Linearization of electrostatically actuated surface micromachined 2-D optical scanner

Abstract

This paper presents an effective method of linearizing the electrostatic transfer characteristics of micromachined two-dimensional (2-D) scanners. The orthogonal scan angles of surface micromachined polysilicon scanner are controlled by using quadrant electrodes for electrostatic actuation. By using a pair of differential voltages over a bias voltage, we could improve the distortion of projected images from 72% to only 13%. A theoretical model has been developed to predict the angle-voltage transfer characteristics of the 2-D scanner. The simulation results agree very well with experimental data. Differential voltage operation has been found to suppress the crosstalk of two orthogonal scan axes by both experimentally and theoretically. We have found that a circular mirror is expected to have the lowest angular distortion compared with square mirrors. Perfect grid scanning pattern of small distortion (0.33%) has been successfully obtained by predistorting the driving voltages after calibration.[604]Index Terms-Electrostatic analysis, electrostatic force, microactuators, optical 2-D scanner, torsion mirror.

A Characteristic Study of Micromirror with Sidewall Electrodes

“…Global coordinate system is fixed on the substrate and the origin of body-fixed coordinate system is set on the centre of the micromirror plate. These definitions are the same as Toshiyoshi et al (2001).…”

“…When the micromirror plate is inclined, we can define the angles between the micromirror plate, and the bottom electrodes and the sidewall electrodes by h, u, and w, respectively. The maximum slope angle of the mirror to the bottom electrode, h, is equal to the angle between the normal vector of the mirror, m m 0 and the z-axis (z ¼ (0,0,1)) (Toshiyoshi et al 2001). In addition, as shown in Figure 4a, the maximum slope angle of the mirror to the sidewall electrode (e 12 ), u, is equal to the angle between the normal vector m m 0 and the y-axis (y ¼ (0,1,0)); in Figure 4b, the maximum slope angle of the mirror to the sidewall electrode (e 13 ), w, is equal to the angle between the normal vector m m 0 and the x-axis (x ¼ (1,0,0)).…”

“…A small area (dS) on the mirror in the body-fixed coordinate system, A(x, y, 0), and the normal vector of the mirror, m ¼ (0, 0, 1), in Figure 3, are transferred to the global coordinate system, and corresponding coordinate A 0 and vector m m 0 are respectively (see Toshiyoshi et al 2001). Note that the four group electrodes, e 11 e 12 e 13 ; e 21 e 22 e 23 ; e 31 e 32 e 33 , and e 41 e 42 e 43 are shown in Figure 3.…”

“…As a result, micromirrors with sidewall electrodes are proposed in Pu et al (2004). Although the effect of bottom electrodes is well understood (Dickensheets and Kino 1998;Toshiyoshi et al 2001;Yeow et al 2005), there is no theoretical model to describe the effect of sidewall electrodes on a biaxial micromirror (Toshiyoshi and Fujita 1996;Zhu et al 2006). The purpose of combining sidewall electrodes with bottom electrodes is to increase the electrostatic force on the micromirror plate.…”

“…Therefore, the reduction of driving voltages while increasing the tilt angle range is a core requirement for the next-generation of electrostatic scanners. Traditionally, a biaxial micromirror is actuated by either four separate bottom electrodes (Toshiyoshi et al 2001) and two outer bottom electrodes on the outer attraction plates of the micromirror (Yeow et al 2005). In addition, some micromirror designs adopted comb-drive actuators (Hah et al 2004a;Hah et al 2004b;Kwon et al 2004;Lee et al 2002;Xie et al 2003); however, comb-drive actuator is complex in fabrication and processing.…”