# Investigation of New Accelerometer Based on Capacitive Micromachined Ultrasonic Transducer (CMUT) with Ring-Perforation Membrane

^{*}

## Abstract

**:**

## 1. Introduction

_{2}concentration was investigated in 2016 [14]; and a humidity sensor based on a capacitive micromachined ultrasonic transducer (CMUT) was proposed in 2019 [15,16].

## 2. Theoretical Analysis of CMUT Acceleration Sensor

^{2}. The following is according to its definition:

_{2}insulation layer, and Si substrate. As the structural unit is circular, the Si elastic membrane has a radius (R), thickness (h), and cavity height (g). The overall structure has a radius of R. The overall parameters of the CMUT structure are shown in Table 1, primarily detailing various parameters of the Si membrane material, such as structural dimensions, Young’s modulus (E), Poisson’s ratio (ν), and material density (ρ).

## 3. The CMUT Ring-Perforation Membrane Structure Study

#### 3.1. Analysis of the Effect of the Number of Perforations on Acceleration Sensitivity

_{2}perforations is taken as 70 μm for d

_{1}and 30 μm for d

_{2}. After determining the voltage, radius of the perforations, and the position of the perforations, the study is carried out for the structures with the number of perforations of 0, 3, 6, 9, 12, 18, 24, and 36. The resonant frequency versus acceleration curves are shown in Figure 4—a resonant frequency variation curve with acceleration for the structure with 24 perforations. It can be seen from the figure that the resonant frequency of the device still varies linearly with acceleration at different numbers of perforations, and the linearity is well maintained.

#### 3.2. Analysis of the Effect of the Perforation Radius on Acceleration Sensitivity

_{2}perforation position of 30 μm. As shown in Figure 6, it is a schematic diagram of half of the CMUT structure. The study examines partial perforation radii of 5 μm, 7 μm, and 9 μm. As depicted, when the circular perforations are formed, the position of the perforations remains constant. During the increase in perforation radius, the equivalent thickness of the membrane decreases.

#### 3.3. Analysis of the Effect of C_{2} Perforation Position on Acceleration Sensitivity

_{1}is kept as far away from the electrode as possible. Figure 9 illustrates the C

_{2}perforation positions, denoted as d

_{2}, are 20 μm, 30 μm, and 40 μm, respectively, in schematic diagrams of two-dimensional structures.

_{2}(denoted as d

_{2}) while keeping the C

_{1}perforation position (d

_{1}) fixed at 70 μm. The analysis is carried out at an applied voltage of 1.6 V, with a number of perforations of 24 and a radius of perforations of 7 μm. An acceleration load and an electrostatic load are applied to the structure at C

_{2}position d

_{2}taken as 10 μm, 20 μm, 30 μm, 40 μm, 50 μm, and 70 μm to study the trend of resonance frequency variation. From Figure 10, it is known that the resonant frequency decreases with the increase in acceleration at different perforation positions. Additionally, the linearity of the frequency response curve of the structure is well maintained under different perforation positions.

_{2}position d

_{2}is increased from 10 μm to 70 μm. The acceleration sensitivity when d

_{2}is taken as 10 μm is increased by 50% compared to when d

_{2}is 50 μm. Compared to the acceleration sensitivity at d

_{2}of 70 μm, the acceleration sensitivity increases by 70% at d

_{2}of 10 μm and 13% at d

_{2}of 50 μm. Meanwhile, from Figure 8b, it can be seen that as C

_{2}is closer to the edge of the membrane, the resonant frequency of the device is smaller. As shown in Table 4, in order to ensure the stability of the structure, this paper selects the C

_{2}position of 30 μm for the study. Meanwhile, from Figure 11b, it can be seen that C

_{2}is closer to the edge of the membrane. The resonant frequency of the device is smaller. As shown in Table 4, in order to ensure the stability of the structure, this paper selects the C

_{2}position of 30 μm for the study.

#### 3.4. Analysis of the Effect of Voltage on Acceleration Sensitivity

_{2}perforation position d

_{2}of 30 μm are simulated. The longitudinal displacement of the membrane is calculated for different voltages with only electrostatic force applied. As shown in Figure 12, the membrane displacement increases as the voltage increases. In this case, the membrane displacement of the device at a voltage of 1.6 V is 0.065 μm, while the device perforation height is 0.2 μm, and the device has not reached the maximum displacement during collapse at this voltage.

^{−9}MPa, which is much smaller than the yield strength of silicon, 7000 MPa. Therefore, both the applied voltage and the structural design are reasonable.

## 4. Contrast and Discussion

_{2}perforation position moves closer to the membrane edge when only the C

_{2}perforation position d

_{2}is changed. A 130% increase in acceleration sensitivity is achieved at 10 μm for the d

_{2}position, and a 40% increase in acceleration sensitivity is achieved at 70 μm for the d

_{2}position. The CMUT ring-perforation membrane structure increases the acceleration sensitivity by 100% compared with the traditional structure of CMUT. In the study of the relationship between voltage and acceleration sensitivity, as the voltage increases, the acceleration sensitivity will be higher, and the elastic membrane displacement will be larger.

