# Microfabrication Process-Driven Design, FEM Analysis and System Modeling of 3-DoF Drive Mode and 2-DoF Sense Mode Thermally Stable Non-Resonant MEMS Gyroscope

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Structural Design of Multi-Degree of Freedom (Multi-DoF) Microelectromechanical Systems (MEMS) Gyroscope

## 3. Microfabrication Process

- (a)
- The process starts with an SOI wafer as shown in Figure 2a. The doping of the top layer of silicon is done by depositing a phosphosilicate glass (PSG) layer and then annealing is done at 1050 °C in Argon. It is followed by the removal of the PSG layer using wet etching.
- (b)
- The lift-off process is then used to deposit the first Padmetal layer which consists of 500 nm gold stack and 20 nm chrome layer, as shown in Figure 2b.
- (c)
- To apply a second mask, a lithography technique is utilized for the patterning of the silicon layer as shown in Figure 2c.
- (d)
- To apply the TRENCH mask, substrate layer of thickness 400 µm is patterned in which lithography technique is used with successive etching through Deep Reactive Ion Etching (DRIE). The final structure is obtained by removing the buried oxide layer in the regions defined by the TRENCH mask, as shown in Figure 2d.

#### 3.1. Microfabrication Process Limitations

#### 3.1.1. Limitation 1

_{3b,}is provided by routing the silicon fixed beams from one side of the outer mass m

_{1}as shown in Figure 1.

#### 3.1.2. Limitation 2

#### 3.1.3. Limitation 3

#### 3.2. Process Driven Design Modifications

## 4. Analytical Modeling of the Multi-DoF MEMS Gyroscope

#### 4.1. Equations of Motion for the Drive and Sense Mode Oscillators

#### 4.2. Calculation of Mechanical Stiffness

_{f}and the sense masses ${m}_{3a}$ and ${m}_{3b}$ to behave as a single mass in the drive direction.

_{,}with length ${L}_{{k}_{1}}$ and width ${w}_{{k}_{1}}$, connect the mass ${m}_{1}$ with the external anchor. Two double-folded springs ${k}_{2}$, with length and width given by ${L}_{{k}_{2}}$ and ${w}_{{k}_{2}}$, respectively, are used to connect the mass ${m}_{2}$ to the anchors. Two double-folded springs ${k}_{3}$, are used to connect the decoupling frame m

_{f}to the anchors and their lengths and widths are given by ${L}_{{k}_{3}}$ and ${w}_{{k}_{3}}$ respectively. Two mechanical springs, ${k}_{12}$ and ${k}_{23}$, are used to interconnect the drive masses, whereas ${k}_{{y}_{1}}$ and ${k}_{{y}_{2}}$ are used to interconnect the sense masses. A total of four mechanical springs ${k}_{12}$ with their length and width given by ${L}_{{k}_{12}}$ and ${w}_{{k}_{12}}$ respectively, are used to couple the masses ${m}_{1}$ and ${m}_{2}$. Four mechanical springs ${k}_{23}$ with length and width of ${L}_{{k}_{23}}$ and ${w}_{{k}_{23}}$ respectively, are used to connect the mass ${m}_{2}$ and decoupling frame ${m}_{f}$. In the sense direction, four springs ${k}_{{y}_{1}}$ are used to couple the frame ${m}_{f}$ with the sense mass ${m}_{3a}$. Their lengths and widths are given by ${L}_{{k}_{{y}_{1}}}$ and ${w}_{{k}_{{y}_{1}}}$ respectively. Another set of four springs ${k}_{{y}_{2}}$, is used to interconnect the masses ${m}_{3a}$ and ${m}_{3b}$, with length and width given by ${L}_{{k}_{{y}_{2}}}$ and ${w}_{{k}_{{y}_{2}}}$. The mechanical springs, both in drive and sense direction, can be modeled as fixed-guided beams and their equivalent mechanical stiffness can be written as:

