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

^{*}

^{†}

## Abstract

**:**

^{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

- Li, C.; Zhao, Y.; Cheng, R.; Yu, Z.; Liu, Y. A resonant sensor composed of quartz double ended tuning fork and silicon substrate for digital acceleration measurement. Rev. Sci. Instrum.
**2014**, 85, 35004. [Google Scholar] [CrossRef] [PubMed] - He, Y.; Si, C.; Han, G.; Zhao, Y.; Ning, J.; Yang, F. A Novel Fabrication Method for a Capacitive MEMS Accelerometer Based on Glass-Silicon Composite Wafers. Micromachines
**2021**, 12, 102. [Google Scholar] [CrossRef] [PubMed] - Jency, J.G.; Sekar, M.; Sankar, A.R. Damping analysis of a quad beam MEMS piezoresistive accelerometer. Int. J. Model. Simul.
**2021**, 41, 256–264. [Google Scholar] [CrossRef] - Liu, Y.; Hu, B.; Cai, Y.; Liu, W.; Tovstopyat, A.; Sun, C. A Novel Tri-Axial Piezoelectric MEMS Accelerometer with Folded Beams. Sensors
**2021**, 21, 453. [Google Scholar] [CrossRef] - Han, C.; Li, C.; Zhao, Y.; Li, B. High-Stability Quartz Resonant Accelerometer with Micro-Leverages. J. Microelectromechanical Syst.
**2021**, 30, 184–192. [Google Scholar] [CrossRef] - Chen, C.; Hone, J. Graphene Nanoelectromechanical Systems. Proc. IEEE
**2013**, 101, 1766–1779. [Google Scholar] [CrossRef] - Butscher, S.; Milde, F.; Hirtschulz, M.; Malić, E.; Knorr, A. Hot electron relaxation and phonon dynamics in graphene. Appl. Phys. Lett.
**2007**, 91, 203103. [Google Scholar] [CrossRef] - Du, X.; Skachko, I.; Barker, A.; Andrei, E.Y. Approaching ballistic transport in suspended graphene. Nat. Nanotechnol.
**2008**, 3, 491–495. [Google Scholar] [CrossRef] [Green Version] - Guan, F.; Kumaravadivel, P.; Averin, D.V.; Du, X. Tuning strain in flexible graphene nanoelectromechanical resonators. Appl. Phys. Lett.
**2015**, 107, 193102. [Google Scholar] [CrossRef] [Green Version] - Sharma, A.; Varshney, U.; Lu, Y. Electronic applications of graphene mechanical resonators. IET Circuits Devices Syst.
**2015**, 9, 413–419. [Google Scholar] [CrossRef] - Bunch, J.S.; Van Der Zande, A.M.; Verbridge, S.S.; Frank, I.W.; Tanenbaum, D.M.; Parpia, J.M.; Craighead, H.G.; McEuen, P.L. Electromechanical resonators from graphene sheets. Science
**2007**, 315, 490–493. [Google Scholar] [CrossRef] [Green Version] - Kang, J.W.; Lee, J.H.; Hwang, H.J.; Kim, K.S. Developing accelerometer based on graphene nanoribbon resonators. Phys. Lett. A
**2012**, 376, 3248–3255. [Google Scholar] [CrossRef] - Kang, J.W.; Park, J.H.; Lee, G.Y.; Kim, K.S. Molecular Dynamics Simulation on Crossroad-Type Graphene-Resonator Accelerometer. J. Comput. Theor. Nanosci.
**2015**, 12, 4186–4190. [Google Scholar] [CrossRef] - Byun, K.R.; Kim, K.S.; Hwang, H.J.; Kang, J.W. Sensitivity of Graphene-Nanoribbon-Based Accelerometer with Attached Mass. J. Comput. Theor. Nanosci.
**2013**, 10, 1886–1891. [Google Scholar] [CrossRef] - Moreno, D.; Fan, X.; Niklaus, F.; Villanueva, L.G. Proof of Concept of a Graphene-Based Resonant Accelerometer. In Proceedings of the 2021 IEEE 34th International Conference on Micro Electro Mechanical Systems (MEMS), Gainesville, FL, USA, 25–29 January 2021. [Google Scholar]
- Shi, F.T.; Fan, S.C.; Li, C.; Peng, X.B. Modeling and Analysis of a Novel Ultrasensitive Differential Resonant Graphene Micro-Accelerometer with Wide Measurement Range. Sensors
**2018**, 18, 2266. [Google Scholar] [CrossRef] [Green Version] - Beijing University of Aeronautics and Astronautics. A Resonant Graphene Biaxial Accelerometer. CN201710501462.5, 27 June 2017. [Google Scholar]
- Yang, B.; Wang, X.; Dai, B.; Liu, X. A new z-axis resonant micro-accelerometer based on electrostatic stiffness. Sensors
