Analysis of dynamic force microscopy measuring nano-scale electrostatic force and working function

The analytical method to determine the frequency shift in dynamic force microscopy subjected to the electrostatic force is proposed. The frequency shift of higher mode can be determined easily and precisely by the proposed method. It is well known that the second resonant frequency is used to measure the potential difference between a tip and a sample’s surface. Unfortunately, because the conventional perturbation method considers one degree of freedom only, one cannot determine correctly the second resonant frequency by using this method. Alternatively, for the gradient method the effect of the amplitude of vibration is neglected, a significant error will occur in this conventional method especially for small tip-surface distance. The detailed assessment of the perturbation method and the proposed method determining the frequency shift is made. Besides, Atomic force microscopy (AFM) is now widely used for imaging the surfaces of materials from the micrometer to the sub-nanometer scale. Kelvin probe force microscopy which is based on atomic force microscopy (AFM) is a powerful measuring technique on a nanometer scale using an atomic force microscopy with an electrostatic force, obtained when a.c and d.c. biased voltages are applied to a conventional AFM. With KPFM, the work function of surfaces can be observed at atomic or molecular scales. The work function relates to many surface phenomena, including catalytic activity, reconstruction of surfaces, doping and band-bending of semiconductors. It is well known that the second resonant frequency is used to measure the contact potential difference between a tip and a sample’s surface. Finally, the effects of several parameters on the first two frequency shifts are investigated.