2D-finite-element simulations for long-range capacitive position sensor

This paper presents the results of 2D-finite-element simulations of the periodic change in capacitance between two periodic structures, one sliding and one fixed (i.e. sense-structure). These structures are potentially interesting for long-range and high-accuracy position detection of microactuators. The use of periodic geometries and the combination of a discrete (incremental) and analog measurement relieves the demands for accuracy. The discrete measurement involves counting the number of periods. The (capacitance) analog measurement determines the position within one period, preferably with nm-accuracy. Two concepts are presented: (i) open-loop measurement of capacitance change versus slider displacement, (ii) closed-loop control of capacitance change versus slider displacement (i.e. sense-structure is actuated in orthogonal direction to the slider motion). These concepts are independent of their application in micro-scale devices but the realization raises particular challenges involving capacitance measurement and micromachining techniques. The periodic patterns examined in these simulations contain rectangular, triangular and sinusoidal shapes and several combinations. Simulation results for both concepts show measurable periodic changes in capacitance. For two arrays of 50 rectangular finger pairs along the sides of the slider the capacitance Cs ≈ 15 fF and Cmax ≈ 7 fF are predicted. Application of this concept in a micromachined device is advantageous because sensor and actuator are integrated in the same structural layer and allows fabrication using one lithographic mask only.