System-level modeling and verification of a Micro Pitch-tunable Grating

Micro Pitch-tunable Grating based on microeletromechanical systems(MEMS) technology can modulate the grating period dynamically by controlling the drive voltage. The device is so complex that it is impossible to model and sumulation by FEA method or only analysis macromodel. In this paper, a new hybrid system-level modeling method was presented. Firstly the grating was decomposed into function components such as grating beam, supporting beam, electrostatic comb-driver. Block Arnoldi algorithm was used to obtain the numerical macromodel of the grating beams and supporting beams, the analytical macromodels called multi-port-elements(MPEs) of the comb-driver and other parts were also established, and the elements were connected together to form hybrid network for representing the system-level models of the grating in MEME Garden, which is a MEMS CAD tool developed by Micro and Nano Electromechanical Systems Laboratory, Northwestern Polytechnical University. Both frequency and time domain simulation were implemented. The grating was fabricated using silicon-on-glass(SOG) process. The measured working displacement is 16.5 mu m at a driving voltage of 40V. The simulation result is 17.6 mu m which shows an acceptable agreement with the measurement result within the error tolerance of 6.7%. The method proposed in this paper can solve the voltage-displacement simulation problem of this kind of complex grating. It can also be adapted to similar MEMS/MOEMS devices simulations.