QUESTION

*********Short version************

How to calculate the local electrostatic potential near metal surface (covered by oxide layers) and between two metal surfaces with imposed bias voltage (i.e., STM tunnel junction struction with biased potential,  and ~2nm distance)

*********Long version************

Hello everyone, I am currently investigating the optical and transport properties of the single molecule in STM. The tip and substrate of the STM are both metal, and single molecule is  decoupled from the substrate using oxide multilayers.

Now I want to explain the theoretical data, e.g., the difference cnductance or dI/dV. As far as I know, for dI/dV often the peak for positive bias corresponds to the LUMO while that of the negative bias corresponds to the HOMO. 

Therefore I want to figure out how the energy levels are aligned between the work function of metal and the HOMO&LUMO (IP&EA) of the molecule.

Besides the image charge effect which often lower the HOMO-LUMO gap, the local electrostatic potential should be relavent, because it decides the how bias voltage drops in the STM junction. So how can I calculate the electrostatic potential? Especially with the imposed bias voltage in the STM junction?

In a former research, the oxide layers were simply treated as dielectric material, is it really sufficient? e.g. see attached PDF file.

Can you give me any suggestions? Thanks very much!