Enhancing the multiple harmonics by step-like cantilever

Abstract

In atomic force microscopy (AFM), the higher modes are highly sensitive to the tip-sample interactions which generate many harmonics. When a higher harmonic is close to the natural frequency of a mode, the harmonic signal is enhanced by a resonance. The step-like cantilever is proposed as an effective design to enhance the higher harmonic signals. The natural frequencies are changed with the variations of the step-like cantilever sizes. By carefully designing the step-like cantilever, the first three modes can be simultaneously excited. A comprehensive map is provided as a guidance of selecting the appropriate geometric parameters.

Mode Localization and Eigenfrequency Curve Veerings of Two Overhanged Beams

“…Actually there are three more veering loci as indicated by the arrows, which are formed by the veering. Physically, the variation of the overhang length ( ) changes the mass and stiffness distribution of the system and its impact on different mode is different [ 19 ], which is clearly seen in the wavy variations in Figure 2 . As the two overhangs here are identical, there is only one control parameter, i.e., .…”

“…The other twelve are at the two connecting points at and . Physically, these twelve equations are to ensure the continuity of displacement, slope, moment and shear force at the two connecting points [ 19 ]. The governing equation of the overhang–beams–overhang structure is divided into four in three domains, as indicated by Equation ( 3 ).…”

“…The mode coupling can be enhanced when the ratio of two eigenfrequencies is an integer, which is also called harmonic [ 18 ]. However, most structures with small linear vibrations do not have the harmonic property; various methods, such as the step-like design [ 19 ], are used to make a cantilever beam harmonic. Mode coupling can also be enhanced in nonlinear regime, in which large motion induced tension can effectively change the system stiffness and, therefore, tune the system eigenfrequencies to be harmonic [ 17 , 20 ].…”

Tuning the flexural frequency of overhang-/T-shaped microcantilevers for high harmonics

“…Detection using high-harmonic frequencies Atomic force microscope (AFM) with the microcantilever as central nowadays is becoming a conventional device in the detection of micro to nano-objects that helps to reveal the physical and chemical properties in nanoscale. [1][2][3][4][5] Several studies have been adopted to enhance the functionality of the cantilever via changing its cross-section materials [6][7][8][9][10] and dimensions [11][12][13][14][15] and revealed that the sensitivity of the cantilever sensor could be enhanced if higher modes of oscillation are used [16][17][18][19] and the quality factor could be increased, especially when functioned in liquids. 20,21) This is explained by the fact that the surface-to-bulk ratio is lower at higher-order modes, which leads to lower air/fluid damping.…”

“…Therefore, several efforts have been used to efficiently excite the functionality of the higher modes such as adding another test mass, 22) etching an extra magnetic layer 21) to a specific position on the cantilever, selectively exciting the photo-thermal effect by tuning the heat position, 23,24) facilitating a tip-sample interaction that could alter the stiffness of the cantilever, or changing the cross-section. 7,11) Among that, changing the surface geometry to change the cross-section has been examined in several experiments where one [13][14][15] or two 12) holes were made on the cantilever surface by milling a small cantilever on the interior of a standard cantilever. 25) These holes alter the flexural effective mass of the cantilever and lead to a change in the cantilever frequencies.…”