Relation between the chemical force and the tunnelling current in atomic point contacts: a simple model

The relation between the tunnelling current It and the interaction energy/force E in an atomic-scale contact is discussed in the framework of a theoretical model established here. According to our model, we predict the existence of two characteristic scaling regimes, where the tunnelling current is either proportional to the interaction energy, I-t similar to E, or to the square of the interaction energy, I-t similar to E-2. We show that the existence of a given regime is basically controlled by two parameters: (i) the energy degeneracy Delta and (ii) the hopping t between electronic levels involved in the interaction process. In addition, we discuss the validity of the Bardeen method to determine the tunnelling current in the short tip-sample distances.