Optimization of a Poly-SiGe MEMS Xylophone Bar Magnetometer based on its Equivalent Circuit V. Rochus * , M. A. Farghaly ** , H. A. C. Tilmans * , and X. Rottenberg * * Imec Kapeldreef 75, 3001 Leuven, Belgium Rochus@imec.be, Rottenberg@imec.be, Tilmans@imec.be ** Department of Electrical Engineering, Faculty of Engineering, Assiut University, Assiut, Egypt, Farghaly@eng.au.edu.eg ABSTRACT This paper presents a design procedure to enhance the sensitivity of a poly-SiGe-based MEMS Xylophone Bar Magnetometer (XBM). Based on a novel characterization method proposed in previous work, the XBM is treated as a two-port network and the measurement of the magnetic field is performed by monitoring resonant peak amplitudes of forward/backward transmission gains S21/S12. More specifically, the optimization is performed using an equivalent circuit that models the electro-magneto- mechanical behavior of the system. A simplified expression of the S21 parameter and its sensitivity to the magnetic field are developed, highlighting the design parameters useful for the optimisation. In order to enhance the sensitivity, the shape of the release holes as well as the gap are chosen to increase the sensitivity by a factor 15. Keywords: magnetometers, optimization, equivalent circuit 1 INTRODUCTION MEMS-based inertial measurement units (IMUs) have gained the status of mainstream commodities for consumer electronics in the past years. From the simple 1-axis accelerometer, IMUs have evolved to provide 3 degrees-of freedom (DOFs) accelerometer sensing and eventually 6 DOFs modules, including angular rate sensors. In particular, the synergy of multi-DOF inertial sensors turned out to be key in improving the navigation capabilities of inertial modules. The trend towards development of multi- DOF modules goes on [1]. On-chip magnetometers are seen as key components to further improve the performance of IMUs and navigation modules [2]. The first xylophone bar magnetometers (XBMs) designed using imec’s poly-SiGeMEMS technology were reported at IEEE Sensors 2012 [6], based on the multi- physics simulations presented in [5]. In [7], the magnetometers were electrically characterized using a Vector Network Analyzer (VNA). These measurements were shown to be in good agreement with a proposed equivalent circuit. In particular, the real parts of the S21 and S12 parameters showed a clear linear dependency on the applied magnetic B-field. This paper presents analytical expressions for transmission parameters S21 and S12, and in particular their real parts, establishing their representativity as measurant for the magnetic field as well as their representativity for later measurements through, for example, transimpedance amplifier readout. Finally, we present design-based optimization strategies to enhance the sensitivity of the device. 2 XBM MODEL 2.1 Working Principle The working principle of the magnetometer under study is based on a classical resonating xylophone bar [3]. Xylophones are mechanical structures supported at the nodes of the first fundamental transverse mode of vibration. Placed at the non-moving part of the oscillating structure, as shown in Figure 1, the supports have a lower effect on the dynamics of the bar. A sinusoidal current is supplied to the system at its first resonance frequency and when an external magnetic field is present, the resulting Lorentz force causes the bar to vibrate at its fundamental frequency with an amplitude directly proportional to the y-component of the ambient magnetic field. Figure 1: Sketch of a typical Xylophone Bar Magnetometer. The material properties of the imec’s Poly-SiGe [4] and the initial dimensions used for the design optimization in this paper are listed in Tables 1 and 2. Table 1: Material properties of the poly-SiGe [4]. Young Modulus E 130GPa ±10% Mass density  4400kg/m 3 ±5% Poisson ration  0.22 Resistivity e 7.6µΩm ±15% Table 2: Initial dimensions of the poly-SiGe XBM. Length L 500μm Support length Ls 10μm Width b 50μm Support width ws 2μm Thickness t 4μm Hole length Lh1 1μm Gap d0 3μm Hole width Lh2 1μm 2.2 Model Description The magnetometer is seen as a two-port system with an electrodynamic port (Port 1) and an electrostatic port (Port 2), cf. Figure 2. As explained in the previous section, the NSTI-Nanotech 2014, www.nsti.org, ISBN 978-1-4822-5827-1 Vol. 2, 2014 41