Simultaneous force and conduction measurements in atomic force microscopy

We used an ultrahigh-vacuum atomic force microscope (AFM) to measure lateral forces and conductivity simultaneously as a function of the applied normal force for nanometer-sized elastic contacts. Metal-coated or bare Si AFM tips are used on cleaved NbSe₂ or graphite surfaces. Results are used to compare various means of obtaining the tip-sample contact area (A₀). We find that simple continuum models can give a reasonable description of the mechanical behavior of the contact. Specifically, the Maugis-Dugdale model [D. Maugis, J. Colloid Interface Sci. 150, 243 (1992)] provides a good basis for describing the elastic contact between an AFM tip and a smooth sample. The theoretical variation in contact radius with load is in good agreement with the experimental variation in friction force, conductivity, and lateral tip-sample contact stiffness. To find the contact area A₀, the best approaches appear to be either to fit the applied force data to an appropriate continuum model (provided the contact is elastic) or to measure the lateral tip-sample contact stiffness. In principle we show that conduction AFM methods can be used to find A₀ for Ohmic contacts. However, the uncertainty in the conduction properties of available AFM tips means that at present the absolute value of A₀ cannot be found with confidence. In this regard the use of metal-coated tips can often be misleading for conduction and mechanical measurements because metal wears rapidly off all or some of the tip apex.