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Mitigation of MEMS switch contact bouncing: Effectiveness of dual pulse actuation waveforms and robustness against variations in switch and waveform parameters
Sensors and Actuators A 194 (2013) 188–195
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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Mitigation of MEMS switch contact bouncing: Effectiveness of dual pulse actuation waveforms and robustness against variations in switch and waveform parameters Wallace S.H. Wong a , C.H. Lai a,∗ a
Faculty of Engineering, Computing and Science, Swinburne University of Technology (Sarawak Campus), Kuching, Sarawak, Malaysia
a r t i c l e
i n f o
Article history: Received 31 July 2012 Received in revised form 1 February 2013 Accepted 6 February 2013 Available online 13 February 2013 Keywords: Micro-electromechanical system Switches Radio frequency Bouncing Reliability
a b s t r a c t Dual pulse actuation voltage waveforms that are capable of mitigating micro-electromechanical system (MEMS) switch bouncing are presented. The displacement and velocity of the MEMS switch membrane actuated using these waveforms are then simulated and compared. To eliminate bouncing, the velocity of the membrane should ideally be zero just before contact is made. Otherwise the large momentum from high velocity impact will bounce the membrane back, extending the switching time and bringing about wear and tear to the contact surfaces. The effect of MEMS switch parameter variations on the bouncing membrane is then studied for switches with different gap widths. The impact of the variation in the voltage waveform is also investigated in this paper. The exponentially saturating dual-pulse actuation waveform has shown great robustness against both switch and voltage waveform parameter variations. The waveform also exhibited the fastest switching time for a wider range of parameters variations. Practical experiments were carried out on TeraVicta TT712-68CSP MEMS switch to corroborate the findings. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Microelectromechanical systems (MEMS) switches are promising alternatives in radio frequency (RF) switching application due to its very low insertion loss, high isolation and minimal power consumption [1]. A metal-to-metal MEMS switch in relay configuration generally consists of a thin metal membrane suspended few microns above two separated conducting lines as illustrated in Fig. 1(a). When sufficient actuation voltage is applied to the actuation pad beneath the membrane, the membrane is pulled down towards the contact surface on the conducting lines by the induced electrostatic force. This creates an electrical short between the conducting lines. Apart from metal-to-metal MEMS relays, capacitive MEMS switch is another common configuration where a dielectric layer is deposited between the top membrane and the bottom stationary electrodes. When electrostatic force is applied, the membrane is pulled down towards the dielectric layer, creating a metal-dielectric-metal contact which allows high frequency signal to pass through. In order to reduce switching bounces, voltage drivers for the MEMS switch that generate dual-pulse voltage waveforms have
∗ Corresponding author at: Swinburne University of Technology (Sarawak Campus), Jalan Simpang Tiga, 93350 Kuching, Sarawak, Malaysia. Tel.: +60 82 260 886. E-mail address: [email protected] (C.H. Lai). 0924-4247/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.sna.2013.02.011
been proposed [3–6]. Generally, a dual-pulse actuation waveform consists of a large initial voltage pulse to accelerate the membrane towards the contact surface, followed by a smaller voltage to hold the membrane once it has reached the contact point as illustrated in Fig. 2. This actuation waveform was first introduced by Goldsmith et al., which was inspired by the dual-stage current pulse used to actuate the conventional P–I–N diode [6]. When tuned correctly, the unnecessary large voltage is removed when the membrane is about to land on the contact surface. This reduces the pulling force and therefore the velocity of the membrane as it approaches the contact, thus preventing the membrane from hitting the contact surface hard and bouncing back [3,4]. High velocity impact of the membrane is undesirable as it accelerates the wear and tear of the contacting surfaces. In addition, the bouncing prolongs the time required for the switching process to be completed. As reported in previous studies, the reduced voltage also has the advantage of minimizing the tunnelling of electrical charges into the switch substrate [16] and dielectric layer [2], thus further improving the lifetime of the MEMS switch [5]. Apart from the regular dual pulse (DP) waveform proposed by Goldsmith et al., other notable dual pulse actuation waveforms includes the exponentially saturating dual-pulse waveform (EDP) proposed in [5,9], the soft-landing waveform (SL) in [3] and the learning control waveform (LCA) in [4]. All of them aim at eliminating switching bounces and speeding up the switching process.
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Fig. 1. (a) A cross section view of typical metal-to-metal MEMS relay. (b) A simplified mechanical model of the MEMS relay with effective spring constant keff , effective mass meff , and the electrostatic force Fes .
Ideally, all these actuation waveforms are able to eliminate the bounces if tuned correctly. However each MEMS switches are slightly different from each other in term of the geometrical and mechanical properties even if they are of the same design and developed from the same wafer. Goldsmith et al. in their reliability study found that MEMS switches from the same wafer may have threshold voltage variation of up to 10% [6]. As a result, the optimal setting of the actuation waveform also varies with individual switch. The performance of these dual-pulse actuation waveforms is therefore sensitive to the variation in the switch especially when multiple MEMS switches are employed in the same system. This paper first simulates the dynamic responses of the switch membrane produced by the aforementioned actuation waveforms and investigates the effectiveness of these waveforms in eliminating switching bounces. Next, the robustness of the DP and EDP actuation waveforms against switch and waveform parameters variations are investigated. The robustness of the SL and LCA waveforms were not considered as these waveforms were designed to work optimally for each individual MEMS switch. The LCA waveform iteratively tunes itself based on the discontinuity measured from the switch output terminal. However these waveforms require individual switch testing, measurement and tuning to achieve their optimal settings and hence may not be suitable in applications where large number of MEMS switches exist. Finally, the analysis is corroborated through experiments where the switching time and the duration of switching bounces were measured. The experiments were carried out on the commercially available (but now defunct) TeraVicta TT712-68CSP MEMS switch depicted in Fig. 3. Though this work concentrates specifically on the dual pulse actuation waveforms, the approach used in this work can be extended to study the bouncing and robustness of other more complex actuation waveforms.
Fig. 2. The dual-pulse actuation voltage (DP). A short large voltage pulse VP to pull the membrane down, followed by a smaller holding voltage VH to hold the membrane after contact is made.
Fig. 3. Commercially available TeraVicta (now defunct) TT712-68CSP MEMS switch studied in this work [26].
2. Switching bounces When actuation voltage is applied across the membrane and actuation pad, the membrane is pulled towards the actuation pad by electrostatic force. The electrostatic force experienced by the membrane can be ideally modelled as the force experienced by parallel plates, as depicted in Fig. 1(b) [7]. The electrostatic force acting on the membrane is given by: Fes =
1 ε0 AV 2 2 2(g − x)2
(1)
where ε0 is the permittivity of air, A is the effective area between the membrane and actuation pad, V is the applied actuation voltage, g is the initial gap between the actuation pad and membrane when V = 0, and x is the displacement of the membrane from its initial position. The equation indicates that the electrostatic force Fes behaves non-linearly to the displacement of the moving membrane x. As the membrane moves closer to the actuation pad, the electrostatic force increases rapidly as (g − x) diminishes. The membrane can be actuated and held static at displacements of up to one-third of the gap (g/3), where the structural restoring force is still sufficient to hold the membrane against the electrostatic force. When a larger actuation voltage is applied and the membrane travels beyond g/3, the membrane’s restoring force could no longer match the increasingly strong electrostatic force, causing the membrane to collapse toward the actuation pad [3]. As the membrane moves closer to the actuation pad the electrostatic force becomes much stronger, accelerating the membrane further. The membrane would eventually slams against the contacting lines at high velocity. The amount of voltage needed for the membrane to just exceed g/3 and trigger the instability that turns the switch ON is known as the threshold or pull-in voltage Vpi . Fig. 4 shows the simulated displacement and velocity of the membrane based on the electrostatic force model in Eq. (1) and the dynamic model in Eq. (2) when a step actuation voltage is applied. The geometrical parameters of the MEMS switch used in the model are tabulated in Table 1. The Vpi was calculated to be 65 V but the actual applied actuation voltage Va was set higher at 80 V. This is a common practice to ensure that the MEMS switch is successfully actuated. The TeraVicta TT712-68CSPswitch for example, was found to start switching 10–15 V below the recommended actuation voltage. From the figure, after exceeding the g/3 (about 1.2 m), the membrane accelerates rapidly towards the contact, leading to a high contact velocity of about 0.39 m/s. The maximum distance
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Fig. 4. Simulated displacement and velocity profiles of MEMS switch membrane when a step actuation voltage of 80 V is applied. The membrane accelerates rapidly as it gets closer to the actuation electrode.