#### 4.3. Calculation of Differential Capacitance Change

#### 4.4. Air Damping Analysis

## 5. FEM Analysis for the MEMS Gyroscope

#### 5.1. Modal Analysis

#### 5.2. Pull-in Voltage Analysis

#### 5.3. Frequency Response Analysis

#### 5.4. Oscillation Frequency-Dependent Air Damping Analysis

#### 5.5. Effect of Operating Temperature and Pressure Variations on MEMS Gyroscope

#### 5.6. Thermal Stability Analysis of MEMS Gyroscope

#### 5.7. Analysis of Fabrication Process Tolerances on Frequency Response

## 6. Sensitivity Analysis of MEMS Gyroscope

#### 6.1. Mechanical Sensitivity Analysis

#### 6.2. Integration of MEMS Gyroscope with Readout Electronics and Voltage Sensitivity Analysis

^{TM}MS3110 is considered [40]. This IC is vastly used for signal conditioning of MEMS devices and provides an output voltage proportional to the change in differential capacitance. Figure 20 shows the integration of the proposed MEMS gyroscope with the internal circuitry of the MS 3110 IC in Matlab Simulink environment, which mentions the input and output ports of the MEMS gyroscope model, a combination of actuation voltages in the drive mode and a DC bias voltage applied to the sensing parallel plates. The differential output capacitances from the sensing parallel plates are shown as $Cap1$ and $Cap2$ and are connected as inputs (CS

_{1IN}and CS

_{2IN}) to the MS 3110. The internal circuitry of the MS 3110 IC is shown as a simplified block diagram. The circuit contains a charge amplifier followed by a sample and hold circuit. A low pass filter is used for the signal conditioning and finally, the signal is passed through a buffer amplifier, which has offset trim functionality along with the output level selection. The MS 3110 IC has multiple programmable attributes, including the gain of the charge amplifier, the cut-off frequency of the filter and the buffer amplifier gain. The MS 3110 can operate in two modes with either a single-ended sense capacitor input or a differential input. In differential mode, the output capacitance from the MEMS gyro $Cap1$ and $Cap2$ may have mismatched values and may lead to a DC offset in the output values. In this case, the internal capacitors $CS1$ and $CS2$ of MS3110 are adjusted to reduce the DC offset by balancing the common mode capacitance. The output voltage of MS3110 IC can range between 0.5 V to 4 V and is given as:

