Nonlinear Stiffness and Nonlinear Damping in Atomically Thin MoS₂ Nanomechanical Resonators

Area of Science:

• Nanoscience and Nanotechnology
• Mechanical Engineering
• Materials Science

Background:

• Two-dimensional (2D) materials like molybdenum disulfide (MoS2) offer unique mechanical properties for nanomechanical resonators.
• Understanding nonlinear dynamics is crucial for optimizing the performance and reliability of these resonators, especially at very high frequencies (VHF).

Purpose of the Study:

• To experimentally measure and quantitatively analyze nonlinear dynamic characteristics in single-layer (1L), bilayer (2L), and trilayer (3L) MoS2 nanomechanical resonators.
• To determine cubic and quintic order nonlinear damping and stiffness coefficients for these 2D resonators operating up to ~90 MHz.
• To investigate the origins and engineerable parameter dependencies of nonlinear damping and frequency detuning.

Main Methods:

• Fabrication of ultimately thin nanomechanical resonators using 1L, 2L, and 3L MoS2 vibrating drumhead membranes.
• Experimental measurements of nonlinear dynamic responses in the very high frequency (VHF) band.
• Synergistic approach combining calibrated measurements with analytical modeling to determine nonlinear coefficients.

Main Results:

• Quantification of nonlinear damping and stiffness coefficients at cubic and quintic orders for MoS2 resonators.
• Demonstration that quintic forces can constitute up to ~20% of the Duffing force at larger amplitudes, necessitating their inclusion in analyses.
• First-time quantification of nonlinear damping and frequency detuning characteristics in 2D semiconductor nanomechanical resonators.

Conclusions:

• The study establishes a foundational understanding of nonlinear dynamics in 2D MoS2 nanomechanical resonators.
• Nonlinear damping and stiffness coefficients are quantified, highlighting the significance of higher-order nonlinearities (quintic).
• Findings pave the way for future exploration and utilization of nonlinear dynamics in 2D nanomechanical systems by elucidating parameter dependencies.