Altering and Enhancing Resonator Performances Using Free to Fixed Boundary Ratio (FFBR) Topology

Abstract

A resonator and/or transducer comprising at least one deflectable membrane, a fixed substrate, and at least one cavity defined between the at least one deflectable membrane and the fixed substrate. A Free to Fixed Boundary Ratio (FFBR) of the deflectable membrane is selected to optimize a characteristic of the resonator and/or transducer, such as resonant frequency, displacement, operating voltage, electromechanical coupling coefficient, or mass sensitivity.

Claims

1. A method comprising: determining a Free to Fixed Boundary Ratio (FFBR) of a reference device; determining a reference characteristic of the reference device; comparing the reference characteristic to a target characteristic; and fabricating a modified device that has a different FFBR than the FFBR of the reference device; wherein the FFBR of the modified device is selected to provide a modified characteristic of the modified device that is closer to the target characteristic than the reference characteristic is to the target characteristic; wherein the reference device and the modified device each have at least one deflectable membrane, a fixed substrate, and at least one cavity defined between the at least one deflectable membrane and the fixed substrate; and wherein the reference device and the modified device each comprise at least one of: a resonator and a transducer.

2. The method according to claim 1, wherein the reference device and the modified device each comprise an electromechanical resonator.

3. The method according to claim 1, wherein the reference device and the modified device each comprise at least one of: a Capacitive Micromachined Ultrasonic Transducer (CMUT); a Multiple Moving Membrane Capacitive Micromachined Ultrasonic Transducer (M3-CMUT); a Piezoelectric Micromachined Ultrasonic Transducer (PMUT), a Piezoelectric resonator, a Capacitive resonator, a Microelectromechanical systems (MEMS) piezoelectric ultrasonic transducer, a MEMS sensor, a MEMS transducer, a Mass Resonator Sensor, a MEMS Gas Sensor, a Capacitive-Based Gas Sensor, and a MEMS Resonator.

4. The method according to claim 1, wherein the reference device and the modified device each comprise a Capacitive Micromachined Ultrasonic Transducer (CMUT).

5. The method according to claim 1, wherein the reference characteristic, the target characteristic, and the modified characteristic each comprise a resonant frequency.

6. The method according to claim 1, wherein the reference characteristic, the target characteristic, and the modified characteristic each comprise a magnitude of displacement of the at least one deflectable membrane.

7. The method according to claim 1, wherein the reference characteristic, the target characteristic, and the modified characteristic each comprise a degree of sensitivity.

8. The method according to claim 1, wherein the reference characteristic, the target characteristic, and the modified characteristic each comprise an operating voltage.

9. The method according to claim 1, wherein the reference characteristic, the target characteristic, and the modified characteristic each comprise a surface area of the at least one deflectable membrane.

10. The method according to claim 1, wherein the reference characteristic, the target characteristic, and the modified characteristic each comprise a mass tolerance.

11. The method according to claim 1, wherein the reference characteristic, the target characteristic, and the modified characteristic each comprise a mass sensitivity.

12. The method according to claim 1, wherein the reference characteristic, the target characteristic, and the modified characteristic each comprise an electromechanical coupling coefficient.

13. The method according to claim 1, wherein the FFBR of the modified device is selected to provide the modified characteristic that is closer to the target characteristic, while maintaining a second characteristic of the modified device within a target range relative to a second reference characteristic of the reference device.

14. The method according to claim 13, wherein the second characteristic of the modified device and the second reference characteristic of the reference device are substantially the same.

15. The method according to claim 13, wherein the second characteristic and the second reference characteristic each comprise at least one of: a shape of the at least one deflectable membrane; a surface area of the at least one deflectable membrane; a perimeter length of the at least one deflectable membrane; a width of the at least one deflectable membrane; a length of the at least one deflectable membrane; a thickness of the at least one deflectable membrane; a resonant frequency; a magnitude of displacement of the at least one deflectable membrane; a shape of the at least one deflectable membrane; a degree of sensitivity; an operating voltage; a mass tolerance; and a mass sensitivity.

