# A Novel Micromachined Z-axis Torsional Accelerometer Based on the Tunneling Magnetoresistive Effect

^{1}

^{2}

^{*}

## Abstract

**:**

^{0.5}along the z-axis sensitive direction.

## 1. Introduction

^{0.5}. A small tunneling magnetoresistive accelerometer based on 3D printing has been implemented with a bias stability of 64.40 μg in the literature [26]. However, due to the tolerance limitation of 3D processing technology, the volume of the entire device is too large, and it is difficult to further reduce the minimum gap, which limits the further improvement of sensitivity. A micromachined z-axis tunneling magnetoresistive accelerometer based on microfabrication and micro-assembly technology has been proposed, with a noise floor of 86.2 μg/Hz

^{0.5}, in the literature [27]. Another novel method of acceleration measurement was based on tunneling magnetoresistance, including a tunneling magnetoresistive (TMR) sensor that was used to precisely measure the magnetic field and a micro-cantilever beam bonded with the cylinder permanent magnet, which converted input acceleration to magnetic field changes. The accelerometer demonstrated a linear system response with a sensitivity of 1.145 V/g and was presented in the literature [28].

## 2. Structure Principle

_{t1}and K

_{t2}along the z-axis is neglected, the equivalent equations are:

_{1}is the mass of outer proof mass with a unit of kg and Z

_{2}is the displacement of the outer proof mass with a unit of m. K

_{1}is the equivalent stiffness of U-suspension beams which connect leverage structures to the outer proof mass; K

_{2}is the equivalent stiffness of U-suspension beams which connect leverage structures to the inner proof mass; and K

_{3}is the equivalent stiffness of linkage structures which connect outer proof mass to the inner proof mass. K

_{1}, K

_{2}and K

_{3}have a unit of N/m. L

_{1}is the equivalent torsion arm length of inner proof mass; L

_{2}is the torsional arm length of leverage structures; and L

_{3}is the equivalent torsion arm length of permanent magnetic film. L

_{1}, L

_{2}and L

_{3}have a unit of m. θ

_{1}is the torsional angle of the inner proof mass; θ

_{2}is the torsional angle of the leverage structures. θ

_{1}and θ

_{2}have a unit of rad. K

_{tθ}

_{1}is the equivalent torsional stiffness of the torsional beam connected with the inner proof mass, and K

_{tθ}

_{2}is the equivalent torsional stiffness of the torsional beam connected with leverage structures. K

_{tθ}

_{1}and K

_{tθ}

_{2}have a unit of N·m/rad.

_{t1}and K

_{t2}has little effect on the final output; therefore, it can be ignored in the derivation of the approximate formula. At the same time, when the solid model is simplified to a lumped parameter model, there will be some approximate errors. However, these approximation errors are small and do not significantly affect the output.

_{1}is

_{a}is the equivalent torque coefficient of the input acceleration in the unit of kg·m and k is the equivalent torsional elastic stiffness in the unit of N·m/rad. Therefore, the natural frequency of the plane main structure is

^{2}, and ω

_{n}is the natural frequency of the plane main structure in the unit of rad/s.

_{y}(x,y,z) in the unit of T [29]. Only the magnetic field distribution along the y-axis is given, because the sensitive direction of two tunneling magnetoresistive sensors is along the y-axis.

_{1}, k

_{Bz}has a unit of T/m. Two sense displacements are differentially changed, which results in a differential variation in the magnetic field strength. The magnetic field characteristic only gives a rough theoretical derivation. Therefore, a detailed numerical simulation of the magnetic field distribution and the magnetic field change rate is performed using the finite element solid model in subsequent sections.

_{v}is equivalent to the transforming coefficient of tunneling magnetoresistive sensors from the magnetic field to voltage in the unit of V/T. Then, the output voltage of the interface amplifier circuit is

_{amp}is the equivalent amplification coefficient in the interface amplifier circuit. Obviously, the differential displacement detection method is used significantly to eliminate the influence of the common mode magnetic field in magnetic field detection.

