In this paper a study

In this paper, a study of the differential charge (shielded vs. exposed) on the sense electrodes as a function of MEFM geometry is presented using finite osthole analysis method (FEM). Comparing to the conformal mapping analysis that is commonly used in this area, FEM can more easily deal with a much more complicated structure, such as the structure considered in this paper. Furthermore, FEM readily includes the effect of the fringing electric field through the shutter perforations and incident on the lower electrodes. Accurate consideration of the fringing field is critical to determining the differential charging between shielded and exposed sensor electrodes. With the FEM, the optimization of structural parameters to maximize differential charge signal is studied. In addition, the effect of non-vertical shutter perforation geometry is studied, in order to explore the effect of non-ideal anisotropic etch of shutter perforations. All studies are undertaken for the case of an electrically grounded shutter, and the shutter defined to be metal conductor (gold). Earlier, the case of a silicon dielectric shutter was investigated in [19].
Simulation parameters The parametric study of MEFM design in this paper focuses on the parameters in Fig. 1 of shielding shutter perforation width S, shutter thickness t, sense electrode width E, and shutter to electrode gap g, in order to determine their effects on the MEFM signal. In all studies, the thickness of the sense electrodes was 0.5μm. All these four parameters are fully investigated using FEM simulations. The definitions of the different MEFM design parameters are given in Table 1. If we were to neglect fringing under the shutter, the amount of the induced charge on the surface of the electrodes exposed to the electric field would follow:where Q is the amount of the induced charge on the surface of the electrodes, ε is the permittivity of free space, ε is the relative permittivity of the medium, E is the incident electric field strength orthogonal to the surface of the sensing electrodes, and A is the area of the electrodes. According to this equation, the induced current is proportional to the incident field strength, and the rate of change of the surface area of the electrodes, as they are covered by the moving shutter. However, in a real MEFM, fringing electric field under the shutter can induce charge on visibly shielded electrodes. The proportion of the dc field, which reaches the sensing electrodes, can depend greatly on S, t, and g. Therefore, to account for the fringing electric field, FEM was used to model the MEFM in operation. The FEM simulation settings are discussed in detail below.
Simulation settings Finite element simulations were done with COMSOL Multi-physics. The electrostatic interface of the AC/DC module was used. Both 3-D simulations and 2-D simulations were carried out. The 3-D simulation was done first, with the shutter and electrodes electrically grounded and the electric field vertically incident from above the shutter. Since the results of the simulations for electrode charging are simply proportional to incident electric field strength, a field of 0.1V/m was applied. The induced charge on the sense electrodes when fully exposed to the incident field was compared to the result from the similar simulations done by Gong et al. [18], and a strong agreement was found. With the simulation model verified, subsequent analysis was undertaken using 2-D simulations due to the lower computation time. The simulations were done along a line bisecting the MEFM shutter following the x-axis for symmetry. The 2-D simulations are valid as long as S is much larger than the other dimensions. The setup of 2-D simulations is shown in Fig. 2. The substrate used in the simulation is not shown in Fig. 2, in order to give a simpler picture which better illustrates the gold electrodes. In the simulation, the substrate lies directly under the electrodes, and was set to be intrinsic silicon. The far side of the substrate opposite to the electrodes was electrically grounded as it would be in a packaged device.