## 7. Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Wu, G.Q.; Chua, G.L.; Gu, Y.D. A dual-mass fully decoupled MEMS gyroscope with wide bandwidth and high linearity. Sens. Actuators A Phys.
**2017**, 259, 50–56. [Google Scholar] [CrossRef] - Shakoor, R.I.; Marc, B.; Iqbal, S. Experimental evaluation of resonant frequencies with associated mode shapes and power analysis of thermally actuated vibratory microgyroscope. Microsyst. Technol.
**2018**, 24, 3601–3613. [Google Scholar] [CrossRef] - Yang, J.S.; Fang, H.Y. A new ceramic tube piezoelectric gyroscope. Sens. Actuators A Phys.
**2003**, 107, 42–49. [Google Scholar] [CrossRef] - Dellea, S.; Giacci, F.; Longoni, A.F.; Langfelder, G. In-plane and out-of-plane MEMS gyroscopes based on piezoresistive NEMS detection. J. Microelectromech. Syst.
**2015**, 24, 1817–1826. [Google Scholar] [CrossRef] - Bochobza-Degani, O.; Seter, D.J.; Socher, E.; Nemorivsky, Y. A novel micromachined vibrating rate-gyroscope with optical sensing and electrostatic actuation. Sens. Actuators A Phys.
**2000**, 83, 54–60. [Google Scholar] [CrossRef] - Chuang, W.C.; Lee, H.L.; Chang, P.Z.; Hu, Y.C. Review on the modeling of electrostatic MEMS. Sensors
**2010**, 10, 6149–6171. [Google Scholar] [CrossRef] - Nguyen, M.N.; Ha, N.S.; Nguyen, L.Q.; Chu, H.M.; Vu, H.N. Z-axis micromachined tuning fork gyroscope with low air damping. Micromachines
**2017**, 8, 42. [Google Scholar] [CrossRef] - Xu, Q.; Hou, Z.; Kuang, Y.; Miao, T.; Ou, F.; Zhuo, M.; Xiao, D.; Wu, X. A Tuning Fork Gyroscope with a Polygon-Shaped Vibration Beam. Micromachines
**2019**, 10, 813. [Google Scholar] [CrossRef] [Green Version] - He, C.; Zhao, Q.; Huang, Q.; Liu, D.; Yang, Z.; Yan, G. A MEMS vibratory gyroscope with real-time mode-matching and robust control for the sense mode. IEEE Sens. J.
**2014**, 15, 2069–2077. [Google Scholar] [CrossRef] - Balachandran, G.K.; Petkov, V.P.; Mayer, T.; Balslink, T. A 3-axis gyroscope for electronic stability control with continuous self-test. IEEE J. Solid-State Circ.
**2015**, 51, 177–186. [Google Scholar] - Jia, J.; Ding, X.; Gao, Y.; Li, H. Automatic Frequency tuning technology for dual-mass MEMS gyroscope based on a quadrature modulation signal. Micromachines
**2018**, 9, 511. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Dyck, C.W.; Allen, J.J.; Huber, R.J. Parallel-plate electrostatic dual-mass resonator. In Micromachined Devices and Components V; International Society for Optics and Photonics: Santa Clara, CA, USA, 1999; Volume 3876. [Google Scholar]
- Acar, C.; Shkel, A.M. Nonresonant micromachined gyroscopes with structural mode-decoupling. IEEE Sens. J.
**2003**, 3, 497–506. [Google Scholar] [CrossRef] - Schofield, A.R.; Trusov, A.A.; Shkel, A.M. Effects of operational frequency scaling in multi-degree of freedom MEMS gyroscopes. IEEE Sens. J.
**2008**, 8, 1672–1680. [Google Scholar] [CrossRef] - Trusov, A.A.; Schofield, A.R.; Shkel, A.M. Performance characterization of a new temperature-robust gain-bandwidth improved MEMS gyroscope operated in air. Sens. Actuators A Phys.
**2009**, 155, 16–22. [Google Scholar] [CrossRef] - Sahin, K.; Sahin, E.; Alper, S.E.; Akin, T. A wide-bandwidth and high-sensitivity robust microgyroscope. J. Micromech. Microeng.
**2009**, 19, 074004. [Google Scholar] [CrossRef] [Green Version] - Erismis, M. Design and modeling of a new robust multi-mass coupled-resonator family with dynamic motion amplification. Microsyst. Technol.
**2013**, 19, 1105–1110. [Google Scholar] [CrossRef] - Saqib, M.; Mubasher Saleem, M.; Mazhar, N.; Awan, S.U.; Shahbaz Khan, U. Design and analysis of a high-gain and robust multi-DOF electro-thermally actuated MEMS gyroscope. Micromachines
**2018**, 9, 577. [Google Scholar] [CrossRef] [Green Version] - Saleem, M.M.; Bazaz, S.A. Design and robustness analysis of structurally decoupled 3-DoF MEMS gyroscope in the presence of worst-case process tolerances. Microsyst. Technol.
**2011**, 17, 1381–1391. [Google Scholar] [CrossRef] - Verma, P.; Khan, K.Z.; Khonina, S.N.; Kazanskiy, N.L.; Gopal, R. Ultraviolet-LIGA-based fabrication and characterization of a nonresonant drive-mode vibratory gyro/accelerometer. J. Micro-Nanolithogr. MEMS MOEMS
**2016**, 15, 035001. [Google Scholar] [CrossRef] - Acar, C.; Shkel, A.M. Inherently robust micromachined gyroscopes with 2-DOF sense-mode oscillator. J. Microelectromech. Syst.