## 3. Simulation Analysis

^{o}/g, is linearly related to the input acceleration, which indicates that the plane main structure can efficiently convert the input acceleration into the linear torsional displacement of the permanent magnetic film. The maximum displacement mechanical sensitivity at the diagonal boundary of the permanent magnetic film is 3.48 μm/g.

_{a}, illustrated in Figure 5b. The simulation results are basically consistent with the theoretical formula. Therefore, the decrease in first-order mode frequency and the increase in outer proof mass can effectively improve the mechanical sensitivity in the process of structural optimization.

_{tθ}

_{1}, which leads to the monotonic increase in the first mode frequency. Moreover, the first-order modal frequency decreases with the rise of the amplification ratio of the rotational inertia, as can be seen from Figure 6b. In summary, the above simulation results are in good agreement with the theoretical formula, which confirms the correctness of the theoretical analysis.

## 4. Measurement and Control Circuit

## 5. Experiment

^{0.5}, to measure the magnetic field variation caused by acceleration input [30]. Moreover, the height of the 3D printing frame is accurately adjusted to guarantee that the tunneling magnetoresistive sensors operate in the unsaturated region with high magnetic field sensitivity.

^{0.5}, as shown in Figure 15. Simultaneously, the performance comparisons of tunneling magnetoresistive accelerometers recently reported are shown in Table 4. This work has certain advantages in the miniaturization and integration of the device but needs further improvement in device sensitivity and noise performance.

