# Instability and Drift Phenomena in Switching RF-MEMS Microsystems

## Abstract

**:**

## 1. Introduction

## 2. RF-MEMS Switch as a Device Based on an Electrical Instability

_{0}is the vacuum permittivity.

_{0}is the thickness of the dielectric layer above the electrodes and ε

_{r}is its relative permittivity. More complex formulas can be derived for rectangular cantilever beams [13,14]. Complex beam geometries require simulation work in order to determine their actuation and release voltages, but in some special cases, useful approximate analytical formulas can be derived [2,15].

_{act}and V

_{rel}remain stable for an infinite time and after an infinite number of switching cycles. In the real world, instabilities and drift in both actuation and release voltages are fairly common and have different origins. The most frequent sources are charging of the dielectric, temperature variations, fabrication uncertainties, and material wear.

## 3. Instabilities Due to Dielectric Charging

## 4. Instabilities Due to Temperature Variations

_{total}and σ

_{Tamb}are the beam’s total stress and residual stress at room temperature, E is the beam’s elastic modulus, ΔT is the temperature difference, and α

_{beam}and α

_{substrate}are the LTE coefficients of the suspended beam and the substrate, respectively. The variations of beam shape, internal stress, and actuation voltage as a function of temperature are schematized in Figure 4.

_{elastic}(E) is the part of the spring constant which is stress independent and determined only by the elastic modulus E and B is a constant which depends on the beam geometry. A detailed analytical derivation of this formula is reported in [30].

