Optimal design of a tapping-mode atomic force microscopy cantilever probe with resonance harmonics assignment

In tapping-mode atomic force microscopy, the higher harmonics generated in the tapping process provide evidence for material composition imaging based on material property information (e.g. elasticity). But problems of low amplitude and rapid decay of higher harmonics restrict their sensitivity and accessibility. The probe’s characteristic of assigning resonance frequencies to integer harmonics results in a remarkable improvement of detection sensitivity at specific harmonic frequencies. In this article, a systematic structural optimization framework is demonstrated for designing a three-layer probe with specified ratios between eigenfrequencies. An original regular cantilever probe is divided into three layers, from which the cross-sectional width of the symmetrical top and bottom layers is the design variable, while the middle layer is unchanged. Optimization constraints are the integer ratios between eigenfrequencies, and the objective is to maximize the first eigenfrequency. Numerical examples with single- and multiple-frequency constraints are investigated, which enhance significantly the frequency response at specific harmonic positions.