## 5. Summary and Prospects

_{2}perforation position d

_{2}from 70 μm to 10 μm, and acceleration sensitivity increased by 70%. An increase in the number of perforations and perforation radius causes an increase in acceleration sensitivity, and the closer the C

_{2}perforation location is to the edge of the membrane, the higher the acceleration sensitivity. In this paper, the feasibility of acceleration measurement based on CMUT arrayed sensors is verified by simulation. Due to their excellent resonance characteristics, better stability, and array integration, CMUT sensors have great advantages in future miniaturization and multi-functionalization, with more and more in-depth research on CMUT sensors.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**(

**a**) Resonant frequency versus acceleration curves for the number of perforations 0, 3, 6, 9, 12, 18, 24, and 36; (

**b**) resonant frequency variation curve with acceleration for the structure with 24 perforations.

**Figure 5.**(

**a**) Variation curve of acceleration sensitivity with the number of perforations; (

**b**) variation curve of resonance frequency with the number of perforations for acceleration of 0.

**Figure 6.**Two-dimensional diagrams of perforated structures with perforation radii of 5 μm, 7 μm, and 9 μm.

**Figure 8.**(

**a**) Curve of acceleration sensitivity versus perforation radius; (

**b**) curve of resonance frequency versus perforation radius for acceleration of 0.

**Figure 9.**Schematic diagrams of two-dimensional structures with C

_{2}perforation positions (d

_{2}) of 20 μm, 30 μm, and 40 μm.

**Figure 11.**(

**a**) Variation curve of acceleration sensitivity with perforation position; (

**b**) variation curve of resonance frequency with perforation position at the acceleration of 0.

**Figure 13.**(

**a**) CMUT cell resonant frequency versus voltage curve; (

**b**) acceleration sensitivity versus voltage curve.

**Figure 14.**Maximum stress on the membrane of the CMUT cell structure at a voltage of 1.6 V and an acceleration of 20 g.

Parameter | Value |
---|---|

Radius R | 170 µm |

Thickness h | 1 µm |

Poisson’s ratio v | 0.29 |

Separation distance g | 0.2 µm |

Young’s modulus E | 169 GPa |

Density ρ | 2.332 kg/m^{3} |

Acceleration Sensitivity | 5.4 (Hz/g) |

**Table 2.**Performance parameters of the ring-perforation membrane structure with different numbers of perforations.

Numbers of Perforations | Resonance Frequency at Acceleration 0 (kHz) | Sensitivity (Hz/g) |
---|---|---|

0 | 146.6 | 5.4 |

3 | 146.2 | 5.4 |

6 | 142.5 | 5.9 |

9 | 136.3 | 7.0 |

12 | 130.8 | 8.3 |

18 | 127.5 | 9.3 |

24 | 123 | 10.9 |

36 | 111.8 | 16.1 |

**Table 3.**Performance parameters of ring-perforation membrane structure with different perforation radii.

The Radius of Perforation (μm) | Resonance Frequency at Acceleration 0 (kHz) | Sensitivity (Hz/g) |
---|---|---|

0 | 146.6 | 5.4 |

1 | 133.4 | 7.7 |

3 | 132.8 | 7.8 |

5 | 127.1 | 9.5 |

7 | 123.0 | 10.9 |

9 | 121.5 | 11.4 |

11 | 117.3 | 13.2 |

**Table 4.**Performance parameters of the ring-perforation membrane structure with different C

_{2}positions.

Perforation Position d_{2} (μm) | Resonance Frequency at Acceleration 0 (kHz) | Sensitivity (Hz/g) |
---|---|---|

70 | 134.5 | 7.5 |

50 | 130.4 | 8.5 |

40 | 126.4 | 9.7 |

30 | 123.0 | 10.9 |

20 | 122.7 | 10.9 |

10 | 118.5 | 12.5 |

Voltage (V) | Displacement (μm) | Resonance Frequency at Acceleration 0 (kHz) | Sensitivity (Hz/g) |
---|---|---|---|

1.2 | 0.03 | 146 | 2.4 |

1.3 | 0.036 | 142.5 | 3.2 |

1.4 | 0.044 | 137.9 | 4.5 |

1.5 | 0.053 | 131.8 | 6.6 |

1.6 | 0.065 | 123.0 | 10.9 |

1.7 | 0.082 | 107.7 | 23.1 |

Number | Radius | d_{2} | Resonance Frequency at Acceleration 0 (kHz) | Sensitivity (Hz/g) | Percentage Upgrade |
---|---|---|---|---|---|

0 | 0 | 0 | 146.6 | 5.4 | |

6 | 7 | 30 | 142.5 | 5.9 | 9.30% |

36 | 7 | 30 | 111.8 | 16.1 | 198.10% |

24 | 1 | 30 | 133.4 | 7.7 | 42.60% |

24 | 11 | 30 | 117.3 | 13.2 | 144.40% |

24 | 7 | 10 | 118.5 | 12.5 | 131.50% |

24 | 7 | 70 | 134.5 | 7.5 | 38.90% |

24 | 7 | 30 | 123.0 | 10.9 | 101.90% |

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**MDPI and ACS Style**

Gou, L.; Wang, H.; Ding, Q.; Liu, Y.; Yang, R.; Zhang, F.; Zhang, P.; Cao, G.
Investigation of New Accelerometer Based on Capacitive Micromachined Ultrasonic Transducer (CMUT) with Ring-Perforation Membrane. *Micromachines* **2024**, *15*, 279.
https://doi.org/10.3390/mi15020279

**AMA Style**

Gou L, Wang H, Ding Q, Liu Y, Yang R, Zhang F, Zhang P, Cao G.
Investigation of New Accelerometer Based on Capacitive Micromachined Ultrasonic Transducer (CMUT) with Ring-Perforation Membrane. *Micromachines*. 2024; 15(2):279.
https://doi.org/10.3390/mi15020279

**Chicago/Turabian Style**

Gou, Luhao, Hongliang Wang, Qi Ding, Yulong Liu, Runze Yang, Feng Zhang, Pengcheng Zhang, and Gang Cao.
2024. "Investigation of New Accelerometer Based on Capacitive Micromachined Ultrasonic Transducer (CMUT) with Ring-Perforation Membrane" *Micromachines* 15, no. 2: 279.
https://doi.org/10.3390/mi15020279