Pull-in voltage uniformity analysis of digitally operated micro mirror array with torsional springs

Abstract

This paper reports on the analysis and characterization of the pull-in voltage (PV) uniformity for a digitally operated micro mirror array (MMA). The designed micro mirror has a square mirror plate of dimension 210 µm, two torsional springs 42 µm long, and is operated by an electrostatic force. A numerical analysis of the PV was performed by calculating its variations with respect to four-dimensional parameters, namely, the spring width (ws), the spring thickness (ts), the mirror gap (Z0) and the level of misalignment (dm). The spring width and spring thickness are the dominant factors for obtaining uniform PVs, assuming the spring thickness and the mirror gap are independent of each other, but the remaining silicon thickness becomes more important if the spring thickness and the mirror gap are correlated with each other. Two kinds of silicon substrates were used for the silicon structures to compare the silicon thickness effects. The bonding temperature of silicon on glass (SiOG) wafers has been optimized at 370 °C in order to minimize the wafer bow due to the difference of the thermal expansion between the silicon and the glass wafers; however, the normalized standard deviation of PVs of all micro mirrors was much higher (20.8%) than the results of the SOI wafers (7.2%). The severe deformation of the spring widths was alleviated by changing the final release process from the sample level to the wafer level. Finally, the misalignments inside a wafer were analyzed by comparing the left and right side PV difference to find that misalignments of 5.1 µm existed.