# Novel High-Capacitance-Ratio MEMS Switch: Design, Analysis and Performance Verification

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## Abstract

**:**

## 1. Introduction

## 2. Design of the High OFF/ON Capacitance Ratio RF MEMS Switch

_{0}. When the DC voltage is applied to the DC electrodes, electrostatic force pulls the metallic beam down, the RF signal will be cut by this MEMS metallic beam.

## 3. Analysis of High OFF/ON Capacitance Ratio RF MEMS Switch

#### 3.1 Restriction Factors of the Conventional RF MEMS Off-to-On Capacitance Ratio

_{0}is initial air gap between RF MEMS switch beam and the Si

_{3}N

_{4}dielectric when no actuating voltage is applied to the beam, ${\epsilon}_{r}$ is relative dielectric constant of Si

_{3}N

_{4}dielectric, t

_{e}is the thickness of Si

_{3}N

_{4}dielectric layer, A

_{up}and A

_{dn}are the overlapping electrode area of up and down state, respectively. Hence, when the fringe effect is neglected, the off-to-on capacitance ratio of conventional RF MEMS switch can be expressed as:

_{up}and A

_{dn}were constant after the switch was fabricated. Therefore, the capacitance ratio is limited by three factors, namely: (a) the relative dielectric constant ${\epsilon}_{r}$; (b) the thickness of dielectric t

_{e}; (c) the initial gap g

_{0}. These limiting factors are not resolved easily. First, when the fabrication process is determined, the relative dielectric constant ${\epsilon}_{r}$ is determined as well; second, the dielectric charging issue is serious when the thin dielectric layer is used; third, the larger initial gap g

_{0}will cause high actuating voltage. Hence, the methods used in [5,6,7] are not the most appropriate as mentioned in Section 1.

#### 3.2 The High OFF/ON Capacitance Ratio of the Proposed RF MEMS Switch

_{dn}when it is in the down state. Hence, the capacitance ${C}_{0}$, ${C}_{on}$ and ${C}_{off}$ are respectively expressed as:

^{−12}F/m, ${\epsilon}_{r}$ is relative dielectric constant, which depends on the dielectric material. According to the equation, the capacitance ratio ${r}_{c}$ is related to the electrode area ratio $x$, instead of the specific value of the ${A}_{0}$, ${A}_{up}$ and ${A}_{dn}$. The relationship between $x$ and ${r}_{c}$ is shown in Figure 5.

## 4. Fabrication, Measurements and Discussions

#### 4.1. Fabrication

_{2}layer, which acts as an insulating layer, with a thickness of 0.3 μm, was formed by thermal oxidation. Then, 0.2 μm thickness of Au was deposited and patterned to define DC bias pads afterwards and to form the CPW transmission lines. Next, thin CrSi (approximately 0.05 μm) was patterned by lifting off to form the bias lines after deposition. A Si

_{3}N

_{4}layer with thickness of 1000 Å was patterned on the top of the electrode and bias lines by plasma enhanced chemical vapor deposition (PECVD) process. 1μm Au was evaporated as the MIM floating metallic membrane. 3 μm thickness of Au, which acts as the anchors, was evaporated. Polyimide as the sacrificial layer was cut down by chemical mechanical polishing (CMP) process. The beam used 1 μm of Au. Finally, the wafer was released in a plasma dryer to avoid collapsing the membrane. The photograph of the proposed RF MEMS switch is shown in Figure 6.

#### 4.2. Measurement and Results

#### 4.2.1. Insertion Loss and Isolation

#### 4.2.2. Capacitance Ratio

#### 4.2.3. Actuation Voltage

_{e}is effective elastic coefficient, ${\epsilon}_{0}$ is dielectric constant in the free space, g

_{0}is air gap between RF MEMS switch beam and the Si

_{3}N

_{4}dielectric when no actuating voltage is applied to the beam, ${\epsilon}_{r}$ is relative dielectric constant of Si

_{3}N

_{4}dielectric, t

_{e}is the thickness of Si

_{3}N

_{4}dielectric layer, W is the width of MEMS switch beam, and L

_{d}is the length of Si

_{3}N

_{4}dielectric, respectively. The calculated value of effective elastic coefficient k

_{e}is 19.5 N/m, and the actuating voltage ${V}_{p}$ is 12.6 V approximately.

#### 4.2.4. Actuation and Releasing Time

^{5}cycles (when the test was terminated for convenience).

#### 4.3. Advancements

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Designed high-capacitance-ratio MEMS switch model. (

**a**) Conventional MEMS switch; (

**b**) The top view of the proposed MEMS switch; (

**c**) The dismantling figure of the MEMS switch. (The gold material is illustrated by yellow and green for the sake of representing different layers.)

**Figure 3.**Models of the proposed switch. (

**a**) 3D model; (

**b**) Equivalent model of down state; (

**c**) Equivalent model of up state (some details were neglected for simplification).

**Figure 5.**The relationship between $x$ and ${r}_{c}$. (

**a**) $x\in \left[0,1\right]$; (

**b**) $x\in \left[1,10\right]$.

**Figure 7.**Measurement and simulation S parameters results of the proposed high-capacitance-ratio RF MEMS switch. (

**a**) Up state; (

**b**) Down state.

**Figure 8.**The structure of the MEMS beam. (

**a**) A quarter of the beam; (

**b**) Computer simulation technology (CST) simulation of the force of the switch beam.

Reference | Insertion Loss (dB) | Insulation (dB) | Up Capacitance (fF) | Down Capacitance (pF) | Actuating Voltage (V) | Air Gap (μm) | Response Time (μs) | Capacitance Ratio |
---|---|---|---|---|---|---|---|---|

[4] | 0.08 | 42 | 83 | 50 | 8 | 2.5–3.5 | - | 600 |

[7] | 0.15 | 40 | 4–6 | 1–1.5 | 80 | ~15 | 1–20 | 250 |

[10] | 0.35 | 37 | 51 | 6 | 117.6 | 2 | - | 22 |

[11] | 0.2 | 38.5 | 24 | 1.55 | 12 | ~2 | 10–15 | 64.6 |

[12] | 0.7 | 35 | 35 | 3 | 30 | 3~5 | 7 | 85.7 |

[13] | 1.5 | 20 | 22 | 2.2 | 30 | 3.2 | - | 100 |

This paper | 0.5 | 34 | 54.2 | 20.8 | 21 | 2 | <10 | 383.8 |

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**MDPI and ACS Style**

Han, K.; Guo, X.; Smith, S.; Deng, Z.; Li, W.
Novel High-Capacitance-Ratio MEMS Switch: Design, Analysis and Performance Verification. *Micromachines* **2018**, *9*, 390.
https://doi.org/10.3390/mi9080390

**AMA Style**

Han K, Guo X, Smith S, Deng Z, Li W.
Novel High-Capacitance-Ratio MEMS Switch: Design, Analysis and Performance Verification. *Micromachines*. 2018; 9(8):390.
https://doi.org/10.3390/mi9080390

**Chicago/Turabian Style**

Han, Ke, Xubing Guo, Stewart Smith, Zhongliang Deng, and Wuyu Li.
2018. "Novel High-Capacitance-Ratio MEMS Switch: Design, Analysis and Performance Verification" *Micromachines* 9, no. 8: 390.
https://doi.org/10.3390/mi9080390