travelled xmax by the moving membrane is only 2.5 m as the distance between the membrane resting position and the conducting lines surface is shorter than the gap g between the membrane and the actuation pad. This is illustrated in Fig. 1(a). The momentum of the high velocity impact causes the membrane to bounce away from the contact surface, leading to electrical discontinuity. The bouncing continues until the momentum of the membrane is exhausted. The bouncing increases the time for the membrane to completely settle down at the contact surface and therefore prolonging the time for the switching process to be completed. The high velocity impact also increases contact surfaces wear and tear, leading to mechanical and electrical failures such as fusing of contacts, transferring metals between contact surfaces and increasing the contact resistance [3].
Fig. 5. A mechanical model for RF MEMS switch including the squeeze-film damping effect.
The squeeze-film damping effect due to the gas film underneath the switch membrane can be added to the model by using a combination of dampers and springs aligned in series between the two parallel plates [18–20], as illustrated in Fig. 5 [21–25]. The dampers represent the viscous damping force due to the resistance of the membrane plate movement caused by the viscous flow of air, while the springs represent the elastic force contributed by the air compression between the two parallel plates. The coefficient of viscous damping force bd of the squeeze film is given by [25] bd =
3. Model of the switching dynamics
meff
d2 x + keff x = Fes dt 2
(2)
where x is the displacement of the membrane from its initial position. Fes is the applied electrostatic force given by Eq. (1). Initially, when no voltage (0 V) is applied to the switch, the initial conditions are x = 0, dx/dt = 0 at t = 0. This dynamic model is only valid for x ≤ g, which is the working range of the MEMS switch. Table 1 MEMS switch parameters used in the simulation of membrane displacement and velocity [12]. Parameter
Symbol
Value
Effective area Permittivity of air Gap Maximum distance travelled Effective mass Effective spring constant Threshold/Pull-in voltage
A ε0 g xmax meff Keff VPi
15.6 × 10−9 m2 8.85 × 10−12 C2 /N m2 3.6 × 10−6 m 2.5 × 10−6 m 3 × 10−9 kg 42 N/m 65 V
m,n,odd (mn)
m2 + (n/)
2
m2 + (n/)
2
2 2
(3)
+ ( 2 /4 )
and the coefficient of the elastic force ke is given by ke =
The membrane’s dynamic response when the switch closes can be modelled as the response of a non-linear mass-spring-damper system [7]. The model assumes that the membrane does not deform and remain parallel to the actuation pad during the entire actuation and release processes. These assumptions are reasonable as the gap between the moving membrane and the contact surfaces is much lesser than the thickness of the membrane itself in most MEMS switch designs. Hence, the membrane’s dynamic is represented by a lumped effective mass meff with an effective spring constant keff as shown in Eq. (2) [7].
64Pa A 6 g
64 2 Pa A 8 g
m,n,odd (mn)
2
1
m2 + (n/)
2 2
(4)
+ ( 2 /4 )
where m and n are odd integers, Pa is the ambient pressure, A is the area of the squeeze film, g is the thickness of the gas film which is also the gap of the two plates, is the aspect ratio of the rectangular plate and is the squeeze number which can be approximated by [23].
= 2
1+
1 2
(5)
Therefore, by including the squeeze-film effect, Eq. (2) can now be expanded to: meff
d2 x dx + (keff + ke ) x = Fes + bd dt dt 2
(6)
If the switch is moving at a high speed, the air film underneath the moving membrane is compressed and fails to escape. Thus the elastic force in Eq. (6) would dominate and the viscous damping force caused by the air flow can be neglected [25]. In addition, the damping only affects the ringing response after contact has been made but does not significantly affect the dynamics during the switch initial closing period [3]. If the MEMS switch is vacuum packed, the squeeze-film effect can be ignored. The squeeze-film effect can also be reduced significantly by adding holes or slots on the membrane to create more paths for the trapped air underneath the membrane to circulate [25]. In this work, the displacement and velocity of the membrane generated by the different actuation voltage waveforms are simulated using the model described by Eqs. (1) and (2). A fast-switching, small-gap design and vacuum-packed MEMS switch is assumed. Admittedly, the above model is simple and thus may be insufficient to model all the features of different MEMS switch designs.
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The model serves to provide an insight to the dynamics of a generic membrane-type MEMS switch. Similar study can be extended to a particular switch design with an updated model of the MEMS switch. Ideally, the velocity of the moving membrane should be zero just before it touches the contact surface in order to minimize the impact momentum. This would prevent the membrane from bouncing away. Therefore, the actuation voltage applied to the switch must be reduced to slow down the membrane as it approaches the contact point. However, the actuation waveform should accomplish this without substantially slowing down the entire switching process. Investigation into the energy supplied to the switch was carried out for further insights to the performance of the dual pulse waveforms in mitigating bounces. Ideally, the energy required to turn on the switch, Eron , is only for compensating the membrane’s spring energy, with the assumptions that all other forces (contact force, damping force, etc.) are energy conserving and power dissipated during actuation process is negligible. An additional energy Ea may be added to ensure that all switches, despite the variation in their parameters, will turn on successfully. Thus the total energy supplied Es = Eron + Ea . The total energy supplied is the integral of the product of applied electrostatic force Fes and velocity v(t) as:
Es =
t1st
Fes · v dt
(7)
0
since v dt = dx, the energy equation can be simplified to
Es =
xmax
Fes dx.
(8)
0
4. Dual pulse actuation waveforms Dual pulse actuation voltage waveform consists of a large initial voltage to accelerate the membrane towards the contact, followed by a small voltage to hold the membrane in contact. Having a smaller voltage at the later part of the actuation waveform reduces the velocity of the membrane as it approaches the contact. This prevents the membrane from slamming onto the contact surface and bouncing back. Fig. 6 shows notable dual pulse waveforms apart from the regular DP waveform shown earlier in Fig. 2. The EDP waveform shown in Fig. 6(a) gradually increases the large actuation voltage pulse at the beginning of the ON period, rather than a large constant pulse as in the DP waveform. The actuation time tA is tuned precisely to ensure that the switch does not bounce while maintaining a fast switching time. The key advantage of this waveform is the simplicity in its implementation, where only a simple resistor-capacitor network needs to be added to the DP driving circuit. In addition, the EDP waveform has shown to minimize dielectric charging when the switch is actuated continuously, thereby prolonging the switch lifetime [5,15,17]. In Fig. 6(b), the SL waveform turns off the voltage completely after the large initial voltage at time tA . Once the membrane has landed on the contact point at time tH , the waveform resumes with a small holding voltage [3]. The off time allows the membrane to decelerate quickly. The time tA and tH are calculated based on the energy balance between the membrane system and the work done by the electrostatic force. This method requires accurate knowledge of the switch parameters such as the effective stiffness of the switch membrane for calculating the precise timing for each individual switch. The LCA waveform also consists of two separate pulses, one for actuating and the other for holding the membrane, with an off time in between them. However, instead of a step on and off transitions, the LCA waveform follows a cosine increment and decrement during the on and off transitions. The time t1 to t5
Fig. 6. Different dual-pulse actuation waveforms: (a) exponentially saturating dualpulse (EDP); (b) soft-landing waveform (SL); and (c) learning control waveform (LCA).
