SYSTEM (MEMS) RESONATOR

FIELD OF INVENTION

[0001] The embodiments herein generally relate to micro-electromechanical system (MEMS) resonators and, more particularly, relate to an asymmetric phononic crystal (PnC) tethering for radio frequency (RF) MEMS resonators.

BACKGROUND OF INVENTION

[0002] Aluminum nitride (AlN)-on-silicon lateral mode MEMS resonators have emerged as a suitable replacement for their bulky, off-chip Quartz based counterparts because of their small form factor, capability of on-chip integration with CMOS circuitry, low motional resistance and high power handling capability. However, the Q-Factors attained by these resonators is in the few thousands range which is lower than that of Quartz resonators. The primary loss mechanisms that reduce the Q-Factor of these resonators are anchor loss, interfacial dissipation and material losses in the metal electrodes. If a resonator is limited by anchor losses rather than interfacial losses, then there is an opportunity for increasing the overall Q- Factor of the resonator by reducing the former.

[0003] Anchor loss in MEMS resonators has been studied extensively and different techniques have been devised to reduce its effect. Anchor loss is caused by radiation of acoustic waves from resonator body to the substrate through the support tethers resulting in a reduction of the energy retaining capability of the resonator degrading the Q-Factor. Anchor loss reduction methods centered around the modification of support tethers and a surrounding substrate in a way that the leaking acoustic waves are reflected back into the resonator thereby increasing the energy confinement within the resonator.

[0004] The existing systems show that phononic crystals (PnCs), which are periodically elastic structures, exhibit ranges of frequencies known as acoustic band-gaps (ABGs) in their band-structure. Elastic waves having frequencies within the ABGs are not allowed to propagate through the PnC structure. Utilizing this, property of periodic elastic materials, various existing systems have demonstrated one-dimensional symmetric

PnC tethering designs for resonators whose frequency lies within the ABG. However, the existing symmetric PnC structure has low Q-Factor and higher insertion losses.

[0005] The above information is presented as background information only to help the reader to understand the present invention.

Applicants have made no determination and make no assertion as to whether any of the above might be applicable as Prior Art with regard to the present application.

OBJECT OF INVENTION

[0006] The principal object of the embodiments herein is to provide an asymmetric phononic (PnC) crystal tethering for radio frequency (RF) micro-electro-mechanical system (MEMS) resonators.

[0007] Another object of the embodiments herein is to provide an asymmetric unit cell with two semicircular inclusions. The centers of the two semicircular inclusions are displaced from each other by twice the value of distance between any one of the centers and the center of the asymmetric unit cell.

[0008] Another object of the embodiments herein is to provide a tapered connector to attach the asymmetric PnC tethering to the resonator. SUMMARY

[0009] Accordingly the embodiments herein provide an asymmetric phononic (PnC) crystal tethering for radio frequency (RF) micro-electromechanical system (MEMS) resonator. The tethering includes a plurality of asymmetric unit cells. Further each asymmetric unit cell includes two semicircular inclusions each of a radius with their centers displaced from each other by twice the value of distance between the center of each inclusion and the center of the asymmetric unit cell.

[0010] Accordingly the embodiments herein provide an asymmetric unit cell. The asymmetric unit cell includes two semicircular inclusions. Further, the center of each semicircular inclusion is displaced by twice the value of distance between the center of each inclusion and the center of the unit cell.

[0011] These and other aspects of the embodiments herein will be better appreciated and understood when considered in conjunction with the following description and the accompanying drawings. It should be understood, however, that the following descriptions, while indicating preferred embodiments and numerous specific details thereof, are given by way of illustration and not of limitation. Many changes and modifications may be made within the scope of the embodiments herein without departing from the spirit thereof, and the embodiments herein include all such modifications.

