Design and Simulation of Clamped-Clamped and Clamped-Free Resonators

A. Anwar Zainuddin1, Jamilah Karim2,A. Nurashikin Nordin3, M. Soundara Pandian4, Sheroz K.5

1, 2,3, 5 International Islamic University Malaysia, P.O. Box 10, 50728 Kuala Lumpur 1, 4, Silterra Malaysia, Lot 8, Kulim Hi-Tech Park 09000 Kedah D. A Malaysia

E-mail: 1ahmad_anwar@silterra.com, 2jamilah_karim@yahoo.com 3anisnn@iium.edu.my, 4mohanraj_soundara@silterra.com,5sheroz@iium.edu.my

Abstract To date, there have been interests in designing the Micro-Electro-Mechanical System (MEMS) integrated with Complementary Metal-Oxide Semiconductor (CMOS) resonator for RF integrated circuits. This work presents the design of Clamped-Clamped (CC) and Clamped-Free (CF) beam resonators. These resonators provide on-chip low cost solutions for devices with much reduced chip area, besides having considerably reduced insertion losses due to non-existent external bond wires. They can be integrated with amplifiers to form oscillators for generating clocks in the 2MHz and 20MHz range. The resonators require DC voltage maximally 10V for Clamped-Clamped and 7V for Clamped-free and 100mV AC voltage to electrostatically actuate the resonator’s beams. The actuation is simulated and measured using Finite Element modeling software of COMSOL to obtain optimum design parameters. This paper makes a comparative review of different models for evaluating the designed resonator’s performance in terms of resonance frequency under given pull-in voltage, and appropriate displacement.

Keywords Resonators, Resonance Frequency, Capacitance, Beam’s Displacement

1. Introduction Micro-electromechanical systems (MEMS) tend to become the subject of active research and development in a broader spectrum of academic pursuits and industrial applications. MEMS are widely used by systems in high (3–30MHz), very high (30– 300MHz) and even ultra-high (300 MHz–3GHz) frequency ranges [1]. They provide a promising alternative to traditional electronic components especially for RF devices (e.g. mixers, tunable capacitors, inductors, switches, oscillators). From the industrial perspective, these technologies promise exactly what their applications need be, that is, high-capability devices and systems with portability and low power consumption. The use of these elements integrated into a single silicon chip, along with the CMOS circuitry, will improve the performance of systems with added benefits of reduced costs, power consumption and size [2]. MEMS devices result from the integration of mechanical elements (sensors, actuators) and electronic components on a common silicon substrate using micro fabrication technology [3].

2. Resonators Beam Structure Aluminum (Al) material has been used to design and develop these resonators. The difference between Clamped-Clamped beam and Clamped-Free beams is discussed as follows: Clamped-Clamped Beam Resonator Physically, the Clamped-Clamped beam is made of a single beam resonating at the centre with both ends fixed or clamped by the anchors. Fig.1 shows the diagram of clamped-clamped beam resonator and the material layers respectively.

Figure 1: Dimension parameters of Clamped-Clamped beam resonator

Clamped-Free Beam Resonator The Clamp-Free beam resonator has got only one end of the beam clamped by the anchor with a free vibrating second. Fig.2 displays the diagram of Clamped-Free beam resonator.

Figure 2: Dimension parameters of Clamped-Free beam resonator

978-1-4799-1314-5/13/$31.00 ©2013 IEEE 55 5th Asia Symposium on Quality Electronic Design

Figure 3: Structural layers of resonator.

Fig. 3 indicates the MEMS resonators layers fabricated using CMOS process. The silicon substrate is used as ground plane. Silicon oxide is deposited underneath of the anchors. The DC voltage is connected to the anchor. The beam oscillation will generate the electrostatic capacitance with the ground electrodes. Table 1 summarizes all the design parameters of these resonators in this work.

Table 1: Design Parameters of MEMS Aluminum Resonators

Input Parameter Value Unit

Beam length, L 15 µm Beam width, W 1 µm Electrode width, We 0.5 µm Beam thickness, h 1 µm Electrode to resonator Gap,

0.5 µm

Poisson Ratio,v 0.36 - Young Modulus, E 64 GPa Density of Al, ρ 2700 Kg/m3

3. Operation of Resonators Fig. 4 shows the configuration of Clamped-Clamped beam resonator with electrical simulation and Fig.5 for the Clamped-Free beam resonator setup. Basically, the operation of these devices is described when a DC voltage is applied to the anchor and an AC voltage is applied to the excitation electrode, making the microstructures being driven into resonance. The resonators have a setup configuration with separate excitation (input) and read-out (output) electrodes. The beam is suspended so that it can vibrate freely. The applied AC voltage results in an electrostatic force between the electrode and the beam that consequently causes the vibration of the resonator. The capacitance changes between the sense electrode and the beam due to the movement of the beam generates a corresponding current in the readout electrode. The microstructure vibrating (motion) is detected by the sensing electrode, which produces an AC current at the sense electrode of the device. When the frequency of the applied drive AC voltage is equal to that of the mechanical natural frequency of the resonator, motion of the microstructure and consequently the output AC current of the device reach their maximum values.

