A 2 degree-of-freedom SOI-MEMS translation stage with closed loop positioning

This research contains the design, analysis, fabrication, and characterization of a closed loop XY micro positioning stage. The XY micro positioning stage is developed by adapting parallel-kinematic mechanisms, which have been widely used for macro and meso scale positioning systems, to silicon-based micropositioner. Two orthogonal electrostatic comb drives are connected to moving table through 4-bar mechanism and independent hinges which restrict unwanted rotation in 2-degree-of-freedom translational stage. The XY micro positioning stage is fabricated on SOI wafer with three photolithography patterning processes followed by series of DRIE etching and HF etching to remove buried oxide layer to release the end-effector of the device. The fabricated XY micro positioning stage is shown in Fig1 with SEM images. The device provides a motion range of 20 microns in each direction at the driving voltage of 100V. The resonant frequency of the XY stage under ambient conditions is 811 Hz with a high quality factor of 40 achieved from parallel kinematics. The positioning loop is closed using a COTS capacitance-to-voltage conversion IC and a PID controller built in D-space is used to control position with an uncertainty characterized by a standard distribution of 5.24nm and a approximate closed-loop bandwidth of 27Hz. With the positioning loop, the rise time and settling time for closed-loop system are 50ms and 100ms. With sinusoidal input of ω=1Hz, the maximum phase difference of 108nm from reference input is obtained with total motion range of 8μm

A variational perturbation scheme for many-particle systems in the functional integral approach

A variational Perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the thermodynamic potential is established. A modified Wick's theorem is obtained for the variational perturbation expansions. This theorem allows one to carry out systematic calculations of higher order terms without worrying about the double counting problem. A model numerical calculation was carried out on a nucleon gas system interacting through the Yukawa-type potential to test the efficiency of the present method.Comment: accepted for publication in Phys. Rev.