shown in Fig. 6(c) are tuned incrementally and iteratively based on the switch output signal continuity measured using a sensor [4]. The self-adjustment of the actuation waveform ends when the output signal exhibits smooth transition, which indicates that a bounce free contact has been achieved. This closed-looped actuation strategy does not require prior information about the switch parameters. However, it requires additional sensory device and an active driver system to perform the tuning and generate the precise actuation waveform for each individual switch. As MEMS switches are slightly different in their geometrical and mechanical properties, the required optimal actuation voltage waveform also varies for each switch. In the next section, the robustness of the DP and EDP waveforms in the presence of switch parameters and voltage waveform variations is investigated and compared. The SL and LCA actuation waveforms have the advantage that the voltage applied is always at optimum and thus variation in the switch parameters is not a concern. However, in order to maintain the optimum voltage, calculations (SL) and measurements (LCA) must be made for each switch. Moreover, complex active driver circuitry is required to generate the optimal waveforms. For these reasons, the applications of these waveforms may not be suitable for applications that employ a large number of MEMS switches.
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Fig. 7. Simulated displacement and velocity profiles of the switch membrane under different dual-pulse actuation waveforms: (a) DP actuation waveform; (b) EDP actuation waveform; (c) SL actuation waveform and (d) LCA waveform.
5. Robustness analysis Fig. 7 shows the simulated displacement and velocity profiles of the switch membrane when the DP, EDP, SL and LCA voltage waveforms are applied with their respective optimal actuation times. All waveforms have shown to significantly reduce the contact velocity just before contact is made at x = 2.5 m, as compared to the large approaching velocity of about 0.39 m/s produced by the conventional step actuation voltage. As shown in Fig. 7, the SL waveform completed the switching process in the fastest time at about 25.2 s. This is because the membrane is accelerated rapidly by the large initial step voltage. The ensuing voltage-off period allows the membrane to slow down quickly before reaching the contact. As expected, the EDP waveform produced the slowest switching speed at about 41 s due to the membrane slow initial acceleration. The robustness of the voltage waveforms when the gap g between the membrane and the contacting surfaces varies was investigated. This imitates the scenario in the event that the thickness of the sacrificial layer deviates from its set value in the fabrication process. Other switch parameters such as the effective area A of the membrane-actuation pad parallel plate and effective spring constant keff are all assumed to remain unchanged. A ± 6% variation from the nominal gap of 3.6 m was simulated. The maximum distance travelled by the membrane xmax was varied accordingly. Since the gap may vary up to +6%, the actuation waveforms (actuation time tA in this case) were adjusted so that all MEMS switches (within the ±6% gap variation) could be actuated successfully. The peak voltage Vp and holding voltage Vh were still fixed at 80 V and 40 V, but the actuation time tA of both the DP and EDP
actuation waveforms were increased so that the switch with the largest gap (g + 6%) could be actuated successfully with minimal contact velocity. The waveforms were then applied to all switches with gap variation from −6 to 6%. The optimal waveform settings for gap g and g + 6% are tabulated in Table 2 to show the changes in the waveforms’ actuation time. Fig. 8 shows the simulated first contact time t1st and membrane contact velocity vc of switches with different gap g when the voltage waveform tuned for g + 6% is applied. As shown in Fig. 8(a), the switch closes faster (as shown) for smaller gap as the electrostatic force Fes is inversely proportional to the square of gap g. From Fig. 8(b), the vc at g + 6% gap are nearly zero for both DP and EDP waveforms since the waveforms were optimized for this condition. The vc produced by the DP waveform has shown to vary more across the different gaps compared to the EDP waveform. Hence, the waveform is more susceptible to the gap variations. Another approach to assess the robustness of the voltage waveforms to switch parameters variation is by varying the applied tA instead. For example, say the selected optimal tA for a specific switch design is 21 s. 21 s is then applied to the final production switch that has a different optimal actuation time at 17 s due to the variation in the switch parameters picked up during manufacturing. This means that additional 4 s has been added on top of the optimal actuation time. Admittedly, there is no clear relationship between the switch parameters variation and the optimal tA being studied in this paper. This paper focuses on the robustness of the actuation waveform when there is a variation in the switch parameters. The actual relationship between the parameters variations with the changes in the optimal actuation time was not considered.
Table 2 Comparison of MEMS switch dynamic response for nominal gap (g) and maximum gap variation (g = g + 6%) at their optimum waveform setting. Actuation waveform
DP EDP
Vp (V)
80 80
Vh (V)
40 40
Gap = g
Gap = g + 6%
tA (s)
t1st (s)
vc (m/s)
tA (s)
t1st (s)
vc (m/s)
17.1 26.4
31.2 41.0
≈0 ≈0
21.7 29.1
33.1 43.7
≈0 ≈0
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Fig. 8. (a) First contact time and (b) Contact velocity of the membrane of switch with different gap when the same actuation waveform is applied.
Fig. 9. (a) First contact time and (b) contact velocity when tA is increased from its optimal value.
The peak voltage Vp and holding voltage Vh were both retained at 80 V and 40 V throughout the entire simulation. Starting from the optimal value, the tA of both DP and EDP waveforms were incremented by 1 s at each iterations. The first contact time and contact velocity were recorded and plotted in Fig. 9. From Fig. 9(a), the first contact time generated by both DP and EDP waveforms is reduced when the actuation time tA is increased from its optimal value. The EDP waveform generally took approximately 10 s extra to achieve first contact compared to the DP waveform due to the switch membrane slow initial acceleration. In Fig. 9(b), the EDP waveform has demonstrated to be less susceptible to the increase in the applied tA as it produces less contact velocity increment compared to the DP waveform. This is because the total energy supplied by the large voltage pulse is not affected as much by tA due to the exponential nature of the waveform.
Since the energy required to turn on the switch, Eron , is only for compensating the membrane’s spring energy, Eron must equals the elastic energy: Eron =
1 k · x2 2 eff max
(9)
The total energy supplied by the voltage waveform until just before contact, Es , was computed numerically using Eq. (8) based on the displacement profiles generated from earlier simulations. Ideally, to ensure zero velocity upon contact and hence no bouncing, Es should be equal to Eron . Excess energy (Es − Eron ) may cause bouncing. Fig. 10(a) shows the excess energy supplied to the switch when the DP and EDP waveforms optimized for g + 6% were applied to switches with varying gaps. The DP waveform has shown to supply
Fig. 10. (a) Excessive energy supplied during actuation process when the same waveform is applied to the device with variation in gap. (b) Total energy supplied Es during actuation process when actuation waveform shifts from their respective optimum settings.
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Fig. 11. Experiment set-up for testing both the DP and EDP actuation waveforms.
more excess energy compared to the EDP waveform. Fig. 10(b) shows the total energy supplied Es by both DP and EDP voltage waveforms under varying actuation time tA . The energy supplied by the DP voltage waveform increases more significantly and hence it is more sensitive to tA .