BRIEF DESCRIPTION OF FIGURES

[0012] This invention is illustrated in the accompanying drawings, throughout which like reference letters indicate corresponding parts in the various figures. The embodiments herein will be better understood from the following description with reference to the drawings, in which: [0013] FIG. 1 illustrates a schematic of an asymmetric unit cell for an asymmetric one-dimensional phononic crystal (PnC) tethering, according to an embodiment as disclosed herein;

[0014] FIG. 2a illustrates a top view of the asymmetric PnC tethering with a lattice constant, according to the embodiments as disclosed herein;

[0015] FIG. 2b illustrates the cross-section of the asymmetric PnC tether showing different film thickness, according to an embodiment as disclosed herein;

[0016] FIGS. 3a and 3b are graphs showing variation of acoustic band gap (ABG) width as calculated from the band structure with semicircular inclusion with a radius and a distance respectively, according to an embodiment as disclosed herein;

[0017] Fig. 4a illustrates a computed band structure for the asymmetric unit cell with dimensions with the ABG encompassing a frequency, according to an embodiment as disclosed herein;

[0018] Fig. 4b illustrates the computed band structure for the asymmetric unit cell with the ABG encompassing the frequency, according to an embodiment as disclosed herein;

[0019] FIG. 5a illustrates a mode shape and an estimated Q value using a perfectly matched layer (PML) method of a third order longitudinal mode resonator corresponding to the asymmetric PnC tethering with a direct attachment, according to an embodiment as disclosed herein;

[0020] FIG. 5b illustrates the mode shape and the estimated Q value using the PML method of the third order longitudinal mode resonator corresponding to the asymmetric PnC tethering with a tapered connector, according to an embodiment as disclosed herein; and [0021] FIG. 6 is a graph showing a comparison between measured response of the resonators with conventional tethering and asymmetric PnC tethering, according to an embodiment disclosed herein.

DETAILED DESCRIPTION OF INVENTION

[0022] The embodiments herein and the various features and advantageous details thereof are explained more fully with reference to the non-limiting embodiments that are illustrated in the accompanying drawings and detailed in the following description. Descriptions of well- known components and processing techniques are omitted so as to not unnecessarily obscure the embodiments herein. Also, the various embodiments described herein are not necessarily mutually exclusive, as some embodiments can be combined with one or more other embodiments to form new embodiments. The term "or" as used herein, refers to a nonexclusive or, unless otherwise indicated. The examples used herein are intended merely to facilitate an understanding of ways in which the embodiments herein can be practiced and to further enable those skilled in the art to practice the embodiments herein. Accordingly, the examples should not be construed as limiting the scope of the embodiments herein.

[0023] Accordingly the embodiments herein provide an asymmetric phononic (PnC) crystal tethering for radio frequency (RF) micro-electromechanical system (MEMS) resonator. The tethering includes a plurality of asymmetric unit cells. Further each asymmetric unit cell includes two semicircular inclusions with their centers displaced from each other by twice the value of distance between the center of each inclusion and the center of the asymmetric unit cell.

[0024] In an embodiment, each asymmetric unit cell is repeated in same direction.

[0025] In an embodiment, elastic waves undergo scattering by the semicircular inclusions.

[0026] In an embodiment, the asymmetric PnC tethering is attached to the resonator using a tapered connector. [0027] In an embodiment, the tapered connector is triangular in shape.

[0028] Unlike the conventional systems, the proposed asymmetric one-dimensional PnC tethering exhibit larger acoustic band gaps (ABGs) as well as the additional ability to fine tune their properties, which results in significant improvement in Q-Factor as well as insertion loss (IL).

[0029] Referring now to the drawings and more particularly to FIGS. 1 through 6 where similar reference characters denote corresponding features consistently throughout the figures, there are shown preferred embodiments.

[0030] FIG. 1 illustrates a schematic of an asymmetric unit cell 100 for asymmetric one-dimensional phononic crystal (PnC) tethering, according to an embodiment as disclosed herein. As depicted in FIG. 1, the asymmetric unit cell 100 consists of two semicircular inclusions 102a and 102b each of radius r. The centers of the semicircular inclusions (102a and 102b) are displaced from each other by a distance 2d, while the conventional symmetric tether is a special case of the proposed design with d = 0.

[0031] FIG. 2a illustrates a top view of the asymmetric PnC tethering 200 with a lattice constant, according to the embodiments as disclosed herein. As depicted in FIG. 2a, the asymmetric unit cells 100 are repeated in one direction with a period of 'a', which is known as lattice constant, to form the tether 200.