## 6. Conclusions

^{0.5}in z-axis sensitive direction.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Kamada, Y.; Isobe, A.; Oshima, T. Capacitive MEMS Accelerometer with Perforated and Electrically Separated Mass Structure for Low Noise and Low Power. J. Microelectromech. Syst.
**2019**, 28, 401–408. [Google Scholar] [CrossRef] - Zwahlen, P.; Balmain, D.; Habibi, S.; Etter, P. Open-loop and Closed-loop high-end accelerometer platforms for high demanding applications. In Proceedings of the 2016 IEEE/ION Position, Location and Navigation Symposium, Savannah, GA, USA, 11–14 April 2016; pp. 932–937. [Google Scholar]
- Sadeghi, M.-M.; Peterson, R.-L.; Najafi, K. Hair-based sensors for micro-autonomous systems. In Proceedings of the SPIE, Baltimore, MD, USA, 3 May 2012; Volume 8373, p. 83731L-1. [Google Scholar]
- Gerberding, O.; Cervantes, F.-G.; Melcher, J. Optomechanical reference accelerometer. Metrologia
**2015**, 52, 654–665. [Google Scholar] [CrossRef] [Green Version] - Hopkills, R.; Miola, J.; Setterlund, R. The silicon oscillating accelerometer: A High-Performance MEMS accelerometer for Precision Navigation and Strategic Guidance Applications. In Proceedings of the 2005 National Technical Meeting of the Institute of Navigation, San Diego, CA, USA, 24–26 January 2005; pp. 970–979. [Google Scholar]
- Vafaie, A.; Tahmasebipour, M.; Tahmasebipou, Y. A novel capacitive micro-accelerometer made of steel using micro wire electrical discharge machining method. J. Micromech. Microeng.
**2019**, 29, 125018. [Google Scholar] [CrossRef] - Comi, C.; Corigliano, A.; Langfelder, G. A Resonant Microaccelerometer with High Sensitivity Operating in an Oscillating Circuit. J. Microelectromech. Syst.
**2010**, 19, 1140–1152. [Google Scholar] [CrossRef] - Bose, S.; Raychowdhury, A.; Jatolia, M. Design of PID controller for ultra-sensitive Nano-g resolution MEMS tunneling accelerometer. In Proceedings of the 2014 IEEE International Conference on Control System, Computing and Engineering (ICCSCE), Batu Ferringhi, Malaysia, 28–30 November 2014; pp. 658–662. [Google Scholar]
- Mahmood, M.-S.; Butler, Z.-C.; Butler, D.-P. Design, fabrication and characterization of flexible MEMS accelerometer using multi-Level UV-LIGA. Sens. Actuators A
**2017**, 263, 530–541. [Google Scholar] [CrossRef] - Wang, S.-D.; Wei, X.-Y.; Zhao, Y.-L. A MEMS resonant accelerometer for low-frequency vibration detection. Sens. Actuators A
**2018**, 283, 151–158. [Google Scholar] [CrossRef] - Xu, M.-H.; Feng, Y.-J.; Zhou, H.; Sheng, J.-N. Noise analysis of the triaxial piezoelectric micro-accelerometer. In Proceedings of the 2017 Symposium on Piezoelectricity, Acoustic Waves and Device Applications (SPAWDA), Chengdu, China, 27–30 October 2017; pp. 288–292. [Google Scholar]
- Kumar, V.; Guo, X.-B.; Pourkamali, S. Single-mask field emsission based tunable MEMS tunneling accelerometer. In Proceedings of the 2015 IEEE 15th International Conference on Nanotechnology (IEEE-NANO), Rome, Italy, 27–30 July 2015; pp. 1171–1174. [Google Scholar]
- Zotov, S.-A.; Simon, B.-R.; Trusov, A.-A.; Shkel, A.-M. High Quality Factor Resonant MEMS Accelerometer with Continuous Thermal Compensation. IEEE Sens. J.
**2015**, 15, 5045–5052. [Google Scholar] [CrossRef] - Aydemir, A.; Terzioglu, Y.; Akin, T. A new design and a fabrication approach to realize a high performance three axes capacitive MEMS accelerometer. Sens. Actuators A
**2016**, 244, 324–333. [Google Scholar] [CrossRef] - Messina, M.; Njuguna, J.; Palas, C. Computational analysis and optimization of a MEMS-based piezoresistive accelerometer for head injuries monitoring. In Proceedings of the 2017 IEEE SENSORS, Glasgow, UK, 29 October–1 November 2017; pp. 1–3. [Google Scholar]
- Cervantes, F.-G.; Kumanchik, L.; Pratt, J. High sensitivity optomechanical reference accelerometer over 10 kHz. Appl. Phys. Lett.
**2014**, 104, 221111. [Google Scholar] [CrossRef] [Green Version] - Jeong, Y.; Serrano, D.-E.; Ayazi, F. A wide-bandwidth tri-axial pendulum accelerometer with fully-differential nano-gap electrodes. J. Micromech. Microeng.
**2018**, 28, 115007. [Google Scholar] [CrossRef] - Ding, H.; Wang, W.; Ju, B.-F.; Xie, J. A MEMS resonant accelerometer with sensitivity enhancement and adjustment Mechanisms. J. Micromech. Microeng.
**2017**, 27, 115010. [Google Scholar] [CrossRef] - Alaoui, A. MLU Based Accelerometer Using a Magnetic Tunnel Junction. U.S. Patent US20170160308A1, 8 June 2017. [Google Scholar]
- Takada, A. Force Sensing MEMS Device for Sensing an Oscillating Force. U.S. Patent 6,722,206, 20 April 2004. [Google Scholar]
- Fries, D.-P. Giant Magnetoresistance Based Gyroscope. U.S. Patent 7,113,104, 26 September 2006. [Google Scholar]
- Phan, K.-L. Methods to correct for creep in elastomer-based sensors. In Proceedings of the 2008 IEEE Sensors, Lecce, Italy, 26–29 October 2008; pp. 1119–1122. [Google Scholar]
- McNeil, K.-R.; Shankar, B.; Vogel, A.-B.; Gibson, S. Magnetoresistive-Based Position Sensor for Use in an Implantable Electrical Device. U.S. Patent 6,430,440, 6 August 2012. [Google Scholar]
- Olivas, J.-D.; Lairson, B.-M.; Ramesham, R. Ultra-Sensitive Magnetoresistive Displacement Sensing Device. U.S. Patent 6,507,187, 14 January 2003. [Google Scholar]
- Phan, K.-L.; Mauritz, A.; Homburg, F.-G.-A. A novel elastomer-based magnetoresistive accelerometer. Sens. Actuators A
**2008**, 145, 109–115. [Google Scholar] [CrossRef] - Yang, B.; Wang, B.L.; Gao, X.Y. Research on a small tunnel magnetoresistive accelerometer based on 3D printing. Microsyst. Technol.
**2019**, 25, 2649–2660. [Google Scholar] [CrossRef] - Yang, B.; Wang, B.-L.; Yan, H.-Y. Design of a Micromachined Z-axis Tunneling Magnetoresistive Accelerometer with Electrostatic Force Feedback. Micromachines
**2019**, 10, 158. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Yao, Y.; Xue, C.; Wang, P. A Novel Method of Acceleration Measurement Based On Tunneling Magnetoresistance. In Proceedings of the Asia-Pacific Conference of Transducers and Micro-Nano Technology 2018, Hong Kong, China, 24–27 June 2018; pp. 1–2. [Google Scholar]
- Camacho, J.-M.; Sosa, V. Alternative method to calculate the magnetic field of permanent magnets with azimuthal symmetry. Rev. Mex. Física E
**2013**, 59, 8–17. [Google Scholar] - The Date Sheet of TMR9001. Available online: http://www.dowaytech.com/1884.html (accessed on 11 February 2019).

