Simple model for the topographic imaging process in a scanning tunneling microscope

Abstract

Electron tunneling is considered within a model simulating the geometry of topographic imaging by a scanning tunneling microscope. Both tip and sample electrodes are approximated by square-well potentials filled up with non-interacting electrons up to their corresponding Fermi energies. The tip electrode extends infinitely along the vertical tip axis and has a small rectangular cross section facing the sample surface. The sample electrode is infinitely extended. The electrodes can change their mutual positions. This enables one to simulate a movement of the tip within any distance from the sample surface. Approaching in this manner an edge or a corner of the sample will help to understand the scanning over topographic features on real sample surfaces. Calculating the tunnel current between the electrodes via Bardeen's transfer Hamiltonian formalism, we can analyze the contribution of single electron states to the total tunnel current. This reveals remarkable differences between k directions and also between different symmetries of the tunneling electrons (tip) state. A constant-current profile is calculated for the three-dimensional version of the model and compared with the results from the literature.