A method for atomic force microscopy cantilever stiffness calibration under heavy fluid loading

Abstract

This work presents a method for force calibration of rectangular atomic force microscopy ͑AFM͒ microcantilevers under heavy fluid loading. Theoretical modeling of the thermal response of microcantilevers is discussed including a fluid-structure interaction model of the cantilever-fluid system that incorporates the results of the fluctuation-dissipation theorem. This model is curve fit to the measured thermal response of a cantilever in de-ionized water and a cost function is used to quantify the difference between the theoretical model and measured data. The curve fit is performed in a way that restricts the search space to parameters that reflect heavy fluid loading conditions. The resulting fitting parameters are used to calibrate the cantilever. For comparison, cantilevers are calibrated using Sader's method in air and the thermal noise method in both air and water. For a set of eight cantilevers ranging in stiffness from 0.050 to 5.8 N/m, the maximum difference between Sader's calibration performed in air and the new method performed in water was 9.4%. A set of three cantilevers that violate the aspect ratio assumption associated with the fluid loading model ͑length-to-width ratios less than 3.5͒ ranged in stiffness from 0.85 to 4.7 N/m and yielded differences as high as 17.8%.

Noncontact Method for Calibration of Lateral Forces in Scanning Force Microscopy

“…In liquids, the SHO model represents the experimental thermal noise spectrum poorly, causing systematic errors in the spring constant calculation . The thermal spectrum can be described correctly with a fluid−structure interaction model, , but the fitting procedure is often problematic or inaccurate in practice . Pirzer and Hugel have shown that the Lorentzian A normalS normalM 2 ( ν ) = true( A D C 2 true) 2 normalν 0 2 false( ν − ν 0 false) 2 + true( ν 0 2 Q true) 2 + A 0 2 describes the shape of the PSD of cantilevers in viscous fluids (up to ∼7 cP) quite well .…”

A novel method and system for calibrating the spring constant of atomic force microscope cantilever based on electromagnetic actuation

“…The error of electromagnetic force For the accuracy analysis of the suspension mechanism. According to (7) and (8), the standard deviation S  of the suspension mechanism can be obtained by where s, k and n are the standard deviation, the mean value of the spring constant and the number of the measurements using to calculate the mean value for the cantilever. According to TABLE III, the relative standard deviation ( / s k ) is 1.3% and n is 10.…”

“…The loaded force along z-axis acts at the central point of the suspension mechanism, and the vector force to the central can be defined. According to(7) and(8), the calculation stiffness of the suspension mechanism is 31.14 N/m.In the FEA process of the suspension mechanism, the geometrical model is established in the Unigraphics NX 8.0 software, and then imported into the ANSYS Workbench software to generate mesh and further simulate the static and dynamic property. The material is cooper alloy with Young's module 128 GPa, Poisson's ratio 0.34 and density 8300 kg/m 3 .…”

Study of thermal and acoustic noise interferences in low stiffness atomic force microscope cantilevers and characterization of their dynamic properties

“…Indeed, the thermal method can be highly inaccurate if interference with other noise sources (acoustic or mechanical noise from the environment) occurs during the characterization process leading to an underestimation of the spring constant. This issue has been raised in many papers 18,25 and remains unanswered. Although the thermal fluctuations are often considered as a major source of noise in the AFM, studies demonstrate that acoustic noises have also an important effect on microelectromechanical systems.…”