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We extend the orbital-dependent electron tunneling model implemented withinthe three-dimensional (3D) Wentzel-Kramers-Brillouin (WKB) atom-superpositionapproach for simulating scanning tunneling microscopy (STM) by includingarbitrary tip orientations. The orientation of the tip is characterized by alocal coordinate system centered on the tip apex atom obtained by a rotationwith respect to the sample coordinate system. The rotation is described by theEuler angles. Applying our method, we highlight the role of the real-spaceshape of the electron orbitals involved in the tunneling, and analyze theconvergence and the orbital contributions of the tunneling current above theW(110) surface depending on the orientation of a model tungsten tip. We alsosimulate STM images at constant-current condition, and find that their qualitydepends very much on the tip orientation. Some orientations result inprotrusions on the images that do not occur above W atoms. The presence of suchapparent atom positions makes it difficult to identify the exact position ofsurface atoms. It is suggested that this tip orientation effect should beconsidered at the evaluation of experimental STM images on other surfaces aswell. The presented computationally efficient tunneling model could prove to beuseful for obtaining more information on the local tip geometry and orientationby comparing STM experiments to a large number of simulations withsystematically varied tip orientations.

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