Cantilever contribution to the total electrostatic force measured with the atomic force microscope

Abstract

The atomic force microscope (AFM) is a powerful tool for surface imaging at the nanometer scale and surface force measurements in the piconewton range. Among long-range surface forces, the electrostatic forces play a predominant role. They originate if the electric potentials of the substrate and of the tip of the AFM cantilever are different. A quantitative interpretation of the AFM signal is often difficult because it depends in a complicated fashion on the cantilever-tip-surface geometry. Since the electrostatic interaction is a long-range interaction, the cantilever, which is many microns from the surface, contributes to the total electrostatic force along with the tip. Here we present results of the electrostatic interaction between a conducting flat surface and horizontal or tilted cantilevers, with and without tips, at various distances from the surface. As addressed in a previous work, we show that the contribution of the cantilever to the overall force cannot be neglected. Based on a predictive model and on 3D confocal measurements, we discuss the influence of the tilting angle of the cantilever.

Ultrahigh dielectric constant of thin films obtained by electrostatic force microscopy and artificial neural networks

“…Understanding the electric field effect in nanostructured thin films is a key issue in nanoscience nowadays. 1 By applying a voltage between a force microscope tip and a sample, electrostatic force microscopy (EFM) [2][3][4][5][6][7][8] has been used to analyze different properties of thin films at the nanoscale. 9 Recently, single and few layer graphene (FLG) 10 have attracted much attention because of its atypical response to electrostatic fields, which is in sharp contrast with that expected for conventional conducting or semiconducting films.…”

In‐Plane Potential Gradient Induces Low Frictional Energy Dissipation during the Stick‐Slip Sliding on the Surfaces of 2D Materials

“…In contrast to the increase in adhesion at the tip–sample interface upon the application of an out‐of‐plane bias, no significant change in adhesion is observed under an in‐plane potential gradient (Figure S7, Supporting Information), implying that the induced interaction due to the potential gradient contributes little to the attractive intermolecular interaction. The electrostatic interaction between the array of electrodes and the cantilever can be amplified and estimated as where ε 0 is the vacuum dielectric constant, V is the potential difference between the electrodes and the cantilever, W cant and L cant are the width and length of the cantilever beam, H cant is the height of the tip, and β is the inclination angle of the cantilever. Here, ε 0 = 8.85 × 10 −12 Fm −1 , W cant = 25 × 10 −6 m, L cant = 225 × 10 −6 m, H = 14 × 10 −6 m, β = 16°.…”

Finite Conductivity Effects in Electrostatic Force Microscopy on Thin Dielectric Films: A Theoretical Model

“…This solution is the most adequate for geometries like the one in this paper (see Figure 1) since the cylindrical symmetry around the -axis allows us to easily obtained the specific solution of the electrostatic potential at any region by applying the electrostatic boundary conditions. Equations 3and (4) give the exact values of the coefficients from regions 0 to 2, which are the only parameters that are unknown in (2). The same procedure can be done for any other geometry with the same axial symmetry.…”

“…In recent years, Electrostatic Force Microscopy (EFM) has become a useful tool in quantitative characterization of different properties at the nanoscale [1][2][3][4][5][6]. These technical improvements have been especially relevant in the characterization of thin films [7][8][9][10].…”