# Research on Novel CMUTs for Detecting Micro-Pressure with Ultra-High Sensitivity and Linearity

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory and Design

#### 2.1. Basic Theory of CMUT for Micro-Pressure Detection

#### 2.2. Design of the Structure

#### 2.2.1. CMUT of Inverted Frustum Cone-Like Cavity

#### 2.2.2. CMUT of Slotted Membrane

## 3. Simulation and Comparison of CMUTs

#### 3.1. Simulation and Analysis

#### 3.1.1. Simulation of C1

#### 3.1.2. Simulation of C2

#### 3.1.3. Simulation of C3–C5

#### 3.2. Comparison and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of a typical capacitive micromachined ultrasonic transducer (CMUT) cell (C1).

**Figure 3.**Schematic diagrams of different CMUT designs: C3, C4, and C5: (

**a**) front view of C3; (

**b**) top view of C3; (

**c**) front view of C4; (

**d**) top view of C4; (

**e**) front view of C5; (

**f**) top view of C5.

**Figure 4.**(

**a**) Resonance frequency of C1 with different cavity heights of 2 $\mathsf{\mu}\mathrm{m}$, 2.5 $\mathsf{\mu}\mathrm{m}$, 3 $\mathsf{\mu}\mathrm{m}$, 3.5 $\mathsf{\mu}\mathrm{m}$, and 4 $\mathsf{\mu}\mathrm{m}$ for pressure detection in the range of 0–10 kPa. (

**b**) Resonance frequency of C1 with different cavity heights of 3 $\mathsf{\mu}\mathrm{m}$ for pressure detection in the range of 0–10 kPa.

**Figure 5.**(

**a**) Pressure sensitivity and linear fit of C1 with cavity heights of 2 $\mathsf{\mu}\mathrm{m}$, 2.5 $\mathsf{\mu}\mathrm{m}$, 3 $\mathsf{\mu}\mathrm{m}$, 3.5 $\mathsf{\mu}\mathrm{m}$, and 4 $\mathsf{\mu}\mathrm{m}$ and membrane thickness of 5 $\mathsf{\mu}\mathrm{m}$ under pressures of 0–10 kPa. (

**b**) Pressure sensitivity and linear fit of C1 with membrane thicknesses of 4 $\mathsf{\mu}\mathrm{m}$, 4.5 $\mathsf{\mu}\mathrm{m}$, 5 $\mathsf{\mu}\mathrm{m}$, 5.5 $\mathsf{\mu}\mathrm{m}$, and 6 $\mathsf{\mu}\mathrm{m}$ and cavity height of 5 $\mathsf{\mu}\mathrm{m}$ under pressures of 0–10 kPa.

**Figure 7.**(

**a**) Pressure sensitivity of C2 under pressures of 0–10 kPa (0 $\mathsf{\mu}\mathrm{m}\text{}$≤${r}_{\mathrm{c}}$ ≤ 200 $\mathsf{\mu}\mathrm{m}$ ). (

**b**) Comparison of resonant frequencies of C1 and C2 under pressure of 0 Pa (0 $\mathsf{\mu}\mathrm{m}\text{}$ ≤${r}_{\mathrm{c}}$ ≤ 200 $\mathsf{\mu}\mathrm{m}$ ).

**Figure 8.**Collapse voltage of C2 with different values of bottom radius of cavity under pressure of 10 kPa (0 $\mathsf{\mu}\mathrm{m}\text{}$≤${r}_{\mathrm{c}}$ ≤ 200 $\mathsf{\mu}\mathrm{m}$ ).

**Figure 9.**(

**a**) Pressure sensitivity of C3 with different groove widths (n = 3, ${g}_{1}$= 3.5$\mathsf{\mu}\mathrm{m}$, ${g}_{2}$ = 3.5$\mathsf{\mu}\mathrm{m}$ ). (

**b**) Resonance frequency of C3 with different adjacent groove spacing (n = 3, ${g}_{2\text{}}$ = 3.5$\mathsf{\mu}\mathrm{m}$, ${t}_{\mathrm{i}}$ = 3.5$\mathsf{\mu}\mathrm{m}$ ).

**Figure 10.**Pressure sensitivity of C3 with different numbers of grooves (${t}_{\mathrm{i}\text{}}$= 3.5 $\mathsf{\mu}\mathrm{m}$, ${g}_{1\text{}}$ = 3.5 $\mathsf{\mu}\mathrm{m}$, ${g}_{2}$ = 3.5 $\mathsf{\mu}\mathrm{m}$ ).

$\mathit{\rho}/\mathbf{k}\mathbf{g}{\mathbf{m}}^{-3}$ | $\mathit{E}/\mathbf{G}\mathbf{P}\mathbf{a}$ | $\mathit{v}$ | ${\mathit{\epsilon}}_{\mathit{\gamma}}$ | |
---|---|---|---|---|