**Figure 1.**Structural schematic of the micromachined z-axis tunnel magnetoresistive accelerometer. (

**a**) The micro-assembly structure layout of tunnel magnetoresistive accelerometer. (

**b**) The plane main structure of tunnel magnetoresistive accelerometer.

**Figure 3.**The selected modes of the plane main structure. (

**a**) Torsional movement of inner proof mass in first mode. (

**b**) Translational movement of inner and outer proof mass along z direction in second mode. (

**c**) Torsional movement of outer proof mass in third mode. (

**d**) Torsional movement of outer proof mass in fourth mode.

**Figure 5.**The effect of first-order mode frequency and the outer proof mass on mechanical sensitivity. (

**a**) The relationship between mechanical sensitivity and first-order modal frequency. (

**b**) The relationship between mechanical sensitivity and the outer proof mass.

**Figure 6.**The effect of the width of the torsional beam and the magnification ratio of rotational inertia on the first-order mode frequency. (

**a**) The relationship of the first-order mode frequency versus the width of the torsional beam. (

**b**) The relationship of the first-order mode frequency versus the magnification ratio of rotational inertia.

**Figure 7.**Finite element simulation of magnetic field distribution along y-axis. (

**a**) Three-dimensional magnetic field distribution of finite element simulation. (

**b**) Magnetic field distribution of finite element simulation in the plane main structure along the y-axis.

**Figure 8.**Magnetic field characteristic along y-axis under various conditions. (

**a**) Magnetic field distribution versus different vertical gaps. (

**b**) Magnetic field distribution versus different magnetic field strength (d = 1 mm).

**Figure 9.**The change rate of the magnetic field intensity along y-axis due to a displacement variation in the z direction in various conditions. (

**a**) The change rate of the magnetic field intensity under different vertical gaps. (

**b**) The maximum change rate of the magnetic field intensity under different vertical gaps. (

**c**) The change rate of the magnetic field intensity under different structure dimensions of permanent magnet film.

**Figure 11.**The optical micrograph of the fabricated tunnel magnetoresistive accelerometer. (

**a**) The torsional beam. (

**b**) U-suspension beam. (

**c**) L-suspension beam. (

**d**) The plane main structure.

**(e)**The plane main chip bonded with the permanent magnetic film. (

**f**) Microassembly structure with the tunneling magnetoresistive sensors. (

**g**) The prototype of the tunneling magnetoresistive accelerometer.

**Figure 12.**Acceleration input and output response characteristics of the tunneling magnetoresistive accelerometer under various horizontal shifts. (

