Advancing simulation efficiency for MEMS electrostatic actuators

This paper presents an overview of the research progress on Multiphysics simulation of MEMS electrostatic actuators. MEMS electrostatic actuators have shown significant development potential in applications such as ADWSS and VOA. However, the increasing size and complexity of these devices have posed challenges to traditional Multiphysics simulation methods, leading to lengthy computational times that hinder the overall device development process. In order to enhance simulation efficiency and meet the demands of device development, the use of simplified single physics field models have been explored. The results have demonstrated that the simplified single physics filed simulation model yields comparable results to traditional Multiphysics simulations with an error tolerance of within 10%, while reducing simulation time by 80-90%.


Introduction
In recent years, there has been rapid progress in the development and engineering of MEMS actuators, particularly MEMS electrostatic actuators.These devices have witnessed notable advancements in applications like ADWSS (Arrayed Waveguide Sensing Systems) and VOA (Variable Optical Attenuators).As the engineering of these devices continues, the size and complexity of these actuators are swiftly increasing to meet stringent technical specifications and reliability requirements.
Finite element simulation is an indispensable tool in the DFM (design for manufacturing) process of these devices.MEMS electrostatic actuators inherently involve Multiphysics simulations, including electromechanical coupling.However, the current limitations in parallel computing capabilities of finite element software have started to impact the overall device development iteration progress.Therefore, there is a need to enhance simulation efficiency of the existing finite element simulation techniques to meet the demands of research and development.
In this regard, a finite element simulation method specifically tailored for MEMS electrostatic actuators have been developed, aiming to improve simulation efficiency.By implementing this approach, we have successfully achieved faster simulations, enabling accelerated device development and meeting the required objectives.Taking a specific MEMS electrostatic actuator as an example, the simulation was performed using COMSOL Multiphysics 6.0 (COMSOLCo.,Ltd.,Stockholm,Sweden),as shown in Figure 1.The device consists of two layers of comb fingers, and the simulation requires the inclusion of air units and dynamic meshing.Therefore, the electromechanical coupling multiphysics finite element simulation for this device involves over 500,000 body elements and more than 10 million degrees of freedom.The simulation also accounts for the nonlinearity in the electromechanical coupling process and the success rate of dynamic mesh remeshing.The simulation duration for the device typically ranges from 12 to 48 hours and requires multiple iterations and debugging.

Finite element analysis
To improve simulation efficiency, we attempted to obtain electromechanical coupling data for driving the comb fingers using a single unit electrostatic force simulation.To simulate the comb fingers array, a single unit was constructed with three upper comb fingers and two lower comb fingers.The data extraction was performed on the middle comb fingers, as shown in Figure .2. The upper comb fingers were grounded, while the lower comb fingers were subjected to a driving voltage.Assuming that the deformation of the comb fingers under the electrostatic force can be neglected, a static electrostatic force physics field model was employed in the simulation.By setting different rotation angles and applying varying driving voltages, the static electrostatic driving force data were obtained as a function of rotation angle and driving voltage, as shown in Figure 3.The electrostatic driving force data assumed that the upper layer of the device mainly underwent rotational motion, achieving force balance in the X-direction.The electrostatic forces in the Y-direction and Z-direction were assumed to be functions of the rotation angle and driving voltage.After comparing the data with the torque data, the approximate point of the force application was determined to be the geometric center of the comb fingers.Using the obtained data as input conditions for interpolation functions, the simulation was simplified from electromechanical coupling Multiphysics simulation to a mechanical physics field simulation, as shown in Figure 4.The simulation model excluded the fixed lower comb fingers electrode and the air domain.As a result, the number of mesh elements in the model was reduced to below 100,000, and the number of degrees of freedom decreased to below 500,000.Moreover, due to the removal of dynamic meshing, the model's meshing complexity was significantly reduced.Reduced-Dimensional Solid Mechanics Simulation Model

Results and Discussion
The simulation of a single unit obtained the static driving force data, including the force in the Z-direction and Y-direction.The simulation time for a single unit was within 10 minutes.
By employing the simplified model based on the mechanical physics field, steady-state simulations were conducted.The computed results from this simplified model exhibited an error of less than 10% when compared to the Multiphysics model, as shown in Figure 5.The computation time was reduced from 2 hours to 10 minutes.

Conclusion
Compared to the electromechanical coupling Multiphysics simulation, utilizing a simplified single physics field model can reduce the simulation computation time by 80% to 90%.The use of separation electrostatic force simulation and mechanical simulation allows for finer meshing in the electrostatic force simulation without the need to consider dynamic meshing, thereby improving the accuracy of the electrostatic force simulation.In the mechanical part, the exclusion of Multiphysics coupling significantly enhances simulation efficiency.
However, this approach is only suitable for devices with relatively stable operating modes and clear electromechanical coupling responses.The simulation efficiency could be significantly improved.For simulations involving non-operating modes like impact, collision, and ESD (electrostatic discharge), it is a challenge for this method.

Figure 1 Figure 2 .
Figure 1.Simplified Multiphysics model of MEMS electrostatic actuator with reduced anchors.

Figure 3 .
Figure 3. Interpolated results of electrostatic force of Single Unit: (a) Electrostatic force in the Z-direction, (b) Electrostatic force in the Y-direction.

Figure 5 .
Figure 5.Comparison of results between reduced-dimensional single physics field simulation and Multiphysics simulation