Fig. 13. (a) The first contact time, t1st and (b) the bouncing duration, tb as the actuation time tA of both DP and EDP actuation waveforms increased from their respective optimal settings.
6. Experiment results
Fig. 12. Oscilloscope plots showing the (a) DP and (b) EDP actuation waveforms and the respective switched DC signal.
Fig. 11 shows the block diagram of the experimental setup to observe the bouncing of the MEMS switch when the DP and EDP actuation waveforms were applied. SL and LCA waveforms were not considered as bouncing should not occur if these waveforms were tuned optimally for each individual switch. The MEMS switch used is the commercially available TT712-68CSP SPDT RF MEMS switch fabricated by TeraVicta (now defunct) [10]. For both the DP and EDP actuation waveforms, the MEMS switch was actuated at 200 Hz, with a high peak voltage at 80 V applied for tA followed by a 50 V holding voltage for the rest of the on time. In order to facilitate the observation of the bouncing effect, a small DC voltage was applied at the input pin of the MEMS switch and the output of the switch is captured using oscilloscope (Tektronix TDS 1002B). A 200 Hz, 0–5 V square wave signal was applied to the voltage driver circuit to generate the desired actuation waveform. Note that the DP and EDP waveforms generation differs only in the addition of R-C network in the driver circuit [5]. First, the actuation time tA of both waveforms were increased slowly from 0 s until switching is made without any bouncing. For the DP waveform, switching is made without any bouncing when tA = 17 s whereas for the EDP waveform, the actuation time is longer at tA = 27 s. This is in agreement with the simulation analysis. To assess the sensitivity of the waveforms to switch parameters variation, tA is then varied to simulate the optimal time that different MEMS switches required. Snapshots of the MEMS switch response captured using oscilloscope are shown in Fig. 12. CH 1 shows the DC signal at the output terminal and CH 2 shows the actuation waveform applied. From the oscilloscope plot, the time taken for the switch to turn ON the first time t1st was measured.
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If the switch bounces, the settling time ts for the bouncing to settle down and the switch to be permanently ON was measured as well. In an ideal switching process, there should be no bouncing and therefore t1st = ts . Although the contact velocity of the switch membrane could not be measured in the experiment due to the unavailability of measuring apparatus, the duration of the bouncing tb = ts − t1st captured by the oscilloscope gives a good indication of the velocity. The t1st and tb when tA is increased from its optimal setting were plotted in Fig. 13. Note that t1st in the experiment does not match the simulation result quantitatively as a different MEMS switch was used in the experiment. Nonetheless, in agreement with the simulation findings, both the DP and EDP waveforms exhibit qualitatively similar t1st trends when tA is increased. The bouncing duration tb measured experimentally also shows similar trend to the change in the contact velocity simulated earlier, where both showed that bouncing is amplified as tA increases. The result also shows that the EDP waveform is less susceptible to the change in tA compared to the DP waveform, where it took up to 6 s increment in the tA before any bouncing was detected.
[4]
[5]
[6]
[7]
[9] [10] [12]
[15]
[16]
7. Conclusion [17]
Dual pulse actuation voltage waveforms reduce MEMS switch bouncing by slowing down the switch membrane prior to contact. The soft-landing (SL) and learning control voltage (LCA) waveforms have shown to provide the fastest switching speed and are immune to variations in the switch parameters. SL requires accurate knowledge of the switch parameters and LCA requires iterative measurement of the switch continuity. Therefore, they may not be suitable for applications where many MEMS switches are employed. In the ideal setting, the conventional dual pulse (DP) waveform switches faster than the exponentially saturating (EDP) dual pulse actuation voltage. However DP waveform is more sensitive to the variations in the switch parameters and actuation voltage waveform. When longer than necessary actuation voltage is applied, the EDP waveform actually switches faster than DP waveform as bouncing is minimized. EDP waveform also has the added advantage of simple implementation and minimizes charge builtup in the switch. For an optimal switching speed and minimum bouncing over a wider range of switch variations, the EDP waveform could therefore be applied. Acknowledgement This work was supported by the Malaysian Ministry of Science, Technology and Innovation (MOSTI) under ScienceFund Scheme 03-02-14-SF0002. References [1] R. Chan, R. Lesnick, D. Becher, M. Feng, Low-actuation voltage RF MEMS shunt switch with cold switching lifetime of seven billion cycles, Journal of Microelectromechanical Systems 12 (October 5) (2003) 713–719. [2] X. Yuan, J.C.M. Hwang, D. Forehand, C.L. Goldsmith, Modeling and characterization of dielectric-charging effects in RF MEMS capacitive switches, IEEE MTT-S International Microwave Symposium Digest (June) (2005) 753–756. [3] D.A. Czaplewski, C.W. Dyck, H. Sumali, J.E. Massad, J.D. Kuppers, I. Reines, W.D. Cowan, C.P. Tigges, A soft-landing waveform for actuation of a
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single-pole single-throw ohmic RF MEMS switch, Journal of Microelectromechanical Systems 15 (December 6) (2006) 1586–1594. J.C. Blecke, D.S. Epp, H. Sumali, G.G. Parker, A simple learning control to eliminate RF-MEMS switch bounce, Journal of Microelectromechanical Systems 18 (2) (2009) 458–465. W.S.H. Wong, C.H. Lai, Longer MEMS switch lifetime using novel dual-pulse actuation voltage, IEEE Transactions on Device and Materials Reliability 9 (4) (2009) 569–575. C.L. Goldsmith, J. Ehmke, A. Malczewski, B. Pillans, S. Eshelman, Z. Yao, J. Brank, M. Eberly, Lifetime characterization of capacitive RF MEMS switches, IEEE MTTS International Microwave Symposium Digest 1 (June) (2001) 227–230. B.M. Jeremy, M.R. Gabriel, Nonlinear electro-mechanical modeling of MEMS switches, IEEE MTT-S International Microwave Symposium Digest 3 (2001) 2119–2122. C.H. Lai, W.S.H. Wong, Novel Dual-Pulse Actuation Voltage for Longer MEMS Switch Lifetime, World Congress on Engineering 1 (July) (2009). TeraVicta Technologies Inc. TeraVicta TT712-68CSP SPDT 7 GHz RF MEMS Switch Datasheet V2.4, March 2007. R.W. Herfst, P.G. Steeneken, H.G.A. Huizing, J. Schmitz, Center-shift method for the characterization of dielectric charging in RF MEMS capacitive switches, IEEE Transactions on Semiconductor Manufacturing 21 (May 2) (2008) 148–153. W. Merlijn van Spengen, R. Puers, R. Mertens, Ingrid De Wolf, A comprehensive model to predict the charging and reliability of capacitive RF MEMS switches, Journal of Micromechanics and Microengineering 14 (January 4) (2004) 514–521. Wang G, RF MEMS switches with novel materials and micromachining techniques for SOC/SOP RF front ends, Thesis of School of Electrical and Computer Engineering, Georgia Institute of Technology 2006. R. Marcelli, G. Bartolucci, G. Papaioannu, G. De Angelis, A. Lucibello, E. Proietti, B. Margesin, F. Giacomozzi, F. Deborgies, Reliability of RF MEMS switches due to charging effects and their circuital modelling, Journal of Microsystem Technologies 16 (7) (2010) 1111–1118. R.P. Larose, K.D. Murphy, Impact dynamics of MEMS switches, Nonlinear Dynamics 60 (May 3) (2010) 327–339. T. Veijola, H. Kuisma, J. Lahdenperä, T. Ryhänen, Equivalent-circuit model of the squeezed gas film in a silicon accelerometer, Sensors and Actuators A: Physics 48 (1995) 239–248. P.G. Steeneken, T.G.S.M. Rijks, J.T.M. van Beek, M.J.E. Ulenaers, J. De Coster, R. Puers, Dynamics and squeeze film gas damping of a capacitive RF MEMS switch, Journal of Micromechanics and Microengineering 15 (2005) 176–184. W.E. Langlois, Isothermal squeeze films, Quarterly of Applied Mathematics XX (2) (1962) 131–150. W.S. Griffin, H.H. Richarson, S. Yamanami, A study of squeeze film damping, ASME Journal of Basic Engineering (1966) 451–456. J.J. Blench, On isothermal squeeze films, ASME Journal of Lubrication Technology 105 (1983) 615–620. R. Darling, C. Hivick, J. Xu, Compact analytical modeling of squeeze film damping with arbitrary venting conditions using a green’s function approach, Sensors and Actuators A 70 (1998) 32–41. Minhang Bao, Heng Yang, Squeeze film air damping in MEMS, Sensors and Actuators A 136 (2007) 3–27. John McKillop, RF MEMS switch ASICS, in: Proceedings of Asia-Pacific Microwave Conference, 2007.
