Micromachined III-V Multimorph Actuator Model and Design using Simulated Annealing (SA)-Based Global Optimization
A. Ongkodjojo, F.E.H. Tay and R. Akkipeddi
Institute of Materials Research & Engineering, SG
Keywords: multimorph, microactuator, III-V materials, optical MEMS, global optimization
A new AlAs/GaAs-based multimorph microactuator (Fig. 1) is designed and modeled for micro-opto-electro-mechanical systems (MOEMS) applications. As the piezoelectric-based III-V materials such as AlAs/GaAs have small piezoelectric constants, we have developed the Simulated Annealing (SA)-based global optimization  to obtain the optimum solution for the structure with a high sensitivity. This optimization method has shown that it can easily escape from the local optimum tending to the global optimum as shown in Fig. 2. This figure shows the results of the SA run, in which the solution has converged to the global maximum. As the temperature falls, one can observe the algorithm moving on the global maximum. Our proposed optimization method can efficiently lead the design for achieving the highest sensitivity as the structure materials can be grown epitaxially with a minimum thickness of 10 nm for each layer. This capability is supported by the fact that the optimal thickness for the piezoelectric layer is given by the thinnest achievable film based on either breakdown field or fabrication constraints under a constant voltage . In this case, the smallest thickness of the structure layers and then the highest sensitivity can easily be achieved by the optimization method. For more realistic design and model, we develop the constraint optimization using the SA algorithm, which can satisfy the specified constraints such as geometry constraints, resonance frequency, quality factor, output linearity, support beam buckling, stiction, contact during fabrication process, and collapse under its own weight as presented in Table 1. These constraints of the design can be specified to avoid the anticipated problems from the fabrication process and the measurement of MEMS structures. The design variables, the design constraints, and the optimization results are shown in Table 1. To ensure that our model are valid and accurate, the optimization results were verified with another paper  and the FEA using ANSYSTM. According to Fig. 3 - Fig. 6 and Table 2, there is an excellent agreement among the mathematical modeling, the proposed model, and the FEM (finite element modeling). The discrepancies (as shown in Fig. 6) are caused by the fact that the derived mathematical modelings didn't consider the piezoelectric effect of the structure width. Considering the piezoelectric effect across the model width, there is an excellent agreement between the SA and the FEA results. Thus, the results demonstrate that our model and design are valid and accurate. Based on the design, the AlAs/GaAs-based microactuator has a sensitivity of 3.395 x 10-3 mm/V with a resonance frequency of 530.2 kHz and a quality factor of 253 in air without violating the multidisciplinary design constraints. In addition, the validity of our designs have been confirmed by Fig. 5 (resonance frequency as a function of the cantilever microbeam length for GaAs) of the paper . Therefore, very high resonance frequencies can be achieved by the small dimension (length) of the structure by using the growth control in III-V materials. In addition, the valid driving voltage range of the applied DC voltage (Vdc) is 0 - 87.5 Volt with a fixed applied AC voltage (Vac) of 714 mV for deflecting the structure up to 10% of the gap. Considering the breakdown field of the piezoelectric materials, the valid driving DC bias voltage is up to about 20 Volts, which can be applied to the material structure. The III-V materials-based multimorph shows potential applications for monolithic integration of optoelectronic components with MEMS devices enabling the realizations of MOEMS (micro-opto-electro-mechanical systems). In the near future, the proposed design will be fabricated and tested for a class of wavelength tunable electrooptic devices as MOEMS applications.
Nanotech 2004 Conference Technical Program Abstract