16. A device comprising: at least one deflectable membrane; a fixed substrate; and at least one cavity defined between the at least one deflectable membrane and the fixed substrate; wherein a Free to Fixed Boundary Ratio (FFBR) of the at least one membrane is selected to optimize a characteristic of the device; and wherein the device comprises at least one of: a resonator and a transducer.

17. The device according to claim 16, wherein the device comprises an electromechanical resonator.

18. The device according to claim 16, wherein the device comprises at least one of: a Capacitive Micromachined Ultrasonic Transducer (CMUT); a Multiple Moving Membrane Capacitive Micromachined Ultrasonic Transducer (M3-CMUT); a Piezoelectric Micromachined Ultrasonic Transducer (PMUT), a Piezoelectric resonator, a Capacitive resonator, a Microelectromechanical systems (MEMS) piezoelectric ultrasonic transducer, a MEMS sensor, a MEMS transducer, a Mass Resonator Sensor, a MEMS Gas Sensor, a Capacitive-Based Gas Sensor, and a MEMS Resonator.

19. The device according to claim 16, wherein the characteristic comprises at least one of: a resonant frequency; a magnitude of displacement of the at least one deflectable membrane; a degree of sensitivity; an operating voltage; a surface area of the at least one deflectable membrane; a mass tolerance; a mass sensitivity; and an electromechanical coupling coefficient.

20. The device according to claim 16, further comprising a sensing material that is attached to the at least one deflectable membrane.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Further aspects and advantages of the invention will appear from the following description taken together with the accompanying drawings, in which:

[0089] FIG. 1 is a schematic side view of a fully clamped conventional circular CMUT (as a transducer);

[0090] FIG. 2 is a schematic side view of a fully clamped conventional circular CMUT (as a gas sensor);

[0091] FIG. 3 is a schematic top view of the example structures utilizing novel FFBR, (a) conventional circular CMUT, which is fully clamped at the surrounding, (b) proposed Greek Bridge clamped at the arms' width and (c) proposed Greek Cross clamped at the arms' width;

[0092] FIG. 4 shows utilizing the proposed FFBR approach in developed Greek Bridge structure designed and analyzed in COMSOL Multiphysics;

[0093] FIG. 5 shows frequency (MHz) vs FFBR for Greek Bridge structure. As examples of FFBR, FFBR parameter is investigated for values as 1.2, 1.5, 2.2, 3.6 and 7.9 for a Greek Bridge with 120 m total length, 50 m radius, 750 nm cavity height, 1.5 m thickness when arm's width is altered from 20 m to 100 m range. In this example, the structure is biased with 20 V DC;

[0094] FIG. 6 shows utilizing the proposed free to fixed boundary ratio in proposed Greek Cross geometry designed in COMSOL Multiphysics;

[0095] FIG. 7 shows frequency (MHz) vs FFBR for Greek Cross structure. FFBR values 0.7, 0.9, 1.6 and 4 are investigated as FFBR examples for a Greek Cross with 120 m total length, 50 m radius, 750 nm cavity height, 1.5 m thickness when arm's width is altered within 20 m and 100 m range. The structure is biased with 20 V DC;

[0096] FIG. 8 shows utilizing the proposed FFBR in circular geometry designed in COMSOL Multiphysics. As an example, the structure is symmetrically clamped at two positions, however, the topology can be symmetrically or asymmetrically clamped at any number of the clamped edges;

[0097] FIG. 9 shows frequency (MHz) vs FFBR for circular structure where it is symmetrically clamped at two positions as an example of utilizing FFBR. FFBR values 0, 0.5, 1, 2 and 5 are investigated as examples for a circular structure with 120 m diameter, 750 nm cavity height and 1.5 m thickness. The structure is biased with 20 V DC;

[0098] FIG. 10 shows utilizing the FFBR in circular geometry designed in COMSOL Multiphysics. The resonator can be symmetrically or asymmetrically clamped. As an example, the structure is symmetrically clamped at four positions;

