Theoretical simulation of Kelvin probe force microscopy for Si surfaces by taking account of chemical forces

A new method of theoretical simulation for Kelvin probe force microscopy (KPFM) imaging on semiconductor or metal samples is proposed. The method is based on a partitioned real space (PR) density functional based tight binding (DFTB) calculation of the electronic states to determine the multi-pole electro-static force, which is augmented with the chemical force obtained by a perturbation treatment of the orbital hybridization. With the PR-DFTB method, the change of the total energy is calculated together with the induced charge distribution in the tip and the sample by their approach under an applied bias voltage, and the KPFM images, namely the patterns of local contact potential difference (LCPD) distribution, are obtained with the minimum condition of the interaction force. However, since the interaction force is due to electro-static multi-poles, the spatial resolution of the KPFM images obtained by PR-DFTB is limited to the nano-scale range and an atom-scale resolution cannot be attained. By introducing an additional chemical force, i.e., the force due to the orbital hybridization, we succeeded in reproducing atom-scale resolution of KPFM images. Case studies are performed for clean and impurity embedded Si surfaces with Si tip models.