[0032] FIG. 2b illustrates a cross-section of the asymmetric PnC tethering showing different film thickness, according to an embodiment as disclosed herein. The cross section of the asymmetric PnC tethering 200 indicating thickness of molybdenum (tMo), aluminium nitride (ΪΑΙ ) and silicon (ts layers respectively as shown in the FIG. 2b. [0033] In the proposed asymmetric PnC tethering 200, elastic waves undergo scattering from periodically located semicircular inclusions or holes (102a and 102b) with the centers on one edge being displaced from those on the other by a distance 2d. This arrangement of the semicircular inclusions (102a and 102b) introduces asymmetry in the lattice, unlike the conventional tethering geometries which are symmetric with respect to the direction of propagation of the acoustic waves.

[0034] A third order longitudinal mode AlN-on-Silicon resonator is designed with a resonance frequency of 300 MHz to demonstrate the efficacy of the tether 200 design. The band structure for the asymmetric unit cell 100 is computed using the finite element package COMSOL Multiphysics® with Bloch periodic boundary conditions (PBC) applied at the two ends as shown in FIG. 1. The geometrical parameters of the asymmetric unit cell 100 i.e., V and 'd' are varied independently and their effect on ABG is studied. The proposed design provides a large ABG encompassing the resonant frequency of the resonator. The main advantage of having a large ABG is that the enhancement in the Q-Factor is obtained over a large range of frequencies without having to rely on additional deaf bands which may interact with the resonator in an unwanted manner. Also, a larger ABG ensures that in spite of minor changes in the geometry if the structure during fabrication the resonant frequency lies within the ABG. The use of asymmetric tether 200 enables to tune the ABG over a wider range at the design stage, depending upon the specific application requirement.

[0035] FIGS. 3a and 3b are graphs showing variation of ABG width as calculated from the band structure with semicircular inclusion with a radius and a distance respectively, according to an embodiment as disclosed herein. In the conventional designs, the spatial impedance variation and the filling fraction (f _r ) of the asymmetric unit cell are the factors that govern the frequency span of the ABGs. The filling fraction denotes the ratio of volume occupied by the asymmetric unit cell 100 after removing the semicircular holes 102a and 102b to the total volume. Maximum acoustic impedance mismatch occurs between the AIN-Mo-Si composite structure and air resulting in large ABG in the band structure for the asymmetric unit cell 100. The radius V is varied and the corresponding band structure is calculated to obtain the variation of ABG span. The volume fraction change of the asymmetric unit cell 100 that is caused by the V variation in turn results in a change in the ABG width. The bounds on the value of V were set by the minimum dimension capable of being reliably printed by the lithography tool which was around 1 μιη. As shown in FIG. 3a, as the value of r varies from 1.5 μιη to 2.5 μιη, the ABG width reaches a maximum value of 63 MHz at around 2 μιη.

[0036] The distance d ' can also be varied while keeping r as constant to study the effect on the ABG width. Another advantage of the proposed design is that d can be varied independently without changing f _r since V remains constant. This essentially provides another degree of freedom to adjust the value of the ABG width as per the specification. As shown in FIG. 3b, as the value of d is varied from 1.5 μιη to 2.5 μιη, it is observed that the ABG attains a maximum value at a value of about 2 μιη.

[0037] FIG. 4a illustrates a computed band structure for the asymmetric unit cell with dimensions with the ABG encompassing a frequency, according to an embodiment as disclosed herein. As shown in FIG. 4a, complete ABGs of span 40MHz and 63 MHz exist in the band structure with the latter incorporating the resonance frequency of the resonator (300 MHz). The calculated band-gap of 63 MHz is much larger than the band gap of about 45 MHz for a one-dimensional LAB ring PnC.

[0038] FIG. 4b illustrates the computed band structure for the asymmetric unit cell with the ABG encompassing the frequency, according to an embodiment as disclosed herein. The computed band structure for the symmetric unit cell with d = 0 depicted in FIG. 4b yields an ABG width of 50 MHz, which is lesser compared to the asymmetric case. This clearly demonstrates the ability of the proposed asymmetric structure to provide higher ABG.

