###### Abstract  
The micro-electro-mechanical systems (MEMS)-based sensor technologies are considered to be the enabling factor for the future development of smart sensing applications, mainly due to their small size, low power consumption and relatively low cost. This paper presents a new structurally and thermally stable design of a resonant mode-matched electrostatic \(z\)-axis MEMS gyroscope considering the foundry constraints of relatively low cost and commercially available silicon-on-insulator multi-user MEMS processes (SOIMUMPs) microfabrication process. The novelty of the proposed MEMS gyroscope design lies in the implementation of two separate masses for the drive and sense axis using a unique mechanical spring configuration that allows minimizing the cross-axis coupling between the drive and sense modes. For frequency mismatch compensation between the drive and sense modes due to foundry process uncertainties and gyroscope operating temperature variations, a comb-drive-based electrostatic tuning is implemented in the proposed design. The performance of the MEMS gyroscope design is verified through a detailed coupled-field electric-structural-thermal finite element method (FEM)-based analysis. MES; mechanical design; FEM analysis; resonant gyroscope; electrostatic tuning; microfabrication +
Footnote †: journal: Applied Sciences  
e1 Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso duca degli Abruzzi 24, 10129 Torino, Italy; [EMAIL_ADDRESS]. high-temperature operating conditions. To minimize the effect of external factors on the performance of MEMS gyroscopes, complex multi-degree of freedom (multi-DoF) mechanical structures, based on nonresonant operation, have been reported in the literature [7; 8; 9]. In addition to the structural complexity, the issue of low mechanical sensitivity is inherent to nonresonant MEMS gyroscope designs. Another method of reducing the frequency difference between the drive- and sense-mode resonant frequency values in MEMS gyroscopes is to implement the additional feedback control electronics for the error compensation, which leads to the addition of electrical noise and operational complexity [10; 11; 12]. As discussed earlier, resonant MEMS gyroscopes usually operate in a closed loop in order to maintain the performance characteristics over a wide range of environmental conditions. There are multiple errors that have to be mitigated in order to obtain optimal performance, and for this reason some design choices have to be made that can help reduce the errors and avoid overly complex feedback electronics. A major error source is the mismatch in the frequencies of drive and sense modes. This can cause the performance of the gyroscope to reduce drastically since even a slight mismatch can reduce the amplitude response of a mode matched gyroscope significantly. To mitigate this error, frequency tuning is required, and for this purpose a phenomenon called electrostatic spring softening is used to change the stiffness of the structure electronically and therefore change the frequency. This method allows the designer to reduce the mismatch and to get the optimal performance of the MEMS gyroscope [13; 14]. The number of proof masses in resonant MEMS gyroscopes can affect the common mode errors and therefore the performance of the gyroscope. The designs utilizing multiple proof masses operate in the antiphase mode, which assures minimization of the net reaction forces and moments on the anchors and thus mitigates the energy loss through the substrate [15]. This design approach results in a larger overall size but better performance. Another approach is to use a single proof mass, which leads to a smaller device footprint but with worse performance. Consequently, tradeoffs have to be made between better performance and keeping the size of the device to a minimum [16; 17; 18].