Simulation method of Kelvin probe force microscopy at nanometer range and its application

The partitioned-real-space density-functional-based tight-binding (PR-DFTB) method is proposed as a simulation method for calculating the quantum electronic states in Kelvin probe force microscopy (KPFM). This method can be used when a tip is set on a sample surface with a nonorbital-hybridization distance and an applied bias voltage. The PR-DFTB method can perform self-consistent calculations of a system that consists of two subsystems (the tip and the sample). Each subsystem is expressed by a block element of the Fock matrix and thus is characterized by the Fermi level in the block element. Consequently, charge distributions on the two subsystems can be calculated individually. Furthermore, charge redistributions in the subsystems induced by approach of them under an applied bias voltage can also be calculated. Using the proposed PR-DFTB method, we can clarify the mechanism by observing the local contact potential difference (LCPD). Unlike the conventional description of the Kelvin force, the force acting between a biased tip and a sample depends not only on the net charge transferred between the tip and the sample but also on the multipole forces generated by the microscopic charge distribution within the tip and the sample. This is the mechanism responsible for observing the apparent LCPD. KPFM images generated from the minimum bias voltage in the force-bias curve (i.e., LCPD images) are theoretically simulated using tip models for a Si or hydrogenated Si cluster for simple models of a Si(111)-c(4 x 2) surface, a monohydride Si(001) surface with/without a defect, and a Si(111)-(5 x 5) dimer-adatom-stacking fault (DAS) surface.