Three-dimensional approach to scanning tunneling spectroscopy and application to Shockley states

The problem of the interpretation of scanning tunneling spectroscopy (STS) data is analytically solved using a three-dimensional (3D) transfer Hamiltonian approach. We present an analytical model capable of including both the electronic structure of the sample and the symmetry of the tip states (s, p _z, d_z²,...) and we discuss the role of these 3D aspects in tunneling. We applied this model to the case of Shockley states. This system, allowing a full analytical treatment, led us to a detailed simulation and comprehension of the tunneling process. A procedure for the recovery of the sample local density of states from STS measurements is then proposed and applied to both the simulated and the experimental STS data of Shockley states. Comparing this approach with other methods proposed in the literature, the importance of considering the 3D aspects in treating and interpreting STS data is demonstrated.