Guidelines for the achievement of true atomic resolution with noncontact atomic force microscopy

We investigated the conditions to achieve true atomic resolution with an atomic force microscope under noncontact mode NC-AFM.. At first, we derived the equation of vertical resolution as a function of the signal-to-noise ratio and the decay length of frequency shift by assuming an exponential tip-to-sample distance dependence of frequency shift. Next, by assuming a single atom probe, we derived the equation of lateral resolution as a function of the vertical resolution and the tip-to-sample distance, from which we clarified the guidelines to achieve true atomic resolution with NC-AFM. At last, we made clear the attainable decay length of frequency shift both for the van der Waals potential and the electrostatic Coulomb.potential. q1999 Elsevier Science B.V. All rights reserved.