**2006**, 15, 380–387. [Google Scholar] [CrossRef] - Riaz, K.; Bazaz, S.A.; Saleem, M.M.; Shakoor, R.I. Design, damping estimation and experimental characterization of decoupled 3-DoF robust MEMS gyroscope. Sens. Actuators A Phys.
**2011**, 172, 523–532. [Google Scholar] [CrossRef] - Verma, P.; Shekhar, C.; Arya, S.K.; Gopal, R. New design architecture of a 3-DOF vibratory gyroscope with robust drive operation mode and implementation. Microsyst. Technol.
**2015**, 21, 2175–2185. [Google Scholar] [CrossRef] - Zhu, X.H.; Chu, H.J.; Shi, Q.; Qiu, A.P.; Su, Y. Experimental study of compensation for the effect of temperature on a silicon micromachined gyroscope. Proc. Inst. Mech. Eng. Part N J. Nanoeng. Nanosyst.
**2008**, 222, 49–55. [Google Scholar] [CrossRef] - Guo, Z.; Fu, P.; Liu, D.; Huang, M. Design and FEM simulation for a novel resonant silicon MEMS gyroscope with temperature compensation function. Microsyst. Technol.
**2018**, 24, 1453–1459. [Google Scholar] [CrossRef] - Cui, M.; Huang, Y.; Wang, W.; Cao, H. MEMS Gyroscope Temperature Compensation Based on Drive Mode Vibration Characteristic Control. Micromachines
**2019**, 10, 248. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Dwivedi, A.; Khanna, G. Numerical simulation and modelling of a novel MEMS capacitive accelerometer based microphone for fully implantable hearing aid. Microsyst. Technol.
**2019**, 25, 399–411. [Google Scholar] [CrossRef] - Cowen, A.; Hames, G.; Monk, D.; Wilcenski, S.; Hardy, B. SOIMUMPs Design Handbook (Revision 8.0.). Available online: http://www.memscap.com (accessed on 27 June 2020).
- Edalatfar, F.; Yaghootkar, B.; Qureshi, A.Q.A.; Azimi, S.; Bahreyni, B. Design, fabrication and characterization of a high performance MEMS accelerometer. IEEE Sens. J.
**2016**, 1–3. [Google Scholar] [CrossRef] - Bao, M.; Yang, H. Squeeze film air damping in MEMS. Sens. Actuators A Phys.
**2007**, 136, 3–27. [Google Scholar] [CrossRef] - Abdolvand, R.; Amini, B.V.; Ayazi, F. Sub-micro-gravity in-plane accelerometers with reduced capacitive gaps and extra seismic mass. J. Microelectromech. Syst.
**2007**, 16, 1036–1043. [Google Scholar] [CrossRef] - Mol, L.; Rocha, L.A.; Cretu, E.; Wolffenbuttel, R.F. Squeezed film damping measurements on a parallel-plate MEMS in the free molecule regime. J. Micromech. Microeng.
**2009**, 19, 074021. [Google Scholar] [CrossRef] - Syed, W.U.; Brimmo, A.; Waheed, O.; Bojesomo, A.; Ali, M.H.; Ocak, I.; Elfadel, I.A.M. Numerical modeling and validation of squeezed-film damping in vacuum-packaged industrial MEMS. J. Micromech. Microeng.
**2017**, 27, 075016. [Google Scholar] [CrossRef] - Veijola, T.; Raback, P. Methods for solving gas damping problems in perforated microstructures using a 2D finite-element solver. Sensors
**2007**, 7, 1069–1090. [Google Scholar] [CrossRef] [Green Version] - Morris, C.J.; Forster, F.K. Oscillatory flow in microchannels. Exp. Fluids
**2004**, 36, 928–937. [Google Scholar] [CrossRef] - Somà, A.; Saleem, M.M.; De Pasquale, G. Effect of creep in RF MEMS static and dynamic behavior. Microsyst. Technol.
**2016**, 22, 1067–1078. [Google Scholar] [CrossRef] - CoventorWare Analyzer Field Solver Reference; Coventor Inc.: Cary, NC, USA, 2018.
- Wachtman, J.B., Jr.; Tefft, W.E.; Lam, D.G., Jr.; Apstein, C.S. Exponential temperature dependence of Young’s modulus for several oxides. Phys. Rev.
**1961**, 122, 1754. [Google Scholar] [CrossRef] - Gysin, U.; Rast, S.; Ruff, P.; Meyer, E.; Lee, D.W.; Vettiger, P.; Gerber, C. Temperature dependence of the force sensitivity of silicon cantilevers. Phys. Rev. B
**2004**, 69, 045403. [Google Scholar] [CrossRef] - Datasheet MUCRI. MS3110 Universal Capacitive ReadoutTM IC; MicroSensors, Inc.: Costa Mesa, CA, USA, 2004. [Google Scholar]
- Bao, M.H. Micro Mechanical Transducers: Pressure Sensors, Accelerometers and Gyroscopes; Elsevier: San Diego, CA, USA, 2000. [Google Scholar]
- Apostolyuk, V. Theory and Design of Micromechanical Vibratory Gyroscopes in MEMS/NEMS; Springer: Boston, MA, USA, 2006; pp. 173–195. [Google Scholar]

