Simple STM theory

A simple theory for the scanning tunneling microscope is presented. We calculate the tunneling current between the tip and the sample using Bardeen's formalism, as most of the actual theories do. It is usual in most of these theories to calculate the tunneling current under some approximations to make the analytical calculation easier: low temperature, small bias and to choose a particular description for the tip. We think that owing to the presently unknown tip structure and considering these approximations, it is useful to choose a simple model for describing the tip: a box with free electrons inside. In a similar way, the sample consists of extended plane waves. © 1990 Pergamon Press plc.