# A Novel Two-Axis Differential Resonant Accelerometer Based on Graphene with Transmission Beams

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^{†}

## Abstract

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^{4}g, with a sensitivity of 250 Hz/g. To sum up, a feasible design of a biaxial graphene resonant accelerometer is proposed in this work, which provides a theoretical reference for the fabrication of a graphene accelerometer with high precision and stability.

## 1. Introduction

## 2. Model Design and Establishment

#### 2.1. Structure of Accelerometer

#### 2.2. Working Principle of the Accelerometer

## 3. Modeling and Simulation

## 4. Optimization and Results

#### 4.1. Parameter Optimization of Graphene Beam

#### 4.2. Size Optimization of Force Transfer Structure

## 5. Summary

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of accelerometer. (a) Overall structure of accelerometer. (b) Cross section of accelerometer.

**Figure 2.**The total displacement diagram of the accelerometer with the acceleration of 100 g along the positive X axis (

**a**) and the positive Y axis (

**b**), respectively. The fixed frame of the accelerometer is simplified.

**Figure 3.**(

**a**) Variation of the graphene resonant frequency with the stretching or shrinking length. (

**b**) The resonant mode of graphene with a shrinking length of 0.25 nm. (

**c**) The resonant mode of graphene with a stretching length of 0.05 nm. (

**d**) The resonant mode of graphene with a stretching length of 0.2 nm.

**Figure 4.**(

**a**) The resonant frequency of a pair of differential graphene beams varies with acceleration. Two dashed lines are linear baselines with a = 0 as the common origin. (

**b**) The resonant frequency offsets of the graphene in the X axis and Y axis vary with the acceleration along the X axis. δ is the ratio of the frequency offset in the Y axis to the frequency offset in the X axis.

**Figure 5.**The resonant frequency of the four graphene beams (GBs) in the orthogonal axis varies with the angle between the acceleration and the positive X axis with acceleration of 100 g.

**Figure 6.**The resonant frequency of stretching and shrinking graphene beams with different tension varies with acceleration, in which the tension from low to high is $0.01,0.02,0.03,0.04,0.05\mathrm{N}/\mathrm{m}$, respectively.

**Figure 7.**The critical buckling acceleration, critical linear acceleration (

**a**), and sensitivity (

**b**) of the accelerometer vary with the length of graphene. The critical buckling acceleration, critical linear acceleration (

**c**), and sensitivity (

**d**) of the accelerometer vary with the width of graphene.

**Figure 8.**The critical buckling acceleration, critical linear acceleration (

**a**), and acceleration sensitivity (

**b**) of the accelerometer vary with the relative size of the force transfer structure.

Structure | $\mathbf{Size}(\mathbf{Length}\times $$\mathbf{Width}\times \mathrm{Thicness})$ |
---|---|

Proof mass | $60\mathsf{\mu}\mathrm{m}\times 60\mathsf{\mu}\mathrm{m}\times 2.5\mathsf{\mu}\mathrm{m}$ |

H beam (the long) | $15\mathsf{\mu}\mathrm{m}\times 1\mathsf{\mu}\mathrm{m}\times 2.5\mathsf{\mu}\mathrm{m}$ |

H beam (the short) | $3\mathsf{\mu}\mathrm{m}\times 1\mathsf{\mu}\mathrm{m}\times 2.5\mathsf{\mu}\mathrm{m}$ |

Crossbeam | $66\mathsf{\mu}\mathrm{m}\times 1\mathsf{\mu}\mathrm{m}\times 9\mathsf{\mu}\mathrm{m}$ |

The suspended part of graphene | $3\mathsf{\mu}\mathrm{m}\times 1\mathsf{\mu}\mathrm{m}\times 0.34\mathrm{nm}$ |

Reference | Materials | Dimension | Volume $\left(\mathsf{\mu}\mathrm{m}\times \mathsf{\mu}\mathrm{m}\times \mathsf{\mu}\mathrm{m}\right)$ | Sensitivity (Hz/g) | Cross Sensitivity |
---|---|---|---|---|---|

Caspani et al. [28] | Silicon-based | biaxial | $720\times 720\times 15$ | $250$ | $5\%$ |

Ding et al. [29] | Silicon-based | biaxial | $1900\times 1900\times 25$ | $275$ | $3.4\%$ |

Yang et al. [30] | Silicon-based | biaxial | $7500\times 7500\times 70$ | $52.57$ (X-axis) $51.64$ (Y-axis) | $1.08\%$ (X-axis) $1.33\%$ (Y-axis) |

Shi et al. [16] | Graphene-based | uniaxial | $\approx 70\times 70\times 10$ | $21,224$ | - |

Morenoet et al. [15] | Graphene-based | uniaxial | $5\times 5\times 16.4$ (proof mass) | 1935 | - |

This work | Graphene-based | biaxial | $\approx 120\times 120\times 10$ | 50,919 | $0.034\%$ |

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**MDPI and ACS Style**

Xiao, Y.; Hu, F.; Zhang, Y.; Zheng, J.; Qin, S. A Novel Two-Axis Differential Resonant Accelerometer Based on Graphene with Transmission Beams. *Sensors* **2022**, *22*, 641.
https://doi.org/10.3390/s22020641

**AMA Style**

Xiao Y, Hu F, Zhang Y, Zheng J, Qin S. A Novel Two-Axis Differential Resonant Accelerometer Based on Graphene with Transmission Beams. *Sensors*. 2022; 22(2):641.
https://doi.org/10.3390/s22020641

**Chicago/Turabian Style**

Xiao, Yang, Feng Hu, Yuchen Zhang, Jiaxing Zheng, and Shiqiao Qin. 2022. "A Novel Two-Axis Differential Resonant Accelerometer Based on Graphene with Transmission Beams" *Sensors* 22, no. 2: 641.
https://doi.org/10.3390/s22020641