**Figure 1.**Proposed multi-degree of freedom (multi-DoF) microelectromechanical systems (MEMS) gyroscope design with 3-DoF drive mode and 2-DoF sense mode oscillators.

**Figure 4.**Discrete mass–spring–damper model for the proposed MEMS gyroscope. (

**a**) Drive mode and (

**b**) sense mode.

**Figure 7.**Modal analysis results and the corresponding mode shapes for MEMS gyroscope (

**a**) 1st mode (1.607 kHz) (

**b**) 2nd mode (1.707 kHz) and (

**c**) 6th mode (3.329 kHz) and (

**d**) 7th mode (3.709 kHz).

**Figure 11.**Effect of oscillation frequency on (

**a**) squeezed film air damping for frequency up to 6 kHz (

**b**) slide film air damping for frequency up to 6 kHz (

**c**) squeezed film air damping for frequency up to 10 MHz.

**Figure 12.**Energy loss factor for MEMS gyroscope with varying operating temperature and pressure values.

**Figure 13.**Effect of operating temperature variations on the frequency response of (

**a**) drive mass ${m}_{3}$ and (

**b**) sense mass ${m}_{3b}$.

**Figure 14.**Effect of operating air pressure variations on the frequency response of (

**a**) drive mass ${m}_{3}$ and (

**b**) sense mass ${m}_{3b}$.

**Figure 17.**(

**a**) Thermal deformation analysis path along with the sense mass ${m}_{3b}$ (

**b**) thermal deformation at −40 °C. (

**c**) thermal deformation at 100 °C.

**Figure 18.**Effect of fabrication process tolerances on (

**a**) resonant frequencies (

**b**) capacitance change.

**Figure 19.**(

**a**) Input angular velocity of 50 rad/s. (

**b**) Oscillation response of the drive mass ${m}_{3}$. (

**c**) Oscillation response of the sense mass ${m}_{3b}$.

**Table 1.**Multi-degree of freedom (multi-DoF) non-resonant microelectromechanical systems (MEMS) gyroscopes presented in the literature.

References | Structural Layer | Configuration | Device Size | Sensitivity | Bandwidth | |
---|---|---|---|---|---|---|

Material | Thickness (µm) | |||||

Acar et al. [13] | Polysilicon | 2 | 2 DoF drive, 2 DoF sense | 0.7 × 0.5 mm^{2} | 0.72 × 10^{−3} µm/°/s | 23 Hz |

Schofield et al. [14] | Silicon | 75 | 1 DoF drive, 2 DoF sense | - | 2.34 µV/(°/s) | 600 Hz |

Trusov et al. [15] | Silicon | 50 | 1 DoF drive, 2 DoF sense | 3 × 3 mm^{2} | 56 µV/(°/s) | 250 Hz |

Sahin et al. [16] | Silicon | 100 | 1 DoF drive, 2 DoF sense | 131 µV/(°/s) | 1 kHz | |

Saqib et al. [18] | Nickel | 20 | 3 DoF drive, 1 DoF sense | 3.2 × 3 mm^{2} | 0.565 fF/rad/s, 0.052 × 10^{−3} µm/°/s | 1.2 kHz |

Saleem et al. [19] | Nickel | 20 | 2 DoF drive, 1 DoF sense | 2.4 × 1.6 mm^{2} | 0.045 fF/rad/s, 0.0105 × 10^{−3} µm/°/s | 1.71 kHz |

Verma et al. [20] | Nickel | 9 | 1 DoF drive, 2 DoF sense | 2 × 1.9 mm^{2} | - | 100 Hz |

Acar et al. [21] | Polysilicon | 100 | 1 DoF drive, 2 DoF sense | 4 × 4 mm^{2} | 0.0308 mV/°/s | 50 Hz |

Riaz et al. [22] | Nickel | 20 | 2 DoF drive, 1 DoF sense | 2.2 × 2.6 mm^{2} | - | 1.4 kHz |

Verma et al. [23] | Nickel | 8 | 2 DoF drive, 1 DoF sense | 2.13 × 1.93 mm^{2} | - | 1 kHz |