Biographies Wallace S.H. Wong received the B.Eng. degree in electrical and electronic engineering and the Ph.D. degree in motor drives and advanced control from Bristol University, Bristol, U.K., in 1999 and 2003 respectively. After his doctoral work, he looked into actuating MEMS micromotor and microswitches, adapting improvement techniques used for driving their much larger cousins. He is also keen on finding novel applications for MEMS devices and has recently ventured into combining MEMS, RFID and other wireless technologies for accurate indoor positioning. He is currently the Director of the Research Office at Swinburne University of Technology (Sarawak Campus) in Kuching, Malaysia. Chean Hung Lai received the B.Eng. degree in robotics and mechatronics in 2006 and the Ph.D. degree in mechatronics engineering from Swinburne University of Technology, Sarawak, in 2012. His research interests include the reliability studies of microelectromechanical systems (MEMS) switches, intelligent sensor, RFID technology, battery management and robotic systems.
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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Mitigation of MEMS switch contact bouncing: Effectiveness of dual pulse actuation waveforms and robustness against variations in switch and waveform parameters Wallace S.H. Wong a , C.H. Lai a,∗ a
Faculty of Engineering, Computing and Science, Swinburne University of Technology (Sarawak Campus), Kuching, Sarawak, Malaysia
a r t i c l e
i n f o
Article history: Received 31 July 2012 Received in revised form 1 February 2013 Accepted 6 February 2013 Available online 13 February 2013 Keywords: Micro-electromechanical system Switches Radio frequency Bouncing Reliability
a b s t r a c t Dual pulse actuation voltage waveforms that are capable of mitigating micro-electromechanical system (MEMS) switch bouncing are presented. The displacement and velocity of the MEMS switch membrane actuated using these waveforms are then simulated and compared. To eliminate bouncing, the velocity of the membrane should ideally be zero just before contact is made. Otherwise the large momentum from high velocity impact will bounce the membrane back, extending the switching time and bringing about wear and tear to the contact surfaces. The effect of MEMS switch parameter variations on the bouncing membrane is then studied for switches with different gap widths. The impact of the variation in the voltage waveform is also investigated in this paper. The exponentially saturating dual-pulse actuation waveform has shown great robustness against both switch and voltage waveform parameter variations. The waveform also exhibited the fastest switching time for a wider range of parameters variations. Practical experiments were carried out on TeraVicta TT712-68CSP MEMS switch to corroborate the findings. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Microelectromechanical systems (MEMS) switches are promising alternatives in radio frequency (RF) switching application due to its very low insertion loss, high isolation and minimal power consumption [1]. A metal-to-metal MEMS switch in relay configuration generally consists of a thin metal membrane suspended few microns above two separated conducting lines as illustrated in Fig. 1(a). When sufficient actuation voltage is applied to the actuation pad beneath the membrane, the membrane is pulled down towards the contact surface on the conducting lines by the induced electrostatic force. This creates an electrical short between the conducting lines. Apart from metal-to-metal MEMS relays, capacitive MEMS switch is another common configuration where a dielectric layer is deposited between the top membrane and the bottom stationary electrodes. When electrostatic force is applied, the membrane is pulled down towards the dielectric layer, creating a metal-dielectric-metal contact which allows high frequency signal to pass through. In order to reduce switching bounces, voltage drivers for the MEMS switch that generate dual-pulse voltage waveforms have
∗ Corresponding author at: Swinburne University of Technology (Sarawak Campus), Jalan Simpang Tiga, 93350 Kuching, Sarawak, Malaysia. Tel.: +60 82 260 886. E-mail address: [email protected] (C.H. Lai). 0924-4247/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.sna.2013.02.011
been proposed [3–6]. Generally, a dual-pulse actuation waveform consists of a large initial voltage pulse to accelerate the membrane towards the contact surface, followed by a smaller voltage to hold the membrane once it has reached the contact point as illustrated in Fig. 2. This actuation waveform was first introduced by Goldsmith et al., which was inspired by the dual-stage current pulse used to actuate the conventional P–I–N diode [6]. When tuned correctly, the unnecessary large voltage is removed when the membrane is about to land on the contact surface. This reduces the pulling force and therefore the velocity of the membrane as it approaches the contact, thus preventing the membrane from hitting the contact surface hard and bouncing back [3,4]. High velocity impact of the membrane is undesirable as it accelerates the wear and tear of the contacting surfaces. In addition, the bouncing prolongs the time required for the switching process to be completed. As reported in previous studies, the reduced voltage also has the advantage of minimizing the tunnelling of electrical charges into the switch substrate [16] and dielectric layer [2], thus further improving the lifetime of the MEMS switch [5]. Apart from the regular dual pulse (DP) waveform proposed by Goldsmith et al., other notable dual pulse actuation waveforms includes the exponentially saturating dual-pulse waveform (EDP) proposed in [5,9], the soft-landing waveform (SL) in [3] and the learning control waveform (LCA) in [4]. All of them aim at eliminating switching bounces and speeding up the switching process.
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Fig. 1. (a) A cross section view of typical metal-to-metal MEMS relay. (b) A simplified mechanical model of the MEMS relay with effective spring constant keff , effective mass meff , and the electrostatic force Fes .
Ideally, all these actuation waveforms are able to eliminate the bounces if tuned correctly. However each MEMS switches are slightly different from each other in term of the geometrical and mechanical properties even if they are of the same design and developed from the same wafer. Goldsmith et al. in their reliability study found that MEMS switches from the same wafer may have threshold voltage variation of up to 10% [6]. As a result, the optimal setting of the actuation waveform also varies with individual switch. The performance of these dual-pulse actuation waveforms is therefore sensitive to the variation in the switch especially when multiple MEMS switches are employed in the same system. This paper first simulates the dynamic responses of the switch membrane produced by the aforementioned actuation waveforms and investigates the effectiveness of these waveforms in eliminating switching bounces. Next, the robustness of the DP and EDP actuation waveforms against switch and waveform parameters variations are investigated. The robustness of the SL and LCA waveforms were not considered as these waveforms were designed to work optimally for each individual MEMS switch. The LCA waveform iteratively tunes itself based on the discontinuity measured from the switch output terminal. However these waveforms require individual switch testing, measurement and tuning to achieve their optimal settings and hence may not be suitable in applications where large number of MEMS switches exist. Finally, the analysis is corroborated through experiments where the switching time and the duration of switching bounces were measured. The experiments were carried out on the commercially available (but now defunct) TeraVicta TT712-68CSP MEMS switch depicted in Fig. 3. Though this work concentrates specifically on the dual pulse actuation waveforms, the approach used in this work can be extended to study the bouncing and robustness of other more complex actuation waveforms.