Top electrode (Au) | 19,300 | 70 | 0.44 | - |

Membrane (Si) | 2332 | 169 | 0.29 | 11.7 |

Vacuum gap | - | - | - | 1 |

Insulation (SiO_{2}) | 2200 | 70 | 0.17 | 4.2 |

**Table 2.**Pressure sensitivity and linear fit of C3 with a single 2 $\mathsf{\mu}\mathrm{m}$ width groove.

Depth of Groove/μm | Sensitivity/(Hz/kPa) | R-Square |
---|---|---|

0 | 93.42 | 0.9963 |

0.5 | 107.84 | 0.9970 |

1 | 137.89 | 0.9980 |

1.5 | 196.02 | 0.9988 |

2 | 299.82 | 0.9994 |

2.5 | 477.34 | 0.9995 |

3 | 751.41 | 0.9997 |

3.5 | 1006.40 | 0.9999 |

4 | 1208.23 | 0.9999 |

4.5 | 1132.88 | 0.9999 |

C3 | C4 | C5 | |
---|---|---|---|

${\mathit{V}}_{collapse}$(V) | 298 | 299 | 299 |

$\mathbf{Radius}\text{}{\mathit{r}}_{\mathit{m}}\left(\mathsf{\mu}\mathbf{m}\right)$ | $\mathbf{Thickness}\text{}\mathit{h}\left(\mathsf{\mu}\mathbf{m}\right)$ | $\mathbf{Cavity}\text{}\mathbf{Height}\text{}{\mathit{d}}_{\mathbf{0}}\left(\mathsf{\mu}\mathbf{m}\right)$ | |
---|---|---|---|

C1–C5 | 200 | 5 | 3 |

C2 | C3–C5 | C3 | C4 | C5 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{r}}_{\mathit{c}}$ | ${\mathit{g}}_{\mathbf{1}}$ | ${\mathit{g}}_{\mathbf{2}}$ | ${\mathit{t}}_{\mathit{i}}$ | ${\mathit{s}}_{\mathbf{1}}$ | ${\mathit{s}}_{\mathbf{2}}$ | ${\mathit{s}}_{\mathbf{3}}$ | ${\mathit{s}}_{\mathbf{4}}$ | ${\mathit{s}}_{\mathbf{5}}$ | ${\mathit{u}}_{\mathbf{1}}$ | ${\mathit{u}}_{\mathbf{2}}$ | ${\mathit{u}}_{\mathbf{3}}$ | ${\mathit{u}}_{\mathbf{4}}$ | ${\mathit{u}}_{\mathbf{5}}$ |

50 | 2 | 3.5 | 3.5 | 5.5 | 4.5 | 3.5 | 2.5 | 1.5 | 1.5 | 2.5 | 3.5 | 4.5 | 5.5 |

$\mathbf{The}\text{}\mathbf{Maximum}\text{}\mathbf{Displacement}/\mathsf{\mu}\mathbf{m}$ | Enhancement | |
---|---|---|

C1 | 0.2510 | - |

C2 | 0.2912 | 16.01% |

C3 | 0.5126 | 104.22% |

C4 | 0.5128 | 104.30% |

C5 | 0.5132 | 104.46% |

Sensitivity (Hz/kPa) | Enhancement | R-Square | Enhancement | |
---|---|---|---|---|

C1 | 93.41 | - | 0.9968 | - |

C2 | 122.17 | 30.79% | 0.9985 | 0.17% |

C3 | 1832.06 | 1861.31% | 0.9998 | 0.30% |

C4 | 1828.50 | 1857.50% | 0.9998 | 0.30% |

C5 | 1797.61 | 1824.43% | 0.9998 | 0.30% |

Ref. | Structure of Membrane | Size of Membrane | Thickness of Membrane | Frequency | Displacement | Collapse Voltage | Sensitivity |
---|---|---|---|---|---|---|---|

[21] | Not slotted | 400 μm | 5 μm | 200 kHz | 0.53 μm | >500 V | 50.57 Hz/kPa |

[32] | Not slotted | 0.5 mm | 3 μm | - | 0.34 nm | 63 V | 0.2 m V/Pa |

[33] | Slotted | 0.38 mm | 5 μm | 70 kHz | 6.67 nm | 10.47 V | 3.16 m V/Pa |

[34] | Not slotted | 2.43 mm | 3 μm | 1.11 MHz | 0.245 μm | 214 V | $5.33\times $10^{−6} pF/Pa |

Slotted | 1.5 mm | 3 μm | 528.57 kHz | 0.6643 μm | 120 V | $3.87\times $10^{−5} pF/Pa | |

This work | Not slotted | 200 μm | 5 μm | 450.63 kHz | 0.25 μm | 454 V | 93.41 Hz/kPa |

Slotted | 200 μm | 5 μm | 299.08 kHz | 0.51 μm | 298.4 V | 1832.06 Hz/kPa |

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## Share and Cite

**MDPI and ACS Style**

Ding, Q.; Wang, H.; Zhang, H.; Huang, X.; Sun, X.; Qin, Z.; Ren, R.; Zhu, J.; He, C.; Zhang, W.
Research on Novel CMUTs for Detecting Micro-Pressure with Ultra-High Sensitivity and Linearity. *Micromachines* **2021**, *12*, 1340.
https://doi.org/10.3390/mi12111340

**AMA Style**

Ding Q, Wang H, Zhang H, Huang X, Sun X, Qin Z, Ren R, Zhu J, He C, Zhang W.
Research on Novel CMUTs for Detecting Micro-Pressure with Ultra-High Sensitivity and Linearity. *Micromachines*. 2021; 12(11):1340.
https://doi.org/10.3390/mi12111340

**Chicago/Turabian Style**

Ding, Qi, Hongliang Wang, Hanqiang Zhang, Xiao Huang, Xiaolei Sun, Zhenjie Qin, Rui Ren, Jiajun Zhu, Changde He, and Wendong Zhang.
2021. "Research on Novel CMUTs for Detecting Micro-Pressure with Ultra-High Sensitivity and Linearity" *Micromachines* 12, no. 11: 1340.
https://doi.org/10.3390/mi12111340