Parameters | Values |
---|---|

Overall device size | 4.2 mm × 4.2 mm |

Structural layer thickness $\left(t\right)$ | 25 µm |

Mass value of the mass $({m}_{1})$ | 2.5239 × 10^{−7} Kg |

Mass value of the mass $({m}_{2})$ | 1.1203 × 10^{−7} Kg |

Mass value of the decoupling frame $({m}_{f})$ | 3.234 × 10^{−8} Kg |

Mass value of the mass $({m}_{3a})$ | 9.8125 × 10^{−8} Kg |

Mass value of the mass $({m}_{3b})$ | 5.5343 × 10^{−8} Kg |

Length of the parallel sensing plates $\left(l\right)$ | 500 µm |

Width of the parallel sensing plates $\left(w\right)$ | 8 µm |

Number of parallel sensing plates pair $\left({N}_{s}\right)$ | 120 |

Overlap length between the moving and fixed parallel sensing plates $\left({l}_{0}\right)$ | 450 µm |

Smaller sense gap size $\left({d}_{1}\right)$ | 3 µm |

Larger sense gap size $\left({d}_{2}\right)$ | 9 µm |

Number of drive comb pairs $\left({N}_{d}\right)$ | 240 |

Width of drive combs $\left({w}_{d}\right)$ | 6 µm |

Length of drive combs $\left({l}_{d}\right)$ | 120 µm |

Gap between drive combs $\left(d\right)$ | 3 µm |

Mode Shape | Analytical Model (kHz) | FEM Model (kHz) |
---|---|---|

1st (Drive mode) | 1.738 | 1.608 |

2nd (Sense mode) | 1.800 | 1.707 |

6th (Drive mode) | 3.507 | 3.329 |

7th (Sense mode) | 3.867 | 3.709 |

10th (Drive mode) | 4.960 | 4.822 |

References | Structural Layer | Configuration | Device Size | Sensitivity | Bandwidth | |
---|---|---|---|---|---|---|

Material | Thickness (µm) | |||||

Schofield et al. [14] | Silicon | 75 | 1 Dof drive, 2 DoF sense | - | 2.3 µV/(°/s) | 600 Hz |

Trusov et al. [15] | Silicon | 50 | 1 Dof drive, 2 DoF sense | 3 × 3 mm^{2} | 56 µV/(°/s) | 250 Hz |

Acar et al. [21] | Polysilicon | 100 | 1 Dof drive, 2 DoF sense | 4 × 4 mm^{2} | 0.0303 mV/(°/s) | 50 Hz |

Saqib et al. [18] | Nickle | 20 | 3 Dof drive, 1 DoF sense | 3.2 × 3 mm^{2} | 0.565 fF/rad/s | 1.2 kHz |

This work | Silicon | 25 | 3 Dof drive, 2 DoF sense | 4.2 × 4.2mm^{2} | 3.1 fF/rad/s, 198.9 µV/(°/s), 0.04 × 10^{−3} µm/(°/s) | 1.62 kHz |

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bukhari, S.A.R.; Saleem, M.M.; Khan, U.S.; Hamza, A.; Iqbal, J.; Shakoor, R.I.
Microfabrication Process-Driven Design, FEM Analysis and System Modeling of 3-DoF Drive Mode and 2-DoF Sense Mode Thermally Stable Non-Resonant MEMS Gyroscope. *Micromachines* **2020**, *11*, 862.
https://doi.org/10.3390/mi11090862

**AMA Style**

Bukhari SAR, Saleem MM, Khan US, Hamza A, Iqbal J, Shakoor RI.
Microfabrication Process-Driven Design, FEM Analysis and System Modeling of 3-DoF Drive Mode and 2-DoF Sense Mode Thermally Stable Non-Resonant MEMS Gyroscope. *Micromachines*. 2020; 11(9):862.
https://doi.org/10.3390/mi11090862

**Chicago/Turabian Style**

Bukhari, Syed Ali Raza, Muhammad Mubasher Saleem, Umar Shahbaz Khan, Amir Hamza, Javaid Iqbal, and Rana Iqtidar Shakoor.
2020. "Microfabrication Process-Driven Design, FEM Analysis and System Modeling of 3-DoF Drive Mode and 2-DoF Sense Mode Thermally Stable Non-Resonant MEMS Gyroscope" *Micromachines* 11, no. 9: 862.
https://doi.org/10.3390/mi11090862