[0099] FIG. 11 shows frequency (MHz) vs FFBR for circular structure where it is symmetrically clamped at four positions. FFBR values 0, 0.5, 1, 2 and 5 for a circular structure with 120 m diameter, 750 nm cavity height and 1.5 m thickness. The structure is biased with 20 V DC;

[0100] FIG. 12 shows mass sensitivity (kHz/pg) vs FFBR for Greek Bridge, Greek Cross and circular structure with 120 m total length or diameter. The circular structures are symmetrically clamped at two and four positions. Cavity height, thickness and applied DC voltage are considered 750 nm, 1.5 m and 20 V, respectively;

[0101] FIG. 13 shows magnitude of frequency shift versus change in FFBR for circular structures clamped at two and four positions, Greek Bridge and Greek Cross. Total length or diameter, thickness, cavity height and DC voltage are 120 m, 1.5 m, 750 nm and 20V, respectively; and

[0102] FIG. 14 shows designed and fabricated (a) conventional CMUT, (b) Greek Bridge and (c) Greek Cross, which utilizes FFBR approach.

DETAILED DESCRIPTION OF THE DRAWINGS

[0103] A schematic top view of the proposed devices 10, which present the FFBR approach, is illustrated in FIG. 3. Conventional clamped CMUT (a), proposed Greek Bridge (b) and Greek Cross (c) are depicted in FIG. 3 where fixed boundaries are shown in solid and dashed lines define free boundaries of the proposed topologies. In FIG. 3, the total length is represented by numeral 22, the arm's width is represented by numeral 24, and the radius is represented by numeral 26.

[0104] The FFBR parameter is proposed and analyzed for several developed devices, utilizing COMSOL Multiphysics software for Finite Element Analysis (FEA). Greek Bridge geometry is proposed and built in COMSOL Multiphysics where proposed FFBR approach is utilized, as illustrated in FIG. 4. In this structure total length and radius of the circular geometry in the middle are constant at 120 m and 50 m, respectively. The FFBR parameter for Greek Bridge is considered as an example 1.2 (e), 1.5 (d), 2.2 (c), 3.6 (b) and 7.9 (a) when width of the structure is altered between 20 m and 100 m. Parameters of the analyzed Greek Bridge are shown in Table 1. The fixed boundaries are represented by numeral 28.

TABLE-US-00001 TABLE 1 Design parameters of the proposed and simulated Greek Bridge structure. Parameter Dimension Total length 120 m Radius 50 m Thickness 1.5 m Cavity Height 750 nm Arms' Width 20, 40, 60, 80, 100 m DC Voltage 20 V

[0105] FIG. 5 depicts a plot of the resonant frequency and displacement against the FFBR parameter values for the proposed Greek Bridge structure. This shows the FFBR plays a significant role in determining the operating frequency of the design. As illustrated in FIG. 5, increasing FFBR from 1.2 to 7.9 as an example, can decrease the resonant frequency by more than 90%. According to Equation (1), higher masses contribute to lower resonant frequencies. However, utilizing the FFBR in the design criteria as illustrated in FIG. 5, shows that although mass is higher for lower FFBR values, resonant frequency is also increased in the Greek Bridge structure. In addition, displacement of the structure increases for higher FFBRs meaning that this approach increases the design degree of freedom, which results in higher displacement. This can further reduce the required operating DC voltage of the device. The obtained results based on utilization of FFBR indicate that this parameter can significantly affect the resonant frequency and therefore improves the device performance.

[0106] To investigate the concept of FFBR, Greek Cross structure is also proposed with multiple FFBRs, as shown in FIG. 6. This structure can benefit from multiple symmetrical or asymmetrical clamped areas, which increases the robustness of the structure.