## 5. Instabilities Due to Fabrication Uncertainties and Material Wear

## 6. Conclusions

## Funding

## Conflicts of Interest

## References

- Senturia, S.D. Microsystem Design; Springer Science + Business Media: New York, NY, USA, 2001. [Google Scholar]
- Rebeiz, G.M. RF-MEMS: Theory, Design and Technology; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2004. [Google Scholar]
- Witvrouw, A.; Tilmans, H.A.C.; De Wolf, I. Materials issues in the processing, the operation and the reliability of MEMS. Microelectr. Eng.
**2004**, 76, 245–257. [Google Scholar] [CrossRef] - Zhang, W.-M.; Yan, H.; Peng, Z.-K.; Meng, G. Electrostatic pull-in instability in MEMS/NEMS: A review. Sens. Actuators A Phys.
**2014**, 214, 187–218. [Google Scholar] [CrossRef] - Sadeghian, H.; Yang, C.K.; Goosen, J.F.L.; van der Drift, E.; Bossche, A.; French, P.J.; van Keulen, F. Characterizing size-dependent effective elastic modulus of silicon nanocantilevers using electrostatic pull-in instability. Appl. Phys. Lett.
**2009**, 94, 221903. [Google Scholar] [CrossRef] - Yao, J.J. RF MEMS from a device perspective. J. Micromech. Microeng.
**2000**, 10, R9–R38. [Google Scholar] [CrossRef] - Daneshmand, M.; Mansour, R.R. Redundancy RF MEMS multiport switches and switch matrices. IEEE J. Microelectromech. Syst.
**2007**, 16, 296–303. [Google Scholar] [CrossRef] - De Los Santos, H.J. RF MEMS Circuit Design for Wireless Communications; Artech House: Boston, MA, USA, 2002; ISBN 1-58053-329-9. [Google Scholar]
- Brown, E.R. RF-MEMS switches for reconfigurable integrated circuits. IEEE Trans. Microw. Theory Tech.
**1998**, 46, 1868–1880. [Google Scholar] [CrossRef] - Shekhar, S.; Vinoy, K.J.; Ananthasuresh, G.K. Surface-micromachined capacitive RF switches with low actuation voltage and steady contact. J. Microelectromech. Systems
**2017**, 26, 643–652. [Google Scholar] [CrossRef] - De Groot, W.A.; Webster, J.R.; Felnhofer, D.; Gusev, E.P. Review of device and reliability physics of dielectrics in electrostatically driven MEMS devices. IEEE Trans. Device Mater. Rel.
**2009**, 9, 90–202. [Google Scholar] [CrossRef] - Tilmans, H.A.C. MEMS components for wireless communications. In Proceedings of the 16th European Conference on Solid-State Transducers (EUROSENSORS XVI), Prague, Czech Republic, 15–18 September 2002; pp. 1–34. [Google Scholar]
- Mulloni, V.; Resta, G.; Margesin, B. Clear evidence of mechanical deformation in RF-MEMS switches during prolonged actuation. J. Micromech. Microeng.
**2014**, 24, 075003. [Google Scholar] [CrossRef] - Persano, A.; Iannacci, J.; Siciliano, P.; Quaranta, F. Out-of-plane deformation and pull-in voltage of cantilevers with residual stress gradient: Experiment and modelling. Microsyst. Technol.
**2018**. [Google Scholar] [CrossRef] - Marcelli, R.; Lucibello, A.; De Angelis, G.; Proietti, E.; Comastri, D. Mechanical modelling of capacitive RF MEMS shunt switches. Microsyst. Technol.
**2010**, 16, 1057–1064. [Google Scholar] [CrossRef] - Van Spengen, W.M. Capacitive RF MEMS switch dielectric charging and reliability: A critical review with recommendations. J. Micromech. Microeng.
**2012**, 22, 074001. [Google Scholar] [CrossRef] - Papaioannou, G.; Papapolymerou, J.; Pons, P.; Plana, R. Dielectric charging in radio frequency microelectromechanical system capacitive switches: A study of material properties and device performance. Appl. Phys. Lett.
**2007**, 90, 233507. [Google Scholar] [CrossRef] - Marcelli, R.; Papaioannou, G.; Catoni, S.; De Angelis, G.; Lucibello, A.; Proietti, E.; Margesin, B.; Giacomozzi, F.; Deborgies, F. Dielectric charging in microwave microelectromechanical Ohmic series and capacitive shunt switches. J. Appl. Phys.
**2009**, 105, 114514. [Google Scholar] [CrossRef] - Goldsmith, C.; Ehmke, J.; Malczewski, A.; Pillans, B.; Eshelman, S.; Yao, Z.; Brank, J.; Eberly, M. Lifetime characterization of RF MEMS switches. In Proceedings of the 2001 IEEE MTT-S International Microwave Sympsoium Digest, Phoenix, AZ, USA, 20–24 May 2001; p. 227. [Google Scholar] [CrossRef]
- Lamhamdi, M.; Pons, P.; Zaghloul, U.; Boudou, L.; Coccetti, F.; Guastavino, J.; Segui, Y.; Papaioannou, G.; Plana, R. Voltage and temperature effect on dielectric charging for RF-MEMS capacitive switches reliability investigation. Microelectron. Reliab.
**2008**, 48, 1248–1252. [Google Scholar] [CrossRef] - Peng, Z.; Yuan, X.; Hwang, J.C.M.; Forehand, D.I.; Goldsmith, C.L. Dielectric charging of RF MEMS capacitive switches under bipolar control-voltage waveforms. In Proceedings of the IEEE/MTT-S International Microwave Symposium, Honolulu, HI, USA, 3–8 June 2007. [Google Scholar] [CrossRef]
- Mardivirin, D.; Pothier, A.; Crunteanu, A.; Vialle, B.; Blondy, P. Charging in dielectricless capacitive RF-MEMS switches. IEEE Trans. Microwave Theory Tech.
**2009**, 57, 231–236. [Google Scholar] [CrossRef] - Barbato, M.; Cester, A.; Mulloni, V.; Margesin, B.; Meneghesso, G. Transient evolution of mechanical and electrical effects in microelectromechanical switches subjected to long term stresses. IEEE Trans. Electron Devices
**2015**, 62, 3825–3831. [Google Scholar] [CrossRef] - Rottenberg, X.; De Wolf, I.; Nauwelaers, B.K.J.C.; De Raedt, W.; Tilmans, H.A.C. Analytical model of the DC actuation of electrostatic MEMS devices with distributed dielectric charging and nonplanar electrodes. IEEE J. Microelectromech. Syst.
**2007**, 16, 1243–1253. [Google Scholar] [CrossRef] - Mulloni, V.; Colpo, S.; Faes, A.; Margesin, B. A simple analytical method for residual stress measurement on suspended MEM structures using surface profilometry. J. Micromech. Microeng.
**2013**, 23, 025025. [Google Scholar] [CrossRef] - Mulloni, V.; Solazzi, F.; Resta, G.; Giacomozzi, F.; Margesin, B. RF-MEMS switch design optimization for long-term reliability. Analog Integr. Circ. Sig. Process.
**2014**, 78, 323–332. [Google Scholar] [CrossRef] - Mulloni, V.; Lorenzelli, L.; Margesin, B.; Barbato, M.; Meneghesso, G. Temperature as an accelerating factor for lifetime estimation of RF-MEMS switches. Microelectron. Eng.
**2016**, 160, 63–67. [Google Scholar] [CrossRef] - Mulloni, V.; Sordo, G.; Margesin, B. An accelerated thermal cycling test for RF-MEMS switches. Microsyst. Technol.
**2016**, 22, 1585–1592. [Google Scholar] [CrossRef] - Chen, K.-S. Techniques in Residual Stress Measurement for MEMS and Their Applications. In MEMS/NEMS Handbook—Techniques and Applications; Springer: Berlin, Germany, 2006; pp. 1252–1328. [Google Scholar]
- Mulloni, V.; Solazzi, F.; Ficorella, F.; Collini, A.; Margesin, B. Influence of temperature on the actuation voltage of RF-MEMS switches. Microelectron Reliab.
**2013**, 53, 706–711. [Google Scholar] [CrossRef] - Mulloni, V.; Giacomozzi, F.; Margesin, B. Controlling stress and stress gradient during the release process in gold suspended micro-structures. Sens. Actuators A Phys.
**2010**, 162, 93–99. [Google Scholar] [CrossRef] - Persano, A.; Quaranta, F.; Capoccia, G.; Proietti, E.; Lucibello, A.; Marcelli, R.; Bagolini, A.; Iannacci, J.; Taurino, A.; Siciliano, P. Influence of design and fabrication on RF performance of capacitive RF MEMS switches. Microsyst. Technol.
**2016**, 22, 1741–1746. [Google Scholar] [CrossRef] - Yu, A.B.; Liu, A.Q.; Zhang, Q.X.; Hosseini, H.M. Effects of surface roughness on electromagnetic characteristics of capacitive switches. J. Micromech. Microeng.
**2006**, 16, 2157–2166. [Google Scholar] [CrossRef] - Matrecano, M.; Memmolo, P.; Miccio, L.; Persano, A.; Quaranta, F.; Siciliano, P.; Ferraro, P. Improving holographic reconstruction by automatic Butterworth filtering for microelectromechanical systems characterization. Appl. Opt.
**2015**, 54, 3428–3432. [Google Scholar] [CrossRef] - Sawant, V.B.; Mohite, S.S.; Cheulkar, L.N. Comprehensive contact material selection approach for RF MEMS switch. Mater. Today Proc.
**2018**, 5, 10704–10711. [Google Scholar] [CrossRef] - Mulloni, V.; Resta, G.; Giacomozzi, F.; Margesin, B. Influence of fabrication tolerances on the reliability of RF-MEMS capacitive switches. In Proceedings of the 2015 XVIII AISEM Annual Conference, Trento, Italy, 3–5 February 2015; pp. 1–4. [Google Scholar] [CrossRef]
- Mulloni, V.; Barbato, M.; Meneghesso, G. Long-term lifetime prediction for RF-MEMS switches. J. Micromech. Microeng.
**2016**, 26, 74004–74012. [Google Scholar] [CrossRef]

