CHAPTER 4 CHARACTERIZATION OF MICROMECHANICAL RESONATOR
4.2 C HARACTERIZATION OF MICROMECHANICAL RESONATOR
4.2.1 Diamond and CNT incorporation
According to the pervious test, the dimensions of nano particles can be summarized and shown in Table 4.1. The nano diamond particles and CNTs incorporation of the nanocomposite can be verified by the SEM photos taken at the top surface of plated films.
Basically, the nanocomposite synthesis is to electroplate the Ni matrix in the solution with well-dispersed nano particles. The bath with an aerating system could ensure that the particles are uniformly attached to the as-plated Ni film and then engulfed into a metal matrix during the plating processing. In the previous investigation, the nano diamond particles were found to be incorporated randomly in the matrix [40]. The SEM shown in Figure 4.4(a) image also shows the top surface of nanocomposite film where nano diamond particles are well distributed in the Ni-diamond nanocomposite film. On the other hand, the CNTs incorporation is shown in Figure 4.4(b). At the top surface, CNTs partly engulf into Ni film and reveal a random distribution. By the way, no void is observed in the SEM photos.
The amount of nano particle incorporated in the Ni film can be characterized by the elemental analyzer (Heraeus, varioIII-NCH). From the detected carbon concentration, it is found that the volume percentages of incorporated nano-diamond or CNTs are proportion to the nano particle concentrations in the Ni plating bath, as shown in Figure 4.5. With nano diamond particle concentration of 2 g/L, the volume percentage is 0.44%. The volume percentage is 13.9% with CNTs concentration of 1 g/L.
and Ni-CNT resonators (Figure 4.6(b)) electroplated at 0.8 mA/cm2. It indicates that the springs still have a little downward warpage but they have been fully suspended to support the whole micro-resonator structures.
Figure 4.7 shows the frequency response of the comb resonators made of Ni and Ni-diamond, and Ni-CNT indicating the related resonant frequencies are 22.55, 25.75, and 24.45 kHz, respectively. About 14% and 8% resonant frequency enhancement can be realized in the Ni-diamond and Ni-CNT nanocomposite micro-resonators where the composite film is electroplated in a Ni electrolyte with 2 g/L nano-diamond and 0.028 g/L CNTs, respectively.
Meanwhile, the measured response also shows the nanocomposite comb resonators have higher quality factors than that of Ni at atmospheric pressure. The measured quality factors of Ni, Ni-diamond, and Ni-CNT comb resonators are 124, 201, and 217, respectively. The measured dimensions and resonant frequencies are summarized in Table 4.2.
According to rule of mixture [61, 62], the Young’s modulus of two-phase composite can be estimated by the upper and lower bound expressions as follows, respectively,
D secondary phase, respectively. Based on the measured Young’s modulus, the mechanical property of the Ni nanocomposite film with the volume ratio of 0.46% nano-diamonds can only have 2.3% and 0.3% Young’s modulus enhancements estimated by the upper and lower bounds, respectively. Thus, according to the upper bound of the estimated Young’s modulus, it indicates only 1.5% resonant frequency increase can be achieved. In comparison of the measured resonant frequencies of the comb resonators, nano diamond incorporation can bring more enhancement than that estimated by the upper bound. The frequency enhancement can be
attributed to two possible factors which can result in the Young’s modulus increase of the nanocomposite film. According to the previous study [63], it was found that the more compressive-stressed film will come with a higher Young’s modulus. Since the nano diamond incorporation would cause Ni film with more compressive stress [36], it may cause the increase of Young’s modulus of Ni part of nanocomposite so that the Young’s modulus of the nanocomposite can be enhanced with a value larger than the one estimated by the rule of mixture.
Figure 4.8 shows the frequency-response spectrum of the as-fabricated Ni and Ni-CNT nanocomposite comb resonators. The resonant frequency of the SDS treated Ni-CNT nanocomposite resonator is 30.65 kHz which is higher than the one made of pure Ni and the H2SO4/H2O2 mixture treated Ni-CNT nanocomposite which are 29.35 kHz and 30.35 kHz respectively. The measured dimensions and resonant frequencies are summarized in Table 4.3.