Fig. 2. The dual-pulse actuation voltage (DP). A short large voltage pulse VP to pull the membrane down, followed by a smaller holding voltage VH to hold the membrane after contact is made.
Fig. 3. Commercially available TeraVicta (now defunct) TT712-68CSP MEMS switch studied in this work [26].
2. Switching bounces When actuation voltage is applied across the membrane and actuation pad, the membrane is pulled towards the actuation pad by electrostatic force. The electrostatic force experienced by the membrane can be ideally modelled as the force experienced by parallel plates, as depicted in Fig. 1(b) [7]. The electrostatic force acting on the membrane is given by: Fes =
1 ε0 AV 2 2 2(g − x)2
(1)
where ε0 is the permittivity of air, A is the effective area between the membrane and actuation pad, V is the applied actuation voltage, g is the initial gap between the actuation pad and membrane when V = 0, and x is the displacement of the membrane from its initial position. The equation indicates that the electrostatic force Fes behaves non-linearly to the displacement of the moving membrane x. As the membrane moves closer to the actuation pad, the electrostatic force increases rapidly as (g − x) diminishes. The membrane can be actuated and held static at displacements of up to one-third of the gap (g/3), where the structural restoring force is still sufficient to hold the membrane against the electrostatic force. When a larger actuation voltage is applied and the membrane travels beyond g/3, the membrane’s restoring force could no longer match the increasingly strong electrostatic force, causing the membrane to collapse toward the actuation pad [3]. As the membrane moves closer to the actuation pad the electrostatic force becomes much stronger, accelerating the membrane further. The membrane would eventually slams against the contacting lines at high velocity. The amount of voltage needed for the membrane to just exceed g/3 and trigger the instability that turns the switch ON is known as the threshold or pull-in voltage Vpi . Fig. 4 shows the simulated displacement and velocity of the membrane based on the electrostatic force model in Eq. (1) and the dynamic model in Eq. (2) when a step actuation voltage is applied. The geometrical parameters of the MEMS switch used in the model are tabulated in Table 1. The Vpi was calculated to be 65 V but the actual applied actuation voltage Va was set higher at 80 V. This is a common practice to ensure that the MEMS switch is successfully actuated. The TeraVicta TT712-68CSPswitch for example, was found to start switching 10–15 V below the recommended actuation voltage. From the figure, after exceeding the g/3 (about 1.2 m), the membrane accelerates rapidly towards the contact, leading to a high contact velocity of about 0.39 m/s. The maximum distance
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Fig. 4. Simulated displacement and velocity profiles of MEMS switch membrane when a step actuation voltage of 80 V is applied. The membrane accelerates rapidly as it gets closer to the actuation electrode.
travelled xmax by the moving membrane is only 2.5 m as the distance between the membrane resting position and the conducting lines surface is shorter than the gap g between the membrane and the actuation pad. This is illustrated in Fig. 1(a). The momentum of the high velocity impact causes the membrane to bounce away from the contact surface, leading to electrical discontinuity. The bouncing continues until the momentum of the membrane is exhausted. The bouncing increases the time for the membrane to completely settle down at the contact surface and therefore prolonging the time for the switching process to be completed. The high velocity impact also increases contact surfaces wear and tear, leading to mechanical and electrical failures such as fusing of contacts, transferring metals between contact surfaces and increasing the contact resistance [3].
Fig. 5. A mechanical model for RF MEMS switch including the squeeze-film damping effect.
The squeeze-film damping effect due to the gas film underneath the switch membrane can be added to the model by using a combination of dampers and springs aligned in series between the two parallel plates [18–20], as illustrated in Fig. 5 [21–25]. The dampers represent the viscous damping force due to the resistance of the membrane plate movement caused by the viscous flow of air, while the springs represent the elastic force contributed by the air compression between the two parallel plates. The coefficient of viscous damping force bd of the squeeze film is given by [25] bd =
3. Model of the switching dynamics
meff
d2 x + keff x = Fes dt 2
(2)
where x is the displacement of the membrane from its initial position. Fes is the applied electrostatic force given by Eq. (1). Initially, when no voltage (0 V) is applied to the switch, the initial conditions are x = 0, dx/dt = 0 at t = 0. This dynamic model is only valid for x ≤ g, which is the working range of the MEMS switch. Table 1 MEMS switch parameters used in the simulation of membrane displacement and velocity [12]. Parameter
Symbol
Value
Effective area Permittivity of air Gap Maximum distance travelled Effective mass Effective spring constant Threshold/Pull-in voltage
A ε0 g xmax meff Keff VPi
15.6 × 10−9 m2 8.85 × 10−12 C2 /N m2 3.6 × 10−6 m 2.5 × 10−6 m 3 × 10−9 kg 42 N/m 65 V
m,n,odd (mn)
m2 + (n/)
2
m2 + (n/)
2
2 2
(3)
+ ( 2 /4 )
and the coefficient of the elastic force ke is given by ke =
The membrane’s dynamic response when the switch closes can be modelled as the response of a non-linear mass-spring-damper system [7]. The model assumes that the membrane does not deform and remain parallel to the actuation pad during the entire actuation and release processes. These assumptions are reasonable as the gap between the moving membrane and the contact surfaces is much lesser than the thickness of the membrane itself in most MEMS switch designs. Hence, the membrane’s dynamic is represented by a lumped effective mass meff with an effective spring constant keff as shown in Eq. (2) [7].
64Pa A 6 g
64 2 Pa A 8 g
m,n,odd (mn)
2
1
m2 + (n/)
2 2
(4)
+ ( 2 /4 )
where m and n are odd integers, Pa is the ambient pressure, A is the area of the squeeze film, g is the thickness of the gas film which is also the gap of the two plates, is the aspect ratio of the rectangular plate and is the squeeze number which can be approximated by [23].
= 2
1+
1 2
(5)
Therefore, by including the squeeze-film effect, Eq. (2) can now be expanded to: meff
d2 x dx + (keff + ke ) x = Fes + bd dt dt 2
(6)
If the switch is moving at a high speed, the air film underneath the moving membrane is compressed and fails to escape. Thus the elastic force in Eq. (6) would dominate and the viscous damping force caused by the air flow can be neglected [25]. In addition, the damping only affects the ringing response after contact has been made but does not significantly affect the dynamics during the switch initial closing period [3]. If the MEMS switch is vacuum packed, the squeeze-film effect can be ignored. The squeeze-film effect can also be reduced significantly by adding holes or slots on the membrane to create more paths for the trapped air underneath the membrane to circulate [25]. In this work, the displacement and velocity of the membrane generated by the different actuation voltage waveforms are simulated using the model described by Eqs. (1) and (2). A fast-switching, small-gap design and vacuum-packed MEMS switch is assumed. Admittedly, the above model is simple and thus may be insufficient to model all the features of different MEMS switch designs.
