Thermoelastic damping effect analysis in micro flexural resonator of atomic force microscopy

Abstract

In the design of high-Q micro/nano-resonators, dissipation mechanisms may have damaging effects on the quality factor (Q). One of the major dissipation mechanisms is thermoelastic damping (TED) that needs an accurate consideration for prediction. Aim of this paper is to evaluate the effect of TED on the vibrations of thin beam resonators. In particular, we will focus on cantilever beam resonator used in atomic force microscopy (AFM). AFM resonator is actually a cantilever with a spring attached to its free end. The end spring is considered to capture the effect of surface stiffness between tip and sample surface. The coupled governing equations of motion of thin beam with consideration of TED effects are derived. In general, there are four elastic equations that are coupled with thermal conduction equation. Based on accurate assumptions, these equations are simplified and the various boundary conditions have been used in order to validate the computational procedure. In order to accurately determine TED effects, the coupled thermal conduction equation is solved for the temperature field by considering three-dimensional (3-D) heat conduction along the length, width and thickness of the beam. Weighted residual Galerkin technique is used to obtain frequency shift and the quality factor of the thin beam resonator. The obtained results for quality factor, frequency shift and sensitivity change due to thermo-elastic coupling are presented graphically. Furthermore, the effects of beam aspect ratio, stress-free temperature on the quality factor and the influence of the surface stiffness on the frequencies and modal sensitivity of the AFM cantilever with and without considering thermo-elastic damping effects are discussed.