**Figure 1.**Typical clamped–clamped (

**a**) and cantilever (

**b**) switch configurations. Both configurations use mobile suspended beams as actuators.

**Figure 2.**Scheme of capacitance–voltage (C–V) curves of a capacitive MEMS switch with charging phenomena. When the bias is applied, the actuation and release voltages can drift to higher values (positive charging) or lower values (negative charging).

**Figure 3.**C–V curve of a dielectric-less capacitive switch before and after applying a positive bias at 60 V for 12 hours. Charging phenomena are strongly reduced (small shift of the central point) and narrowing effects become visible.

**Figure 4.**Scheme of the interrelation between temperature, beam shape, internal stress, and actuation voltage in a clamped–clamped beam. The precise value of the critical temperature depends on the beam’s geometry and material.

**Figure 5.**Micrograph (

**a**) and surface profile (

**b**) of the mobile membrane of a MEMS capacitive switch at different temperatures. The surface profile was measured with an optical profiler along the red dashed line (

**a**).

**Figure 6.**Evolution of the suspended beam shape at different (increasing) voltages for the RF-MEMS switch reported in Figure 5. The lines have been recorded with an optical profiler while biasing the switch.

**Figure 7.**C–V curve of a capacitive MEMS switch. The inset reports the same curve expanded in the vertical direction. The first and the second collapse are clearly visible.

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Mulloni, V.
Instability and Drift Phenomena in Switching RF-MEMS Microsystems. *Actuators* **2019**, *8*, 15.
https://doi.org/10.3390/act8010015

**AMA Style**

Mulloni V.
Instability and Drift Phenomena in Switching RF-MEMS Microsystems. *Actuators*. 2019; 8(1):15.
https://doi.org/10.3390/act8010015

**Chicago/Turabian Style**

Mulloni, Viviana.
2019. "Instability and Drift Phenomena in Switching RF-MEMS Microsystems" *Actuators* 8, no. 1: 15.
https://doi.org/10.3390/act8010015