Mode selection for electrostatic beam resonators based on motional resistance and quality factor

Area of Science:

• Mechanical Engineering
• Electrical Engineering
• Materials Science

Background:

• Electrostatic beam resonators are vital micro-electromechanical systems (MEMS).
• Understanding vibration mode performance is key for optimizing resonator applications.
• Previous analyses often focused on specific modes without comprehensive comparison.

Purpose of the Study:

• To analytically compare the performance of fundamental and higher vibration modes in electrostatic beam resonators.
• To establish a framework for selecting the optimal vibration mode for resonator applications.
• To investigate the influence of resonator geometry and material properties on mode performance.

Main Methods:

• Derivation of a dynamic model for the electrostatic beam resonator.
• Calculation of motional resistance for various vibration modes.
• Utilization of a validated quality factor model for performance assessment.
• Numerical simulations using silicon resonator parameters.

Main Results:

• The fundamental mode generally exhibits lower motional resistance compared to higher modes.
• The fundamental mode typically offers a higher quality factor.
• Performance advantages of the fundamental mode are most pronounced when aspect ratio or stiffness is constant.
• Analytical equations were derived to compare mode performance based on motional resistance and quality factor.

Conclusions:

• The fundamental mode is often the preferred choice for electrostatic beam resonators due to superior performance metrics.
• The derived analytical framework enables informed selection of vibration modes for specific resonator designs.
• Design considerations, such as aspect ratio and stiffness, significantly impact the optimal mode choice.