Using Hexamodal-Frequency Excitation Scheme to Improve Sensitivity to Tip-Sample Interaction Forces at Flexural Eigenmodes in AFM

Surface topography and material properties of the sample are simultaneously gathered utilizing the multi-frequency excitation schemes in Atomic Force Microscopy (AFM). Driving the micro-cantilever at multiple resonance frequencies increases its sensitivity to tip-sample interaction forces such as van der Waals (vdW) and Casimir forces, when compared with single-frequency excitation scheme. This paper introduces the theoretical results regarding implementation of hexamodal-frequency excitation scheme for enhanced observable sensitivity to vdW forces within the separation distance range of 3-20 nm in non-contact AFM simulations. The oscillatory responses of the AFM micro-cantilevers strongly depend on their mechanical properties and dimensional parameters. In this regard, the effects of elastic stiffness, materials, quality factors, and tip radii of four AFM micro-cantilevers on vibration observables are explored for the fundamental and higher flexural eigenmodes. Monomodal and trimodal operations are also conducted to exhibit the effectiveness of hexamodal-frequency excitation scheme using the responses of amplitude, phase shift, and frequency shift. Additionally, fundamental amplitude ratios ( $$A_{1} / A_{01}$$ ) obtained using the proposed dynamic model for trimodal operations of all AFM micro-cantilevers under the same operating conditions are compared with the simulation results for the separation distance range of around 1.5-3.9 nm in the literature. Theoretical results exhibit good compatibility with the experimental results obtained in other works. Numerical results suggest that application of hexamodal-frequency excitation scheme brings higher sensitivity of amplitude and phase shift for the particular separation distances below 15 nm, when compared with other excitation schemes. For instance, the amplitude response of around 1 nm at the second flexural eigenmode ( $$\triangle A_{2}$$ ) of the micro-cantilever M1 is noted for the tip radius, varying from 7 nm to 20 nm under hexamodal-frequency excitations. It is also noted that the observable responses within the high-sensitivity range of separation distance (the range of 3-15 nm) can be significantly affected by varying features of the AFM micro-cantilevers at the fundamental and higher vibration modes for all excitation schemes. Utilizing hexamodal-frequency excitation schemes provides higher sensitivity to tip-sample interaction forces, depending on the properties of the AFM micro-cantilevers.