**a**) Output voltage versus input acceleration under various horizontal shifts. (

**b**) Sensitivity versus various horizontal shifts.

**Figure 13.**Acceleration input and output response characteristics of the tunneling magnetoresistive accelerometer under different vertical gaps. (

**a**) Output voltage versus input acceleration under different vertical gaps. (

**b**) Sensitivity versus different vertical gaps.

**Figure 14.**Acceleration input and output response characteristics under various thicknesses of the permanent magnet film.

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

Outer proof mass (kg) | 1.02 × 10^{−5} | U-suspension beam (length × width (μm)) | 851 × 15 |

Mode frequency ω_{n} (rad/s) | 1392.98 | L-suspension beam (length × width (μm)) | 203 × 15 |

Length 2a (μm) | 3000 | Torsional beam (length × width (μm)) | 972 × 15 |

Width 2b (μm) | 3000 | Leverage(length × width (μm)) | 3466 × 150 |

Thickness 2c (μm) | 500 | Gap d1(between proof mass and feedback electrode (μm) ) | 10 |

Inner proof mass (length × width(μm)) | 4000 × 4000 | Feedback electrode area (mm^{2}) | 12.16 |

Outer proof mass (length × width(mm)) | 8000 × 8000 | Gap d2(between tunnel magnetoresistive sensor and proof mass (μm) ) | 1000 |

Thickness of main structure(μm) | 120 | Moment density M(mT) | 250 |

Modal | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

Frequency (Hz) | 221.7 | 269.1 | 279.1 | 468 | 510.2 | 794.3 |

(a) Coating the photoresist | |

(b) Etching structural anchors on the silicon wafer | |

(c) Etching the glass groove | |

(d) Sputtering the Cr/Ti/Au electrodes | |

(e) Silicon–glass anode bonding | |

(f) Thinning the silicon structure layer | |

(g) DRIE etching to release structure | |

(h) Pasting the tunnel magnetoresistive sensor | |

(i) Micro-assembling the permanent magnet film by silica gel | |

(j) Micro-assembling the tunnel magnetoresistive sensor with silicon structure using frame |

Parameter | Ref [25] Phan (2008) | Ref [26] Yang (2019) | Ref [27] Yang (2019) | Ref [28] Yao (2019) | This Work |
---|---|---|---|---|---|

Structural integration | High | Low | Medium | Low | Medium |

Core structure area (mm^{2}) | (1.5 × 1.5) × 3.14/4 (1.5mm diameter) | 17 × 17 | 6.4 × 6.4 | 90 × 50 | 8 × 8 |

Sensitivity(mV/g) | 0.96 | 401.3 | 8.85 | 1145 | 1.7 |

Noise floor(ug/Hz^{0.5}) | 35 | 20 | 86.2 | NA | 128 |

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**MDPI and ACS Style**

Yang, B.; Gao, X.; Li, C.
A Novel Micromachined Z-axis Torsional Accelerometer Based on the Tunneling Magnetoresistive Effect. *Micromachines* **2020**, *11*, 422.
https://doi.org/10.3390/mi11040422

**AMA Style**

Yang B, Gao X, Li C.
A Novel Micromachined Z-axis Torsional Accelerometer Based on the Tunneling Magnetoresistive Effect. *Micromachines*. 2020; 11(4):422.
https://doi.org/10.3390/mi11040422

**Chicago/Turabian Style**

Yang, Bo, Xiaoyong Gao, and Cheng Li.
2020. "A Novel Micromachined Z-axis Torsional Accelerometer Based on the Tunneling Magnetoresistive Effect" *Micromachines* 11, no. 4: 422.
https://doi.org/10.3390/mi11040422