Image Force Effects on Tunneling Currents in an STM -- I `Point charge in the Barrier Region' - Model

In a Scanning Tunneling Microscope (STM), when a tunneling electron treated as a point charge enters the barrier region between the tip and the sample, it induces image charges on the conducting surfaces, which modifies the shape of the potential barrier it sees. In this paper, the effect of the modification in the barrier potential due to these induced charges on the tunneling current density and currents in an STM,is studied as a function of the tip-sample distance $d$ and the Bias Potential $eV_b$. The image potential is found to reduce the height and the effective width of the potential barrier, leading to a huge increase in the tunneling current densities. This huge increase (by several order of magnitudes) is however unreasonable, prompting a revisit of the assumption that the electron in the barrier region is a point particle.