THEORY OF THE SCANNING TUNNELING MICROSCOPE

The formula for tunnelling between two objects is fundamental to understanding the scanning tunnelling microscope. Although an exact expression for the one-electron tunnelling current is known, its derivation has previously been complex. Here we present a new derivation which is relatively simple and based on physical arguments. We go on to use our methods to show for the first time the connection between the exact formula and the widely used transfer Hamiltonian method of Bardeen. Finally we emphasize the importance of choosing a formula that minimizes the computational effort required to raster the STM tip across a surface.