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The model serves to provide an insight to the dynamics of a generic membrane-type MEMS switch. Similar study can be extended to a particular switch design with an updated model of the MEMS switch. Ideally, the velocity of the moving membrane should be zero just before it touches the contact surface in order to minimize the impact momentum. This would prevent the membrane from bouncing away. Therefore, the actuation voltage applied to the switch must be reduced to slow down the membrane as it approaches the contact point. However, the actuation waveform should accomplish this without substantially slowing down the entire switching process. Investigation into the energy supplied to the switch was carried out for further insights to the performance of the dual pulse waveforms in mitigating bounces. Ideally, the energy required to turn on the switch, Eron , is only for compensating the membrane’s spring energy, with the assumptions that all other forces (contact force, damping force, etc.) are energy conserving and power dissipated during actuation process is negligible. An additional energy Ea may be added to ensure that all switches, despite the variation in their parameters, will turn on successfully. Thus the total energy supplied Es = Eron + Ea . The total energy supplied is the integral of the product of applied electrostatic force Fes and velocity v(t) as:
Es =
t1st
Fes · v dt
(7)
0
since v dt = dx, the energy equation can be simplified to
Es =
xmax
Fes dx.
(8)
0
4. Dual pulse actuation waveforms Dual pulse actuation voltage waveform consists of a large initial voltage to accelerate the membrane towards the contact, followed by a small voltage to hold the membrane in contact. Having a smaller voltage at the later part of the actuation waveform reduces the velocity of the membrane as it approaches the contact. This prevents the membrane from slamming onto the contact surface and bouncing back. Fig. 6 shows notable dual pulse waveforms apart from the regular DP waveform shown earlier in Fig. 2. The EDP waveform shown in Fig. 6(a) gradually increases the large actuation voltage pulse at the beginning of the ON period, rather than a large constant pulse as in the DP waveform. The actuation time tA is tuned precisely to ensure that the switch does not bounce while maintaining a fast switching time. The key advantage of this waveform is the simplicity in its implementation, where only a simple resistor-capacitor network needs to be added to the DP driving circuit. In addition, the EDP waveform has shown to minimize dielectric charging when the switch is actuated continuously, thereby prolonging the switch lifetime [5,15,17]. In Fig. 6(b), the SL waveform turns off the voltage completely after the large initial voltage at time tA . Once the membrane has landed on the contact point at time tH , the waveform resumes with a small holding voltage [3]. The off time allows the membrane to decelerate quickly. The time tA and tH are calculated based on the energy balance between the membrane system and the work done by the electrostatic force. This method requires accurate knowledge of the switch parameters such as the effective stiffness of the switch membrane for calculating the precise timing for each individual switch. The LCA waveform also consists of two separate pulses, one for actuating and the other for holding the membrane, with an off time in between them. However, instead of a step on and off transitions, the LCA waveform follows a cosine increment and decrement during the on and off transitions. The time t1 to t5
Fig. 6. Different dual-pulse actuation waveforms: (a) exponentially saturating dualpulse (EDP); (b) soft-landing waveform (SL); and (c) learning control waveform (LCA).
shown in Fig. 6(c) are tuned incrementally and iteratively based on the switch output signal continuity measured using a sensor [4]. The self-adjustment of the actuation waveform ends when the output signal exhibits smooth transition, which indicates that a bounce free contact has been achieved. This closed-looped actuation strategy does not require prior information about the switch parameters. However, it requires additional sensory device and an active driver system to perform the tuning and generate the precise actuation waveform for each individual switch. As MEMS switches are slightly different in their geometrical and mechanical properties, the required optimal actuation voltage waveform also varies for each switch. In the next section, the robustness of the DP and EDP waveforms in the presence of switch parameters and voltage waveform variations is investigated and compared. The SL and LCA actuation waveforms have the advantage that the voltage applied is always at optimum and thus variation in the switch parameters is not a concern. However, in order to maintain the optimum voltage, calculations (SL) and measurements (LCA) must be made for each switch. Moreover, complex active driver circuitry is required to generate the optimal waveforms. For these reasons, the applications of these waveforms may not be suitable for applications that employ a large number of MEMS switches.
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Fig. 7. Simulated displacement and velocity profiles of the switch membrane under different dual-pulse actuation waveforms: (a) DP actuation waveform; (b) EDP actuation waveform; (c) SL actuation waveform and (d) LCA waveform.
5. Robustness analysis Fig. 7 shows the simulated displacement and velocity profiles of the switch membrane when the DP, EDP, SL and LCA voltage waveforms are applied with their respective optimal actuation times. All waveforms have shown to significantly reduce the contact velocity just before contact is made at x = 2.5 m, as compared to the large approaching velocity of about 0.39 m/s produced by the conventional step actuation voltage. As shown in Fig. 7, the SL waveform completed the switching process in the fastest time at about 25.2 s. This is because the membrane is accelerated rapidly by the large initial step voltage. The ensuing voltage-off period allows the membrane to slow down quickly before reaching the contact. As expected, the EDP waveform produced the slowest switching speed at about 41 s due to the membrane slow initial acceleration. The robustness of the voltage waveforms when the gap g between the membrane and the contacting surfaces varies was investigated. This imitates the scenario in the event that the thickness of the sacrificial layer deviates from its set value in the fabrication process. Other switch parameters such as the effective area A of the membrane-actuation pad parallel plate and effective spring constant keff are all assumed to remain unchanged. A ± 6% variation from the nominal gap of 3.6 m was simulated. The maximum distance travelled by the membrane xmax was varied accordingly. Since the gap may vary up to +6%, the actuation waveforms (actuation time tA in this case) were adjusted so that all MEMS switches (within the ±6% gap variation) could be actuated successfully. The peak voltage Vp and holding voltage Vh were still fixed at 80 V and 40 V, but the actuation time tA of both the DP and EDP
actuation waveforms were increased so that the switch with the largest gap (g + 6%) could be actuated successfully with minimal contact velocity. The waveforms were then applied to all switches with gap variation from −6 to 6%. The optimal waveform settings for gap g and g + 6% are tabulated in Table 2 to show the changes in the waveforms’ actuation time. Fig. 8 shows the simulated first contact time t1st and membrane contact velocity vc of switches with different gap g when the voltage waveform tuned for g + 6% is applied. As shown in Fig. 8(a), the switch closes faster (as shown) for smaller gap as the electrostatic force Fes is inversely proportional to the square of gap g. From Fig. 8(b), the vc at g + 6% gap are nearly zero for both DP and EDP waveforms since the waveforms were optimized for this condition. The vc produced by the DP waveform has shown to vary more across the different gaps compared to the EDP waveform. Hence, the waveform is more susceptible to the gap variations. Another approach to assess the robustness of the voltage waveforms to switch parameters variation is by varying the applied tA instead. For example, say the selected optimal tA for a specific switch design is 21 s. 21 s is then applied to the final production switch that has a different optimal actuation time at 17 s due to the variation in the switch parameters picked up during manufacturing. This means that additional 4 s has been added on top of the optimal actuation time. Admittedly, there is no clear relationship between the switch parameters variation and the optimal tA being studied in this paper. This paper focuses on the robustness of the actuation waveform when there is a variation in the switch parameters. The actual relationship between the parameters variations with the changes in the optimal actuation time was not considered.
Table 2 Comparison of MEMS switch dynamic response for nominal gap (g) and maximum gap variation (g = g + 6%) at their optimum waveform setting. Actuation waveform
DP EDP
Vp (V)
80 80
Vh (V)
40 40
Gap = g
Gap = g + 6%
tA (s)
t1st (s)
vc (m/s)
tA (s)
t1st (s)
vc (m/s)
17.1 26.4
31.2 41.0
≈0 ≈0
21.7 29.1
33.1 43.7
≈0 ≈0
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Fig. 8. (a) First contact time and (b) Contact velocity of the membrane of switch with different gap when the same actuation waveform is applied.
Fig. 9. (a) First contact time and (b) contact velocity when tA is increased from its optimal value.
