Resonance frequency analysis for surface-coupled atomic force microscopy cantilever in ambient and liquid environments

Abstract

Shifts in the resonance frequencies of surface-coupled atomic force microscope (AFM) probes are used as the basis for the detection mechanisms in a number of scanning probe microscopy techniques including atomic force acoustic microscopy (AFAM), force modulation microscopy, and resonance enhanced piezoresponse force microscopy (PFM). Here, we analyze resonance characteristics for AFM cantilever coupled to surface in liquid environment, and derive approximate expressions for resonant frequencies as a function of vertical and lateral spring constant of the tip-surface junction. This analysis provides a simplified framework for the interpretation of AFAM and PFM data in ambient, liquid, and vacuum environments.

Local probing of ionic diffusion by electrochemical strain microscopy: Spatial resolution and signal formation mechanisms

“…67 For sufficiently high frequencies, the ultimate noise level of SPM is given by the thermomechanical white noise (practically, most commercial AFMs with appropriate vibrational isolation operate within 1-1.5 order of magnitude from this limit). However, for low frequencies the noise is 1/f character, in which case averaging the signal over large times does not allow more precise measurements.…”

Contact dynamics of tapping mode atomic force microscopy

“…It is also worth pointing out that because V T ðtÞ and y 1 are the functions of time, K II needs to be updated in each time step during the contact. The system can have significant difference in stiffness before and after contact, which changes the system eigenfrequencies [27,42,46,47]. To achieve the same accuracy for the system before and after contact, the time step is different.…”

“…Furthermore, the higher harmonics generated by the tip-sample [41,42]. Kalinin et al [46,47] modeled the friction as if the tip hits a linear spring. This study shows that the lateral friction acts as a pulsing axial force and bending moment on the AFM cantilever and its influence increases with the tilting angle.…”

Sequential piezoresponse force microscopy and the ‘small-data’ problem

“…In addition to the material response, the acquired image I ij is expected to contain noise, as well as certain additional non-stochastic variations which have no relation to the concerned phenomena. Such variation in I ij can occur due to (i) varying PFM tip-sample contact conditions, [45][46][47] and/or (ii) the presence of relative drifts between each image (columns of I ij ). The linear drift between the images is easily removed as a part of the preprocessing step (see supplementary material); however, removal of the non-linear drift is not always trivial.…”