Arbitrary tip orientation in STM simulations: 3D WKB theory and application to W(110)

TL;DR

This paper extends a 3D WKB tunneling model for STM to include arbitrary tip orientations, revealing how tip shape affects image quality and atom identification, thus aiding better interpretation of experimental STM data.

Contribution

The authors develop a computationally efficient 3D WKB model that incorporates arbitrary tip orientations, enhancing the realism of STM simulations and analysis.

Findings

Tip orientation significantly influences STM image features.

Certain orientations produce artifacts that complicate atom identification.

The model helps interpret experimental STM images by considering tip geometry.

Abstract

We extend the orbital-dependent electron tunneling model implemented within the three-dimensional (3D) Wentzel-Kramers-Brillouin (WKB) atom-superposition approach for simulating scanning tunneling microscopy (STM) by including arbitrary tip orientations. The orientation of the tip is characterized by a local coordinate system centered on the tip apex atom obtained by a rotation with respect to the sample coordinate system. The rotation is described by the Euler angles. Applying our method, we highlight the role of the real-space shape of the electron orbitals involved in the tunneling, and analyze the convergence and the orbital contributions of the tunneling current above the W(110) surface depending on the orientation of a model tungsten tip. We also simulate STM images at constant-current condition, and find that their quality depends very much on the tip orientation. Some orientations result in protrusions on the images that do not occur above W atoms. The presence of such apparent atom positions makes it difficult to identify the exact position of surface atoms. It is suggested that this tip orientation effect should be considered at the evaluation of experimental STM images on other surfaces as well. The presented computationally efficient tunneling model could prove to be useful for obtaining more information on the local tip geometry and orientation by comparing STM experiments to a large number of simulations with systematically varied tip orientations.