[0107] In this analysis total length and radius of the circular geometry in the middle are constant at 120 m and 50 m, respectively. The novel FFBR parameter is considered in designing Greek Cross structure as 0.7 (d), 0.9 (c), 1.6 (b) and 4 (a) as examples of FFBR when width of the structure is altered between 20 m and 100 m. Parameters of the analyzed Greek Cross are shown in Table 2.

TABLE-US-00002 TABLE 2 Design parameters of the proposed and simulated Greek Cross structure as an example of a topology which utilizes FFBR. Parameter Dimension Total length 120 m Radius 50 m Thickness 1.5 m Cavity Height 750 nm Arms' Width 20, 40, 60, 70 m DC Voltage 20 V

[0108] Resonant frequency versus the FFBR parameter, is illustrated in FIG. 6 for developed Greek Cross structure where FFBR is altered between 0.7 (d), 0.9 (c), 1.6 (b), and 4 (a), as examples of FFBR and the proposed topology which utilizes FFBR parameter. As shown in FIG. 7, this parameter is a critical design factor due to its significant effect on the resonant frequency. This analysis shows that resonant frequency is dropped more than 30% for Greek Cross when the FFBR is increased to 4. Similar to the Greek Bridge, FFBR also adds to the design degree of freedom, hence displacement increases for higher FFBR values. This ratio can also be utilized as a control factor on operating DC voltage of the device for any application.

[0109] FFBR is also shown as a critical design parameter in circular structures. As illustrated in FIG. 8, circular geometries with multiple FFBRs are built and simulated in COMSOL Multiphysics. Fixed boundaries are considered symmetrically as an example at two positions across the structure with FFBR ratios such as values of 0.5 (d), 1 (c), 2 (b), and 5 (a). Design parameters of the structure are illustrated below in Table 3.

TABLE-US-00003 TABLE 3 Design parameters of the simulated circular geometry. Parameter Dimension Radius 60 m Thickness 1.5 m Cavity Height 750 nm DC Voltage 20 V

[0110] As depicted in FIG. 9, FFBR significantly affects the resonant frequency of the circular geometry, which is clamped at two symmetric positions. The plot shows that although mass and other conventional parameters of the structure remain constant, increasing FFBR from zero (conventional fully clamped circular structure) to five decreases the resonant frequency by 200%. Furthermore, displacement of this structure is significantly increased due to the utilized FFBR approach, which can be employed to improve performance of the device and decrease the required operating DC voltage.

[0111] This investigation is further followed by altering the configuration of the clamped area in the above circular geometry, as shown in FIG. 10. The same FFBR, namely 0.5 (d), 1 (c), 2 (b), and 5 (a), is utilized where boundaries are symmetrically fixed at four positions, illustrated in FIG. 10.

[0112] Utilizing FEA shown in FIG. 11, indicates that resonant frequency is also affected by position of the clamped areas. As illustrated in FIG. 11, it is affected by 44% when FFBR parameter is altered from zero to five. Furthermore, the new configuration of the clamping area reduced the change in the structure's displacement from more than 40 nm where it was clamped at two positions, to 6 nm where clamping is doubled for the identical FFBRs.

[0113] Above analysis indicates that the FFBR and clamping area configuration can be utilized in design process due to the substantial effect on resonant frequency and displacement. This finding shows that FFBR can significantly contribute to sensitivity and performance enhancement of the device. As an example, utilizing FFBR in mass sensing applications provides a critical tool to determine the region of opportunity that provides maximum frequency shift for different areas of the device.

[0114] Mass sensitivity versus FFBR is shown in FIG. 12 for devices such as circular geometry clamped at two and four positions, Greek Cross and Greek Bridge structures. In this analysis, 0.027 g mass is considered per unit area when conducting FEA analysis. Thickness, cavity height, diameter or total length are considered 1.5 m, 750 nm, 120 m as an example when 20 V DC is applied to the structures. FIG. 12 depicts that utilizing the FFBR approach provides valuable information where optimization of important factors such as mass sensitivity is required.