Figure 4.9 shows SEM micrographs of as-fabricated Ni-CNT comb resonators where the CNTs are treated by H2SO4/H2O2 and SDS solutions, respectively. In addition, the Energy Dispersive Spectroscopy (EDS) analyses on the resonator springs verify the incorporation of CNTs and further indicate that the embedded CNTs in the SDS treated nancomposite is higher than that treated by H2SO4/H2O2 solution because SDS treated nanocomposite has a higher carbon intensity than that of the nanocomposite treated by H2SO4/H2O2.
4.2.3 Performance measurement of clamped-clamped beam resonators
Figure 4.10(a) and (b) show the SEM images for Ni and Ni-CNT CC-beams, respectively.
The measured thickness of structure and sacrificial layer are 2.27 μm and 531 nm for Ni
Figure 4.11 presents the frequency responses of Ni, Ni-diamond, and Ni-CNT CC-beam resonators at 0.2 mTorr. The measured data is summarized in Table 4.4. It shows resonant frequencies (f0) of 498.75, 725.47, and 634.72 kHz for the Ni and Ni-CNT CC-beam resonators, respectively, designed with the same dimensions. About 45% and 27% frequency enhancement can be realized and attributed to the incorporation of nano diamond particles and CNTs. In addition, it can be found that the electrical sensing results are different from that of the LDV measurement. This frequency reduction is caused by the introduction of electrical stiffness (ke) related to the interaction of the electric field between the resonator and drive electrode, and hence, the effect would lower the effective spring stiffness as follows [64]:
r where kr and mr are the mechanical spring constant and mass of the resonator, respectively.
From (4.4), the electrical spring constants of the Ni and Ni-CNT resonators are calculated as 118.3, 113.2, 140.8 N/m, so the calculated resonant frequencies of the resonators applied with Vbias are 504, 701, and 639 kHz, which are close to the aforementioned measurements. The measured Q values of the Ni, Ni-diamond, and Ni-CNT CC-beam resonators are 781, 612, and 760, respectively, indicating that nano particle incorporations did not cause the Q degradation.
According to the previous research work [23], the electroplated Ni CC-beam resonator indicated the quality factor in 576. This level is lower than poly-Si CC-beam resonators [10].
The anchor loss is to dominate the Q’s of poly-Si CC-beam resonator and it might also applicable in the Ni-based case, since the attachment of Ni resonators to the substrate at their anchors is not as sturdy as the polysilicon counterparts. The anchor loss becomes more severe in the Ni-based case. Poor adhesion caused by the stress of the plated film between the structure and the substrate could result in a weak anchor that ultimately dissipates more energy during vibration. Nevertheless, it is difficult to make a solid conclusion regarding loss
mechanisms based on Ni-based CC-beam resonator measurements and further Q investigation related to material quality is underway by fabricating free-free-beam-typed resonators.
4.2.4 Temperature coefficient of frequency
Resonant frequency variation over temperature is defined as temperature coefficient of frequency (TCF) which is expressed as:
T
T and f0 are the operational temperature and resonant frequency. The frequency shift with changing the temperature is shown in Figure 4.12. The slopes of curves are the TCFs. For Ni, Ni-diamond, and Ni-CNT CC-beam resonators, TCFs are -5.49×10-3, -3.47×10-3, and -4.58×
10-3 /°C respectively. It is found that Ni-diamond and Ni-CNT resonator has lower TCF than Ni one.
Actually, the value of TCF depends on thermal stress, temperature coefficient of Young’s modulus, and thermal expansion coefficient. For the CC-beam design, the TCF can be expressed in terms of these parameters [65],
2 β and σ are the mode constant and axial stress of CC-beam. TCE and α are the temperature coefficient of Young’s modulus and thermal expansion coefficient of material. TCE of Ni was investigated about -7.65×10-4 /°C [66]. Thermal expansion coefficients of Ni, Ni-diamond, and Ni-CNT are 2.3×10-5, 5×10-5, and 3.5×10-5, respectively [38, 40]. Comparing with our
Ni-based structure. The compressive stress would lower the resonant frequency.
