Interpretation of long-range interatomic force

Recent direct mechanical measurements of atomic force microscopy showed that the force between the silicon tip and the silicon sample is long range in the attractive region and its magnitude at maximum is relatively smaller. These features disagree with previous theoretical predictions based on the ab initio calculations. We investigated the nature of forces between a silicon tip and the silicon $\mathrm{}\left(111\right)\mathrm{}-(2\mathrm{}\times 1)$ surface by performing first-principles pseudopotential and classical molecular dynamics calculations and by calculating the van der Waals interaction. The first two methods give forces that are short range in nature. Fair agreement between the experiment and theory is obtained when the van der Waals interaction is included. The effect of the tip induced deformation is analyzed.