(a)

(b)

Figure 4: Electrical setup for (a) Clamped-Clamped (b) Clamped-Free beam resonator.

4. Theory of Resonator’s Beam Among the parameters of interest in the case of MEMS resonators for RF technologies are resonance frequency (fnom), parallel parasitic capacitor (Cp), motional resistor (Rm), quality factor (Q), and frequency tuning (ft). These parameters are important to produce good performance in RF applications. However, in this section a few key components such as electrostatic excitation, equation of resonator movement (displacement), resonance frequency and finally RLC equivalent circuit model are discussed. A. Electrostatic Excitation Theoretically speaking, in filters design the main issues of concerns include nonlinear distortion and electrostatically actuated RF-MEMS filters. In microsystems, most common is the electrostatic actuation due to its low power consumption, fast operation and simplicity of the needed fabrication processes [4]. The mechanical structures utilized in this work are mainly composed of vibrating part and two fixed electrodes of resonator. An AC voltage is applied to the excitation electrode whereas the resonator is biased by application of a fixed DC voltage to anchor.

B. Resonator Movement (Displacement)

Figure 5 : Simplified of resonator model [4]

Fig. 5 indicates the simplified model for resonator that presents the MEMS movement can be modelled using a simple mass-spring-dash system excited by harmonic force. It also describes the equation of motion that transforms the applied force into resonator displacement. The resonator responds to this applied force (Fd) with a displacement that is mainly dominated by the forced harmonic oscillation movement equation:

)cos(..2

2

tAxktx

txm f ω

δδγ

δδ =++

(1)

Where m is resonator mass, γ is damping coefficient, k is the elastic constant and Af is the magnitude of the applied sinusoidal force. The natural resonance frequency (ω0) and the quality factor (Q) can be defined as:

mk=0ω (2)

γγω mkmQ ..0 ==

(3) Where mass (m), elastic constant (k) and x(displacement). Equation (2) and (3) provide a good information for a few constrains of MEMS devices. High Q values can be obtained when high k (stiff devices), high m (big devices for low resonance frequency and small devices for high frequency) and low damping are needed. According to the Equation (4), a maximum displacement can be defined when applied external force has a frequency near to the natural resonance frequency, ωo.

2

02

02 )/()(

/||

Q

mAx f

ωωωω +−=

(4)

C. Pull-In Voltage Since the beam vibrates either in vertical and lateral displacement, it may touch the electrode or substrate when it reaches the maximum DC voltage. In this work, we are interested in the lateral movement of the beam during vibration. The pull-in voltage is as when the lateral movement of beam reaches beyond the gap distance of 0.5µm. This indicates that the beam is already touching the electrode. D. Resonance Frequency

The physical dimension of the device such as shape, vibration mode and the mechanical properties of the material can influence the resonance frequency [4]. By using Equation (5), the analytical calculation of the resonance frequency (fnom) for these resonators can be done. Resonance frequencies of the devices described in this work are located at higher section of HF around 3MHz and lower VHF region, which is at 100MHz. The resonators are simulated using COMSOL have lateral and flexural resonance modes.

.03.1 2LrhEfnom ρ

= (5)

5. Simulation Results and Analysis

Figure 6: Eigenfrequency analysis. Both of anchors are fixed and only beam is free

Both the Clamped-Clamped and Clamped-free Beam resonators were simulated using COMSOLTM. The eigenfrequency analyses were simulated for both the clamped-clamped and clamped-free beams. Fig. 6 shows the eigenfrequency simulation in COMSOL™. This simulation is done for obtaining the resonance frequency and modes of deformation in the structure. The resonance frequency obtained from these Eigenfrequency analysis, will observe the high displacement of the beam movement or the highest point of vibration mode. As shown in Table 2 and 3, the comparison between analytical and simulation is done by using Equation (5) in Section 4 and exhibited a good agreement between them.

Table 2:Resonance frequency for Clamped-clamped beam: Comparison between analytical and simulation result.

Table 3: Resonance frequency for Clamped-free beam: Comparison between analytical and simulation result.

Figure 7: Simulation of resonance frequency for Clamped-clamped, CC beam. Different modes of resonance frequencies exhibit the different movement of the beam.

Figure 8: Simulation of resonance frequency for CF. Different modes of resonance frequencies show the different movement of the beam.