[0039] FIG. 5a illustrates a mode shape and an estimated Q value using a perfectly matched layer (PML) method of a third order longitudinal mode resonator corresponding to the asymmetric PnC tethering with a direct attachment, according to an embodiment as disclosed herein. Even though the asymmetric tethering 200 has the advantage of large ABG and better design flexibility, the problem with the asymmetric tether 200 is their attachment to the resonator body 502. In order to study the effect of tether 200 attachment to the resonator body 502 on the resonator Q-factor, finite element analysis is carried out using PMLs at the asymmetric tethering 200 ends to prevent the elastic waves from getting reflected back. FIG. 5a shows an asymmetric PnC tethering 200 formed by the repetition of seven asymmetric unit cell 100 elements, which is attached to the resonator body 502 at the nodal locations. The Q-Factor obtained with the asymmetric PnC tethering 200 is much higher that the Q-Factor of the conventional symmetric tether, but is still significantly less than the Q-Factor of the tether 200 in a simulated environment. The low value of the Q-factor can be attributed to the fact that the tether 200 couples to the resonator body 502 not just at the nodes but also to regions of non-zero displacement.

[0040] FIG. 5b illustrates the mode shape and the estimated Q value using the PML method of the third order longitudinal mode resonator corresponding to the asymmetric PnC tethering with a tapered connector. In order to overcome the drawback of low Q-Factor associated with the direct attachment of the asymmetric PnC tethering 200 with resonator body 502, an alternative arrangement for the attachment of the tethering 200 to the resonator body 502 is developed by reducing the attachment area. In the proposed design as shown in FIG. 5b, a tapered connector is used such that the attachment is restricted to areas where the displacement is either zero or close to zero. The mode shape of the resonator with the tapered connector is shown in FIG. 5b, wherein it is observed that there is no shape distortion. The Q-factor evaluated using the PML method is 58,529, which is sufficiently high to eliminate the effect of the Q-factor due to anchor loss on the overall Q-factor.

[0041] Resonators with and without asymmetric PnC tethering are fabricated with SOI wafers with a device layer thickness (ts of 2 μιη. Subsequently a Mo-AIN-Mo stack is deposited on top with a Mo thickness (tMo) of 100 nm and A1N thickness (ΪΑΙ ) of 300 nm. The top Mo layer is then etched to form the top electrodes and the contact pads for the signal input and output. This is followed by the etching of the A1N to form the bottom electrode ground contact pads. The device geometry is defined by first etching A1N and bottom Mo and then the Si device layer so as to have vertical sidewalls. The devices are then released using vapor HF.

[0042] The fabricated resonators with and without asymmetric PnC tethering are characterized in Cascade PLV50 Vacuum Probe Station using Agilent E8363C PNA Network Analyzer. The frequency response of the resonators is measured in vacuum conditions and at room temperature.

[0043] FIG. 6 is a graph showing a comparison between measured response of the resonators with conventional tethering and asymmetric PnC tethering, according to an embodiment disclosed herein. The input signal frequency is swept from 290 MHz to 330 MHz for the conventionally tethered resonators. For the resonator without PnC tethering the overall Q- factor obtained is about 147 which make the device more or less unsuitable for any kind of communication applications. The low Q-Factor of the conventionally tethered resonator is attributed to the high anchor loss. Moreover, a significant spurious mode close to the resonant peak is also observed which is undesirable from a spectral purity perspective.

[0044] On the other hand, analyzing the frequency response of the resonator with asymmetric PnC tethering 200 yielded an overall Q-factor of 3482, which is a significant improvement over its conventionally tethered counterpart. The obtained value of the Q-factor is much less than the value predicted by the simulations because the Q-factor is no longer limited by anchor loss but by other mechanisms such as interfacial dissipation. The asymmetric PnC tethering 200 have essentially eliminated the energy lost through the support tethers raising the overall Q-factor of the resonator. It can also be seen that these tethering not only improve the Q-factor but also the Insertion Loss of the resonator.

[0045] The foregoing description of the specific embodiments will so fully reveal the general nature of the embodiments herein that others can, by applying current knowledge, readily modify and/or adapt for various applications such specific embodiments without departing from the generic concept, and, therefore, such adaptations and modifications should and are intended to be comprehended within the meaning and range of equivalents of the disclosed embodiments. It is to be understood that the phraseology or terminology employed herein is for the purpose of description and not of limitation. Therefore, while the embodiments herein have been described in terms of preferred embodiments, those skilled in the art will recognize that the embodiments herein can be practiced with modification within the spirit and scope of the embodiments as described herein.