Contrast changes in STM images and relations between different tunneling models

A change in bias voltage can reverse the contrast of a scanning-tunneling microscopy (STM) image of an adsorbate molecule on a solid surface. This contrast change may take place not only in a case of tunneling in the neighborhood of a resonance level of the adsorbate, but it can also be seen in the case of a wide energy gap between highest occupied molecular-orbital and lowest unoccupied molecular-orbital levels. In order to find a unified description of contrast changes in STM images, we make comparisons between different approaches to tunneling. We especially consider the role of phase differences between possible tunneling channels. These phase differences can be related to the imaginary and real parts of the Green's function of the system which reveal whether the tunneling takes place through a resonant state or a forbidden gap. Finally, we compare experimental and calculated images of oxygen molecules on a silver surface and analyze the mechanisms of the contrast change in terms of phase shifts in different tunneling channels.