4.2.5 Power handling capability of CC-beam resonator
Through coupling, micromechanical resonators can serve as filters [67-69]. For the demand of future systems, increasing power levels of filter is the simplest way to boost system range and capability [70]. Therefore, it is important for micromechanical resonator with high power handling capability. For a capacitivly-transduced resonators, the maximum power handling is defined by the maximum output current Iomax and motional impedance Rm,
2
max max
o o m
P =I ×R
(4.7) By manuplating the above equation, the theoretical maximum power handling can be expressed by 1st and 3rd order equivalent stiffness (k1 and k3) of the resonator [71, 72]: ω0 and Q radian resonant frequency and quality factor of resonator, respectively. For capacitivly-transduced resonators with high dc-bias voltages, the 1st and 3rd order equivalent stiffness can be approximated as
(
f) ( )
m y where ke3 denotes the 3rd-order electrical stiffness. We can find that for two resonators with similar dimension, quality factor, and 3rd-order electrical stiffness, the resonator who has higher mechanical stiffness kre and resonant frequency would get better power handling capabilities.The equivalent mass of CC-beam is expressed in Eq (2.8) and the resonant frequency (or
radian resonant frequency) is proportional to square root of Young’s modulus to density ratio (E/ρ).
E/ρ
0∝
ω (4.11)
For two resonators in the same dimension, we note that the equivalent stiffness kre(y) is proportional to the resonant frequency (f0) square and the material density, i.e.,
( )y k ( )y E k1 = 1e ∝
(4.12) Ni-diamond and Ni-CNT have higher Young’s modulus and lower density. According to Eq.
(4.8), (4.11), and (4.12), both higher Young’s modulus and lower density are helpful to increase the maximum power handling capabilities of CC-beam resonator.
(a)
(b)
Figure 4.1 The in plane motion analysis of comb resonator by MEMS Motion Analyzer (MMA). (a) The setup for displacement characterization of comb resonator. (b) The motion images captured by MMA.
Figure 4.2 The out of plane motion analysis of CC-beam resonator by Laser Doppler Vibrometer (LDV).
(a)
(b)
Figure 4.4 SEM images of top surface of (a) Ni-diamond and (b) Ni-CNT nanocomposites.
(a)
(b)
Figure 4.5 Volume percentage of nano particle in nanocomposite films: (a) Ni-diamond and (b) Ni-CNT.
(a)
(b)
(c)
Figure 4.6 The SEM photos of (a) Ni, (b) Ni-diamond, and (c) Ni-CNT comb resonators plated at 0.8 mA/cm2.
(a)
(b)
(a)
(b)
(c)
Figure 4.8 Frequency responses for (a) Ni, (b) Ni-CNT (H2SO4/H2O2), and (c) Ni-CNT (SDS) comb resonators.
Figure 4.9 SEM photos and EDS analysis results of Ni-CNT comb resonators with CNTs treated by H2SO4/H2O2 and SDS water solution.
(a)
(b)
(c)
Figure 4.10 The SEM photos of (a) Ni, (b) Ni-diamond, and (c) Ni-CNT CC-beam resonators plated at 0.8 mA/cm2.
(a)
(b)
(c)
Figure 4.12 The resonant frequency shift versus temperature.
Table 4.1 Dimensions of nano diamond particles and carbon nanotubes.
Nano diamond particles Carbon Nanotubes (CNTs)
Average diameter, 125 nm Inner diameter, 5-10 nm Outer diameter, 10-20 nm
Length, 0.5-10 μm
Table 4.2 Measured dimensions of Ni, Ni-diamond, and Ni-CNT comb resonators. Motional capacitance, Cx 2.13×10-17 1.75×10-17 2.08×10-17 F Static capacitance, Co 2.35×10-14 2.51×10-14 2.47×10-14 F
Quality factor, Q @ Air 124 201 217 －
Optical measured f0 22.6 25.8 24.5 kHz
Table 4.3 Measured dimensions of Ni and Ni-CNT comb resonators with different dispersion Motional inductance, Lx 2078643 1846808 1874790 H Motional capacitance, Cx 1.42×10-17 1.48×10-17 1.44×10-17 F Static capacitance, Co 2.63×10-14 2.71×10-14 2.67×10-14 F
Quality factor, Q @ Air 190 198 221 －
Table 4.4 Measured dimensions of Ni, Ni-diamond, and Ni-CNT CC-beam resonators.
Effective mass, mr 2.39×10-11 2.47×10-11 2.12×10-11 kg
Motional resistance, Rx 36.5 32.1 32.3 kΩ
Motional inductance, Lx 7.3 4.0 5.1 H
Motional capacitance, Cx 9.02×10-15 1.04×10-14 8.54×10-15 F Static capacitance, Co 2.26×10-14 2.26×10-14 2.26×10-14 F
Quality factor, Q @ 0.2mTorr 781 612 760 －
Optical measured f0 619.4 780.3 760.9 kHz
Electrical measured f0 498.7 725.5 634.7 kHz
Chapter 5 Conclusion
5.1 Summary
In summary, an electroplating process has been successfully demonstrated for Ni, Ni-diamond, and Ni-CNT nanocomposite micromechanical resonator fabrication, including comb and CC-beam. The entire processing temperatures are lower than 90°C that makes this process integral with CMOS process. The incorporation of nano diamond particles and CNTs into the Ni matrix can greatly result in Young’s modulus enhancements in the Ni matrix and increase the resonant frequency of resonator. The frequency enhancement has been verified by the frequency characteristics of resonator. No Q degradation is observed with the nano particle incorporation.
Two important process issues are investigated. First are the dispersions of nano diamond particles and CNTs in electrolyte. A well dispersion of nano particles is helpful to obtain a uniform nanocomposite. We use the commercial nano diamond particles which are pretreated and show good dispersion in electrolyte. On the other hand, CNTs are agglomerated. Before added into electrolyte, they need dispersion treatment. Two CNTs dispersion treatments, H2SO4/H2O2 and SDS water solution, are adopted. According to the experimental results, SDS treated CNTs show better dispersion and higher incorporation than H2SO4/H2O2 treated one that results in higher frequency enhancement of comb resonator. Secondly, the stress gradient of electroplated Ni-based films has been solved. It is found that the formation of larger Ni grains and smaller grain size variance in the electroplated Ni-based films is the key factor to
cantilever beams plated with 0.8 mA/cm2 reveal the stress gradient in -3.23, -5.65, and -4.75 MPa/μm, respectively. The structural warpage of as-fabricated MEMS device can, therefore, be effectively inhibited using lower plating current density (0.8 mA/cm2) to make the device itself fully function.
Two micromechanical resonator designs, comb and CC-beam, are adopted and made by low stress gradient process (current density: 0.8 mA/cm2) in this dissertation. About 14% and 8% resonant frequency enhancement has been found in the nanocomposite comb resonator made of the Ni-diamond and Ni-CNT nanocomposite plated with the current density of 0.8 mA/cm2 in the bath containing 2 g/L nano-diamond and 0.028 g/L CNTs. The same electroplating process has been demonstrated for CC-beam resonator fabrication. By employing the SDS treatment on the surface of CNTs (1 g/L), about 27% resonant frequency increase of Ni-based CC-beam can be realized via the incorporation of CNTs. On the other hand, the nano diamond incorporation (2 g/L) would cause 45% frequency enhancement of CC-beam resonator. According to the frequency response, no Q degradation is observed due to the nano particle incorporation.
5.2 Future work
In this dissertation, we have demonstrated the feasibility of Ni-diamond and Ni-CNT nanocomposites for micromechanical resonator applications. Actually, there are some technical and design issues can be further improved.
Dispersion treatment of nano particle:
The surface treatment of CNTs should be further improved because there are some drawbacks in both treatments used in this dissertation. The drawbacks of SDS: the electrolyte with high SDS concentration would cause foam easily while the electrolyte is pumping with aerating system. This drawback can be eliminated by using stirring system to replace aerating
system. On the other hand, SDS works as a wetting agent which would reduce the Young’s modulus of plated Ni film. The drawbacks of H2SO4/H2O2: it is hard to remove the H2SO4 completely. The residual H2SO4 would lower down the pH level of electrolyte while the treated CNTS is added in it. Extra alkali solution, such as NH4OH, is necessary for modulating the pH level back to usual. The H2SO4 and NH4OH might cause other chemical compositions and make the electrolyte unstable.
