a single shape mode, the two or more isolation trenches formed in the piezoelectric layer to prevent interference between the first and second signals, and wherein the beat frequency is generated in response to the first frequency and the second frequency and is utilized for performing the temperature compensation: