Modeling and Control of Mechanical Nonlinearity in Doubly-Clamped Microelectromechanical System Beam Resonator

MEMS resonators are attractive for sensing applications owing to their inherent high sensitivity. MEMS resonators can induce mechanical resonance of high quality(Q)-factors, which enables precision readout of the shift in their resonance frequencies for various sensing scenarios. However, mechanical nonlinearity in MEMS resonators presents challenges for device applications, such as hysteresis and increased frequency noise, which can degrade device performance. Conversely, nonlinear dynamics also offer new possibilities for advanced functionalities, including enhanced frequency stability and improved thermal responsivity through nonlinear mode coupling. In this study, the tunable nonlinearity of doubly-clamped MEMS beams is modeled, with a particular focus on MEMS beams featuring a small initial center deflection. It is demonstrated that the mechanical nonlinearity of the first bending mode can be significantly tuned by applying internal strain, either thermally induced or resulting from preloaded lattice mismatch strain. Notably, the mechanical nonlinearity can be tuned from hardening to softening, with the possibility of achieving a quasi-zero nonlinearity condition. This condition is very promising for applications requiring ultra-high sensitivity sensing.