Electrostatic comb drive for vertical actuation Page: 6 of 14
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parameters to determine the electrostatic vertical force include the width of the comb fingers, the thickness of the comb fingers,
the gaps between fingers, the position of the moving comb finger, and the vertical gap between the structures and the substrate.
The mechanical folded beam suspension spring constant K5 is determined by the dimensions of the flexures and the number of
folds. Beneath the suspended mass, m, a capacitive pad is designed for vertical position sensing using the parallel plate config-
The voltage-deflection response of the mirror was modeled using a combination of finite element analysis and hand calcu-
lations. Maxwell 2D, an electrostatic finite element code, was used to calculate the electrostatic forces on one comb finger at
voltages ranging from 2 to 20 V and levitation heights from -2 to 2 pm. Figure 4 shows the electric field from one such simu-
lation. Plots of electrostatic force vs. levitation height for different voltages was made from these results (see Fig. 5). From Fig.
5 it is seen that there is a neutral levitation height above the initial position at which the electrostatic force is equal io Ler. in
the current example this neutral position is 1 pmi. A f nrth nrdar nnlymnninl wasv fit to ca'h nnstan vnla- rnnr a a fnoro
balance was used! to determine the mirror's leviation height as a function of voltage. Setting the electrostatic force F_ ernal to
the gravitational fArre F and the susnencion force F, results in the goveming ennation
F(d, v)= F.+ F,(d)
where d is the levitation height. The flexure spring constant and resulting suspension force is calculated by Castigliano's
theory'2. Equation 1 leads to discrete data points for levitation heights at different applied voltages. Figure 6 shows the mod-
eling results for one mirror design with four different suspension stiffnesses.
Figure 4.FEM illustrating electric field lines and equi-potential lines
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Lee, A. P., LLNL. Electrostatic comb drive for vertical actuation, article, July 10, 1997; (https://digital.library.unt.edu/ark:/67531/metadc619911/m1/6/: accessed May 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.