# 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

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**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