**2015**, 15, 687–702. [Google Scholar] [CrossRef] [Green Version] - Li, J.; Fan, S.C.; Li, C.; Yu, C.F. Research progress of silicon resonant MEMS accelerometer. Transducer Microsyst. Technol.
**2011**, 30, 4–7. [Google Scholar] - Seshia, A.A.; Palaniapan, M.; Roessig, T.A.; Howe, R.T.; Gooch, R.W.; Schimert, T.R.; Montague, S. A vacuum packaged surface micromachined resonant accelerometer. J. Microelectromech. Syst.
**2002**, 11, 784–793. [Google Scholar] [CrossRef] [Green Version] - Fardindoost, S.; Alipour, A.; Mohammadi, S.; Gokyar, S.; Sarvari, R.; Demir, H.V. Flexible strain sensors based on electrostatically actuated graphene flakes. J. Micromech. Microeng.
**2015**, 25, 75016. [Google Scholar] [CrossRef] - Ilic, B.; Krylov, S.; Craighead, H.G. Theoretical and experimental investigation of optically driven nanoelectromechanical oscillators. J. Appl. Phys.
**2010**, 107, 34311. [Google Scholar] [CrossRef] - Wang, Q. Simulations of the bending rigidity of graphene. Phys. Lett. A
**2010**, 374, 1180–1183. [Google Scholar] [CrossRef] - Garcia-Sanchez, D.; van der Zande, A.M.; Paulo, A.S.; Lassagne, B.; McEuen, P.L.; Bachtold, A. Imaging Mechanical Vibrations in Suspended Graphene Sheets. Nano Lett.
**2008**, 8, 1399–1403. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Jiang, S.; Shi, S.; Wang, X. Nanomechanics and vibration analysis of graphene sheets via a 2D plate model. J. Phys. D Appl. Phys.
**2014**, 47, 45104. [Google Scholar] [CrossRef] - Ang, W.T.; Khosla, P.K.; Riviere, C.N. Nonlinear Regression Model of a Low-g MEMS Accelerometer. IEEE Sens. J.
**2007**, 7, 81–88. [Google Scholar] [CrossRef] - Pan, J.; Zhang, C.; Cai, Q. An accurate calibration method for accelerometer nonlinear scale factor on a low-cost three-axis turntable. Meas. Sci. Technol.
**2014**, 25, 25102–25108. [Google Scholar] [CrossRef] - Caspani, A.; Comi, C.; Corigliano, A.; Langfelder, G.; Tocchio, A. Compact biaxial micromachined resonant accelerometer. J. Micromech. Microeng.
**2013**, 23, 105012. [Google Scholar] [CrossRef] - Ding, H.; Zhao, J.; Ju, B.F.; Xie, J. A high-sensitivity biaxial resonant accelerometer with two-stage microleverage mechanisms. J. Micromech. Microeng.
**2015**, 26, 15011. [Google Scholar] [CrossRef] - Yang, B.; Zhao, H.; Dai, B.; Liu, X. A new silicon biaxial decoupled resonant micro-accelerometer. Microsyst. Technol.
**2014**, 21, 109–115. [Google Scholar] [CrossRef] - Zhao, L.; Dai, B.; Yang, B.; Liu, X. Design and simulations of a new biaxial silicon resonant micro-accelerometer. Microsyst. Technol.
**2016**, 22, 2829–2834. [Google Scholar] [CrossRef] - Chen, C.; Rosenblatt, S.; Bolotin, K.I.; Kalb, W.; Kim, P.; Kymissis, I.; Stormer, H.L.; Heinz, T.F.; Hone, J. Performance of monolayer graphene nanomechanical resonators with electrical readout. Nat. Nanotechnol.
**2009**, 4, 861–867. [Google Scholar] [CrossRef] [Green Version] - Bunch, J.S.; Verbridge, S.S.; Alden, J.S.; Van Der Zande, A.M.; Parpia, J.M.; Craighead, H.G.; McEuen, P.L. Impermeable atomic membranes from graphene sheets. Nano Lett.
**2008**, 8, 2458–2462. [Google Scholar] [CrossRef] [Green Version] - Zande, A.M.; Barton, R.A.; Alden, J.S.; Ruiz-Vargas, C.S.; Whitney, W.S.; Pham, P.H.; Park, J.; Parpia, J.M.; Craighead, H.G.; McEuen, P.L. Large-Scale Arrays of Single-Layer Graphene Resonators. Nano Lett.
**2010**, 10, 4869–4873. [Google Scholar] [CrossRef] - Kwon, O.K.; Lee, J.H.; Park, J.; Kim, K.S.; Kang, J.W. Molecular dynamics simulation study on graphene-nanoribbon-resonators tuned by adjusting axial strain. Curr. Appl. Phys.
**2013**, 13, 360–365. [Google Scholar] [CrossRef] - Jung, M.; Rickhaus, P.; Zihlmann, S.; Eichler, A.; Makk, P.; Schönenberger, C. GHz nanomechanical resonator in an ultraclean suspended graphene p–n junction. Nanoscale
**2019**, 11, 4355–4361. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Chung, V.P.; Li, X.; Guney, M.G.; Paramesh, J.; Mukherjee, T.; Fedder, G.K. Hourglass-beam Nanogram-proof-mass Array: Toward a High Dynamic Range Accelerometer. In Proceedings of the IEEE International Symposium on Inertial Sensors & Systems, Naples, FL, USA, 1–5 April 2019; IEEE: Piscataway Township, NJ, USA, 2019. [Google Scholar]
- Nam, K.B.; Yeo, J.H.; Hu, Q.; Kim, M.J.; Oh, B.; Yoo, J.B. Fabrication of extreme ultraviolet lithography pellicle with nanometer-thick graphite film by sublimation of camphor supporting layer. Nanotechnology
**2021**, 32, 465301. [Google Scholar] [CrossRef]

**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 | $0.034\%$ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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