Interpretation of force curves in force microscopy

Abstract

Since the introduction of force microscopy in 1986 as a tool for imaging insulators, it has increasingly been acclaimed as a quantitative probe of surface forces such as van der Waals, capillary, electrostatic, capacitive, double-layer, magnetic or adhesive forces. A plot of the force interaction between two surfaces-typically a tip mounted on a cantilever beam and a flat surfac&as a function of relative tipsample separation constitutes a force curve, and such measurements have been termed 'force spectroscopy' (FS). We descfibe how to interpret force curves so as to gain information about (i) the instant of tipsample contact, (ii) the magnitude and functional dependence of adhesive and long-range attractive forces for different tip/sample combinations, (iii) possible mechanisms of long-range force interaction (surface layers, fNed dipoles, patch charges), (i v) tipsample contact area, which relates to the imaging mechanism in contact-mode force microscopy, (v) the elastic modulus and plasticity of thin and thick films, and (vi) how the pull-off force varies as a function of the maximum load.

Theories of scanning probe microscopes at the atomic scale

“…In this section the interactions significant to standard imaging are discussed, with specific reference to those forces important to the applications discussed later. Several other interactions, e.g., image forces, capacitance forces, and forces due to discrete charges, can be important for specific tip-surface setups and environments (Burnham et al, 1993;Capella and Dietler, 1999;Morita et al, 2002). These components of long-range electrostatic interaction between tip and surface can normally be minimized by applying a compensating bias during scanning (Bennewitz et al, 1999a).…”

“…In this section we shall focus on those macroscopic forces most relevant to applications we discuss later. More detailed general information can be found in Burnham et al (1993) and Capella and Dietler (1999).…”

“…By calculating the capacitance force as a function of z alone, it is assumed that the work function is uniform across the surface. On real surfaces, inequivalencies in the work function across the surface can arise due to surface preparation, adsorbates, crystallographic orientation, and variations in local geometry (Burnham et al, 1992(Burnham et al, , 1993. Real surfaces of any material are not perfectly smooth, as is suggested by the very-small-scale NC-SFM images usually seen.…”

Nanoindentation and contact stiffness measurement using force modulation with a capacitive load-displacement transducer

“…The SFA is mainly used for direct measurements of surface and intermolecular forces and not for surface elastic and plastic properties of materials. While the AFM was used early to investigate elastic and plastic properties at nanoscale 4,5 , conventional force detection techniques (inferred from the known spring constant of the lever), small tip size, and unknown tip shape, the contact area is difficult to measure, hence the measured mechanical properties are usually only qualitative. Recent developments in scanning probe microscopy, combining depth sensing nanoindentation with imaging capabilities 6,7 reduces problems in quantifying load-displacement data.…”

Nanoscale Viscoelastic Characterization Using Tapping Mode AFM

“…It has been modeled as a single degree-of-freedom nonlinear oscillator [4][5][6][7][8][9][10][11]. In this model, the tip-sample interactions are described by contact theory with adhesion (Johnson-Kendall-Roberts (JKR) theory) [12][13][14]. The viscoelasticity is considered as a friction force by adding a damping constant.…”