[0115] Magnitude of frequency shift versus change in FFBR is illustrated in FIG. 13 for structures including clamped circular at two and four positions, Greek Bridge and Greek Cross. The slope of this graph indicates the sensitivity of resonant frequency to change in FFBR parameter for proposed devices as examples of devices which utilizes FFBR approach.

[0116] The FFBR factor was utilized to propose and fabricate proof-of-concept Greek Cross (c) and Greek Bridge (b) structures in addition to the conventional clamped circular structure (a), as shown in FIG. 14. Any technique such as sacrificial and wafer bonding can be utilized for fabrication, however, PolyMUMPs sacrificial technique was used at this step as a commercially available and low-cost microfabrication technique. The fabrication process may or may not use holes on the structures and may consist of different fabrication steps and processes.

[0117] A top view of the designed and fabricated conventional CMUT which is fully clamped at the surrounding, is shown in FIG. 14(a). Greek Bridge shown in (b) is designed and fabricated utilizing the proposed FFBR approach to obtain higher sensitivity. Furthermore, Greek Cross shown in (c), which benefits from a significantly lower mass compared to conventional CMUT with similar dimensions, is designed and fabricated as a more robust structure compared to Greek Bridge. In addition, lower FFBR in Greek Bridge and Greek Cross in comparison with conventional CMUT, provide more flexibility as also analyzed in COMSOL Multiphysics to improve displacement.

[0118] It will be understood that, although various features of the invention have been described with respect to one or another of the embodiments of the invention, the various features and embodiments of the invention may be combined or used in conjunction with other features and embodiments of the invention as described and illustrated herein.

[0119] The present invention can be used for designing and fabricating resonators and/or transducers, such as CMUTs, having desired characteristics, such as resonant frequency, mass sensitivity, displacement, electromechanical coupling coefficient, robustness, surface area, and voltage. The invention is not limited to the particular structures and topologies shown and described, which are provided as examples only. Rather, any suitable topology, shape and size of the membrane(s) could be used, with the FFBR approach being used to optimize one or more characteristics of the devices. The FFBR approach may be used, for example, to modify a reference device design to increase the surface area without altering the resonant frequency, or to increase the mass sensitivity while maintaining the size and shape of the top membrane(s). The invention is not limited to the particular voltages used in the examples. Rather, any suitable voltage could be used.

[0120] The invention is not limited to any particular materials or techniques for fabricating the resonators and/or transducers and/or CMUTs. Any suitable materials and techniques known to a person skilled in the art could be employed.

[0121] The invention is not limited to any particular uses of the resonators and/or transducers and/or CMUTs. Rather, the resonators/transducers/CMUTs could be designed and used for any suitable purpose, such as for sensing analytes in a gas or liquid, for ultrasonic imaging, or for other uses.

[0122] Although the invention has been described in the preferred embodiments as pertaining to CMUTs, the invention could also be used with other types of resonators and/or transducers as well. That is, the FFBR approach could be used to optimize the performance and/or characteristics of any resonator and/or transducer having a deflectable membrane/plate, a fixed substrate, and a cavity defined therebetween. The invention could be used, for example, with Piezoelectric Micromachined Ultrasonic Transducers (PMUTs), Piezoelectric resonators, Capacitive resonators, Microelectromechanical systems (MEMS) piezoelectric ultrasonic transducers, MEMS sensors, MEMS transducers, Mass Resonator Sensors, MEMS Gas Sensors, Capacitive-Based Gas Sensors, and/or MEMS Resonators.

[0123] In some embodiments of the invention, the position of the fixed portion or portions of the top membrane/plate can be adjusted, in addition to or in place of adjusting the FFBR, in order to alter various characteristics of the resonators, such as resonant frequency, displacement, operating voltage, mass sensitivity, and mass tolerance.

[0124] Although this disclosure has described and illustrated certain preferred embodiments of the invention, it is to be understood that the invention is not restricted to these particular embodiments. Rather, the invention includes all embodiments which are functional, electrical, electromagnetic, or mechanical equivalents of the specific embodiments and features that have been described and illustrated herein.