Next, the DC simulation analysis is performed in COMSOL™. Fig. 9 indicates that the boundary conditions of the resonator beam. The DC voltage is applied to the beam in air condition. The anchors can be ignored to reduce the complexity and save the time of simulation in this work.

Figure 9: DC simulation analysis. The VDC , voltage is applied to the beam

Figure 10: Simulation of Pull-in voltage for Clamped-clamped, CC and Clamped-Free, CF

Fig.10 displays the pull-in voltage of both resonators whereas Clamped-Clamped beam produces higher value of pull-in voltage than Clamped-Free. The pull-in voltage is obtained for Clamped-Clamped and Clamped-Free are 15V and 7.5V DC voltage respectively. The lower pull-in voltage for the Clamped-Free allows the devices operate with lower power consumption. Fig. 7 and Fig. 8 indicate the simulation result of modes and resonance frequency of clamped-clamped and clamped-free resonators, respectively. Different modes of vibration exhibit the different resonance frequency and the movement of resonator beam. Mode 1 and 2 for Clamped-clamped beam show that the beams are swinging laterally when 10V DC signal is applied to the anchor. The clamped-free beam also vibrates lateral or out-plane when 7.5 V DC voltage is supplied. Fig. 11 indicates the boundary conditions of the resonator beam for AC simulation analysis. This simulation is done for obtaining the beam’s x-displacement during vibration. The x-displacement means the beam moves or swings laterally or in out-plane direction. The 0.1V (AC) voltage is connected to the excitation electrode for both resonators’s simulation. Actually, this AC signal is not the main priority in this work and can be any number.

MODE Simulation (MHz) Analytical (MHz) 1 19.42 18.58 2 23.87 22.66

MODE Simulation (MHz) Analytical (MHz) 1 2.92 1.54 2 3.68 2.45

MODE 1: 19.42MHz MODE 2: 23.87 MHz

MODE 1: 2.92MHz MODE 2: 3.68MHz

Figure 11: AC simulation analysis. AC voltage is applied to the excitation electrode and DC Voltage to the beam.

As depicted in Fig.12 (a), Clamped-Clamped beam shows the first mode resonance frequency at 19.42MHz and the x-displacement at 0.6nm. The second mode of resonance frequency is at 23.87MHz and x-displacement shows at 0.05nm. The Clamped-free beam as shown in Fig. 10 (b) has lower resonance frequency compared to Clamped-Clamped beam resonator. The first mode of resonance frequency for Clamped-free beam is 2.92 MHz and the x-displacement is 2.31nm. The second mode of resonance frequency is at 3.68MHz and the x-displacement is 1.37nm. These results prove that the Clamped-Clamped beam produces high resonance frequency, and can be applied to the higher resonance frequency applications compared to Clamped-free beam resonator 6. Conclusion The Clamped-Clamped and Clamped-Free beam’s structures are designed and simulated in COMSOL™ to obtain the resonance frequency, pull-in voltage and x-displacement. The lower pull-in voltage values for Clamped-free structure show its potential to be applied in low power devices. The Clamped-Clamped structure shows its utility in high resonant circuits and need much voltage to be applied in obtaining the highest capacitance value. This structure can be utilized for high frequency filters and high powering electronic devices. Both of resonators are built using poly-silicon, which can be easily fabricated by the standard CMOS process and hence can be used in on chip RF applications.

7. Acknowledgment This work is supported by Silterra Malaysia Sdn.Bhd and the Ministry of Higher Education,(MOHE) ERGS 11-009-009.

(a)

(b)

Figure 12: The x-displacement and resonance frequency result with 0.1V (AC) voltage. (a) Clamped-clamped, CC beam with 10V DC voltage (b) Clamped-free,CF beam with 7V DC voltage 8. References

[1] Leach, R., Cui, Z., and Flack, D (Eds): ‘Microsystems technology standardization roadmap’. ‘Project IST-2001-37682 funded by the EU IST program, 2001

[2] Nguyen, C.T: ‘Vibrating RF MEMS for low power wireless communications’. Proc. Int. MEMS Workshop (iMEMS’01), July 2001

[3] W.-T. Hsu, “Vibrating RF MEMS for Timing and Frequency References”, 2006 IEEE MTT-S International Microwave Symposium, pp. 672-675, Jun 2006.

[4] J. Teva, G. Abadal, A. Uranga, J.Verd, F.Torres, J.L.Lopez, J.Esteve, F.Perez-Murano, and N. Barniol. “VHF to UHF CMOS-MEMS monolithically integrated in a standard 0.35um CMOS Technology,” in Micro Electro Mechanical Systems, 2007. MEMS. IEEE 20th International Conference on, 2007,pp.779-782.