The peak voltage Vp and holding voltage Vh were both retained at 80 V and 40 V throughout the entire simulation. Starting from the optimal value, the tA of both DP and EDP waveforms were incremented by 1 s at each iterations. The first contact time and contact velocity were recorded and plotted in Fig. 9. From Fig. 9(a), the first contact time generated by both DP and EDP waveforms is reduced when the actuation time tA is increased from its optimal value. The EDP waveform generally took approximately 10 s extra to achieve first contact compared to the DP waveform due to the switch membrane slow initial acceleration. In Fig. 9(b), the EDP waveform has demonstrated to be less susceptible to the increase in the applied tA as it produces less contact velocity increment compared to the DP waveform. This is because the total energy supplied by the large voltage pulse is not affected as much by tA due to the exponential nature of the waveform.
Since the energy required to turn on the switch, Eron , is only for compensating the membrane’s spring energy, Eron must equals the elastic energy: Eron =
1 k · x2 2 eff max
(9)
The total energy supplied by the voltage waveform until just before contact, Es , was computed numerically using Eq. (8) based on the displacement profiles generated from earlier simulations. Ideally, to ensure zero velocity upon contact and hence no bouncing, Es should be equal to Eron . Excess energy (Es − Eron ) may cause bouncing. Fig. 10(a) shows the excess energy supplied to the switch when the DP and EDP waveforms optimized for g + 6% were applied to switches with varying gaps. The DP waveform has shown to supply
Fig. 10. (a) Excessive energy supplied during actuation process when the same waveform is applied to the device with variation in gap. (b) Total energy supplied Es during actuation process when actuation waveform shifts from their respective optimum settings.
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Fig. 11. Experiment set-up for testing both the DP and EDP actuation waveforms.
more excess energy compared to the EDP waveform. Fig. 10(b) shows the total energy supplied Es by both DP and EDP voltage waveforms under varying actuation time tA . The energy supplied by the DP voltage waveform increases more significantly and hence it is more sensitive to tA .
Fig. 13. (a) The first contact time, t1st and (b) the bouncing duration, tb as the actuation time tA of both DP and EDP actuation waveforms increased from their respective optimal settings.
6. Experiment results
Fig. 12. Oscilloscope plots showing the (a) DP and (b) EDP actuation waveforms and the respective switched DC signal.
Fig. 11 shows the block diagram of the experimental setup to observe the bouncing of the MEMS switch when the DP and EDP actuation waveforms were applied. SL and LCA waveforms were not considered as bouncing should not occur if these waveforms were tuned optimally for each individual switch. The MEMS switch used is the commercially available TT712-68CSP SPDT RF MEMS switch fabricated by TeraVicta (now defunct) [10]. For both the DP and EDP actuation waveforms, the MEMS switch was actuated at 200 Hz, with a high peak voltage at 80 V applied for tA followed by a 50 V holding voltage for the rest of the on time. In order to facilitate the observation of the bouncing effect, a small DC voltage was applied at the input pin of the MEMS switch and the output of the switch is captured using oscilloscope (Tektronix TDS 1002B). A 200 Hz, 0–5 V square wave signal was applied to the voltage driver circuit to generate the desired actuation waveform. Note that the DP and EDP waveforms generation differs only in the addition of R-C network in the driver circuit [5]. First, the actuation time tA of both waveforms were increased slowly from 0 s until switching is made without any bouncing. For the DP waveform, switching is made without any bouncing when tA = 17 s whereas for the EDP waveform, the actuation time is longer at tA = 27 s. This is in agreement with the simulation analysis. To assess the sensitivity of the waveforms to switch parameters variation, tA is then varied to simulate the optimal time that different MEMS switches required. Snapshots of the MEMS switch response captured using oscilloscope are shown in Fig. 12. CH 1 shows the DC signal at the output terminal and CH 2 shows the actuation waveform applied. From the oscilloscope plot, the time taken for the switch to turn ON the first time t1st was measured.
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If the switch bounces, the settling time ts for the bouncing to settle down and the switch to be permanently ON was measured as well. In an ideal switching process, there should be no bouncing and therefore t1st = ts . Although the contact velocity of the switch membrane could not be measured in the experiment due to the unavailability of measuring apparatus, the duration of the bouncing tb = ts − t1st captured by the oscilloscope gives a good indication of the velocity. The t1st and tb when tA is increased from its optimal setting were plotted in Fig. 13. Note that t1st in the experiment does not match the simulation result quantitatively as a different MEMS switch was used in the experiment. Nonetheless, in agreement with the simulation findings, both the DP and EDP waveforms exhibit qualitatively similar t1st trends when tA is increased. The bouncing duration tb measured experimentally also shows similar trend to the change in the contact velocity simulated earlier, where both showed that bouncing is amplified as tA increases. The result also shows that the EDP waveform is less susceptible to the change in tA compared to the DP waveform, where it took up to 6 s increment in the tA before any bouncing was detected.
[4]
[5]
[6]
[7]
[9] [10] [12]
[15]
[16]
7. Conclusion [17]
Dual pulse actuation voltage waveforms reduce MEMS switch bouncing by slowing down the switch membrane prior to contact. The soft-landing (SL) and learning control voltage (LCA) waveforms have shown to provide the fastest switching speed and are immune to variations in the switch parameters. SL requires accurate knowledge of the switch parameters and LCA requires iterative measurement of the switch continuity. Therefore, they may not be suitable for applications where many MEMS switches are employed. In the ideal setting, the conventional dual pulse (DP) waveform switches faster than the exponentially saturating (EDP) dual pulse actuation voltage. However DP waveform is more sensitive to the variations in the switch parameters and actuation voltage waveform. When longer than necessary actuation voltage is applied, the EDP waveform actually switches faster than DP waveform as bouncing is minimized. EDP waveform also has the added advantage of simple implementation and minimizes charge builtup in the switch. For an optimal switching speed and minimum bouncing over a wider range of switch variations, the EDP waveform could therefore be applied. Acknowledgement This work was supported by the Malaysian Ministry of Science, Technology and Innovation (MOSTI) under ScienceFund Scheme 03-02-14-SF0002. References [1] R. Chan, R. Lesnick, D. Becher, M. Feng, Low-actuation voltage RF MEMS shunt switch with cold switching lifetime of seven billion cycles, Journal of Microelectromechanical Systems 12 (October 5) (2003) 713–719. [2] X. Yuan, J.C.M. Hwang, D. Forehand, C.L. Goldsmith, Modeling and characterization of dielectric-charging effects in RF MEMS capacitive switches, IEEE MTT-S International Microwave Symposium Digest (June) (2005) 753–756. [3] D.A. Czaplewski, C.W. Dyck, H. Sumali, J.E. Massad, J.D. Kuppers, I. Reines, W.D. Cowan, C.P. Tigges, A soft-landing waveform for actuation of a
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Biographies Wallace S.H. Wong received the B.Eng. degree in electrical and electronic engineering and the Ph.D. degree in motor drives and advanced control from Bristol University, Bristol, U.K., in 1999 and 2003 respectively. After his doctoral work, he looked into actuating MEMS micromotor and microswitches, adapting improvement techniques used for driving their much larger cousins. He is also keen on finding novel applications for MEMS devices and has recently ventured into combining MEMS, RFID and other wireless technologies for accurate indoor positioning. He is currently the Director of the Research Office at Swinburne University of Technology (Sarawak Campus) in Kuching, Malaysia. Chean Hung Lai received the B.Eng. degree in robotics and mechatronics in 2006 and the Ph.D. degree in mechatronics engineering from Swinburne University of Technology, Sarawak, in 2012. His research interests include the reliability studies of microelectromechanical systems (MEMS) switches, intelligent sensor, RFID technology, battery management and robotic systems.