Open area effect:
The width of comb spring/folded beam is 5μm. The width of CC-beam is 25 μm. With the same nano particle concentration, the nanocomposite for CC-beam resonator always reveals higher frequency enhance than comb resonator. It seems that nanoparticle incorporation would be diminished while the open area reduces. It needs to be verified further.
High Q for nanocomposite resonator:
The Ni nanocomposite had been demonstrated in comb and CC-beam resonator but both of them don’t achieve high Q (>1,000). The Q of Ni nanocomposite resonator needs to be verified by the aggressive resonator design, such as free-free beam [11] and disk [13]. Both of them are proposed to achieve high Q.
Reference
[1] C.S. Lam, “A review of the recent development of MEMS and crystal oscillators and their impacts on the frequency control products industry”, Ultrasonics Symposium, San Jose, CA, pp.694-704, 2-5 Nov., 2008.
[2] J. R. Vig, “Quartz crystal resonators and oscillators for frequency control and timing applications-A tutorial”, R&D Technical Report SLCETTR-88-1, AD-A284995, Aug., 1994.
[3] H. C. Nathanson, W. E. Newell, R. A. Wickstrom, J. R. Davis, “The resonant gate transistor”, IEEE Transactions on Electron Devices, 14 (3), pp.117-133, 1967.
[4] W.-T. Hsu and M. Pai, "The new heart beat of electronics-silicon MEMS oscillators", Proc. Electron. Compon. Technol. Conf., pp.1895-1899, 2007.
[5] http://www.discera.com [6] http://www.SiTime.com
[7] K. Wang, “Micromechanical resonator and filter for communications applications”, Ph.D.
Dissertation, Dept. of EECS, University of Michigan, Ann Arbor, 1999.
[8] S. A. Chandorkar, M. Agarwal, R. Melamud, R. N. Candler, K. E. Goodson and T. W.
Kenny, "Limits of quality factor in bulk-mode micromechanical resonators", Proc. IEEE MEMS, Tucson, AZ, pp.74-77, Jan., 2008.
[9] C. T.-C. Nguyen and R. T. Howe, "An integrated CMOS micromechanical resonator high-Q oscillator", IEEE J. Solid-State Circuits, 34, pp.440-455, 1999.
[10] F. D. Bannon III, J. R. Clark, and C. T.-C. Nguyen, “High frequency microelectromechanical IF filters”, Technical Digest, IEEE International Electron Devices Meeting, San Francisco, CA, pp.773-776, 8-11 Dec., 1996.
[11] K. Wang, A.-C. Wong, and C. T.-C. Nguyen, “VHF free-free beam high-Q
micromechanical resonators”, IEEE/ASME J. Microelectromech. Syst., 9 (3), pp.347-360, Sep., 2000.
[12] A. Olkhovets, S. Evoy, D. W. Carr, J. M. Parpia, and H. G. Craighead, “Actuation and internal friction of torsional nanomechanical silicon resonators”, J. Vac. Sci. Technol. B 18, pp.3549-3551, Nov., 2000.
[13] J. R. Clark , W.-T. Hsu , M. A. Abdelmoneum and C.T.-C. Nguyen "High-Q UHF micromechanical radial-contour mode disk resonators", J. Microelectromech. Syst., 14 (6), pp.1298-1310, Dec., 2005.
[14] C. T.-C. Nguyen, "MEMS technology for timing and frequency control", IEEE Trans.
Ultrason., Ferroelectr., Freq. Control, 54 (2), pp.251-270, Feb., 2007.
[15] M. Pandey, R. B. Reichenbach, A T Zehnder, A. Lal, and H. G. Craighead, “ Reducing anchor loss in MEMS resonators using mesa isolation”, IEEE J. Microelectromech.
Syst., 18 (4), pp.836-844, Aug., 2009.
[16] R. Lifshitz, and M. L.Roukes, “Thermoelastic damping in micro- and nanomechanical systems”, Phys. Rev. B, 61, pp.5600-5609, 2000.
[17] Y. Sun, D. Fang, and A.K. Soh, “Thermoelastic damping in micro-beam resonators”, International Journal of Solids and Structures, 43, pp.3213-3229, 2006.
