Contributions of higher angular momentum states to lateral resolution in scanning tunneling microscopy

We investigate the influence of higher angular momentum states (AMS’s) to the formation of a scanning tunneling microscopy (STM) image. We calculate the tunneling current between the STM tip, represented by the rotational paraboloid, and the sample, consisting of hemispherical protrusions on the flat metallic surface, using the Bardeen transfer Hamiltonian method. The electron wave function in the paraboloidal tip is expanded in the AMS’s which are the eigenstates of a spherical tip. The total STM image can be constructed using the matrix elements for the tunneling of these particular states. We numerically simulate the STM image of a sample surface and calculate the contributions of a particular AMS to the STM image and to the lateral resolution, showing that higher AMS’s essentially improve the resolution in the STM iamge. Contributions and lateral resolutions of various angular momentum channels are found to depend strongly on the curvature on the tip apex.