[18] R. Nava, M. P. Vecchi, J. Romero and B. Fernandez, “Akhiezer damping and the thermal conductivity of pure and impure dielectrics”, Phys. Rev. B, 14, (2), pp.800-807, 1975.
[19] W.-L. Huang, Z. Ren, Y.-W. Lin, H.-Y. Chen, J. Lahann, and C. T.-C. Nguyen, “Fully monolithic CMOS nickel micromechanical resonator oscillator”, IEEE 21th International Conference on Micro Electro Mechanical Systems, Tucson, AZ, pp.10-13, 2008.
[20] S. E. Alper, K. M. Silay, and T. Akin, “A low-cost rate-grade nickel microgyroscope”,
15, pp.935-944, 2006.
[22] D. Girbau, L. Pradell, A. Lázaro, and A. Nebot, ”Electrothermally actuated RF MEMS switches suspended on a low-resistibity substrate”, J. Microelectromech. Syst., 16, pp.1061-1070, 2007.
[23] W.-L. Huang, Z. Ren, and C. T.-C. Nguyen, ”Nickel vibrating micromechanical disk resonator with solid dielectric capacitive-transducer gap”, IEEE International Frequency Control Symposium and Exposition, Miami, FL, pp.839-847, 2006.
[24] D. J. Vasquez and J. W. Judy, ”Flexure-based nanomagnetic actuators and their ultimate scaling limits”, IEEE 21th International Conference on Micro Electro Mechanical Systems, Tucson, AZ, pp.737-741, 2008.
[25] C. W. Chang and W. Hsu, ”Three-dimensional micro assembly of a hinged nickel micro device by magnetic lifting and micro resistance welding”, J. Micromech. Microeng., 19, 105026, 2009.
[26] S. A. Lee, J. R. Pinney, M. Bergsneider, and J. W. Judy, ”Magnetic microactuators for MEMS-enabled ventricular catheters for hydrocephalus”, the 3rd International IEEE-EMAS Conference on Neural Engineering, Kohala Coast, HI, pp.65-68, 2007.
[27] A. Cohen, G. Zhang, F. G. Tseng, U. Frodis, F. Mansfeld, and P. Will, ”EFAB rapid, low-cost desktop micromachining of high aspect ratio true 3-D MEMS”, IEEE 12th International Conference on Micro Electro Mechanical Systems, Orlando, FL,
pp.244-251, 1999.
[28] K. Kataoka, T. Itoh, T. Suga, and K. Inoue, ”Contact properties of Ni micro-springs for MEMS probe card”, The 50th IEEE Holm Conference on Electrical Contacts, Seattle, WA, pp.231-235, 2004.
[29] S. E. Alper, I. E. Ocak, and T. Akin, ”Ultrathick and high-aspect-ratio nickel microgyroscope using EFAB multilayer additive electroforming”, J. Microelectromech.
Syst., 16, pp.1025-1035, 2007.
[30] G. Maier, “The search for low-k and ultra-low-k dielectrics: How far can you get with polymers? Part 1: Background”, IEEE Electrical Insulation Magazine, 20 (2), pp.6-17, Dec., 2004.
[31] J. Basu and T. K. Bhattacharyya, “Microelectromechanical resonators for radio frequency communication applications”, Microsystem Technologies , 17, pp.1557-1580, 2011.
[32] W.-T. Hsu and C. T.-C. Nguyen, "Geometric stress compensation for enhanced thermal stability in micromechanical resonators", Proc. IEEE Int. Ultrason. Symp. Dig., pp.945-948, 1998.
[33] W.-T. Hsu, S. Lee, and C. T.-C. Nguyen, "In situ localized annealing for contamination resistance and enhanced stability in nickel micromechanical resonators", Dig. Tech.
Papers, 10th Int. Conf. Solid-State Sensors and Actuators, pp.932 -935, 1999.
[34] S. L. Kuo, Y. C. Chen, M. D. Ger, and W. H. Hwu, “Nano-particles dispersion effect on
[34] S. L. Kuo, Y. C. Chen, M. D. Ger, and W. H. Hwu, “Nano-particles dispersion effect on