# Mapping the perturbation potential of metallic and dipolar tips in tunneling spectroscopy on MoS$_2$

## TL;DR

This study reveals how the shape and dipole moment of tips influence the electrostatic potential in tunneling spectroscopy on MoS$_2$, affecting molecular orbital measurements and enabling tip characterization.

## Contribution

It demonstrates that tip-induced potential perturbations can be modeled and disentangled, providing a new method to probe tip electrostatics using extended molecules on MoS$_2$.

## Key findings

- Perturbation potential varies with tip shape and dipole moment.
- Apparent intramolecular energy shifts are caused by tip-induced potential inhomogeneity.
- Extended molecules on MoS$_2$ can serve as sensors for tip electrostatic profiles.

## Abstract

Scanning tunneling spectroscopy requires the application of a potential difference between the sample and a tip. In metal-vacuum-metal junctions, one can safely assume that the potential is constant along the metallic substrate. Here, we show that the inhomogeneous shape of the electric potential has to be taken into account when probing spatially extended molecules on a decoupling layer. To this end, oligothiophene-based molecules were deposited on a monolayer of molybdenum disulfide (MoS$_2$) on a Au(111) surface. By probing the delocalized molecular orbital along the thiophene-backbone, we found an apparent intramolecular shift of the positive ion resonance, which can be ascribed to a perturbation potential caused by the tip. Using a simple model for the electrostatic landscape, we show that such a perturbation is caused by the inhomogeneity of the applied bias potential in the junction and may be further modified by an electric dipole of a functionalized tip. The two effects can be disentangled in tunneling spectra by probing the apparent energy shift of vibronic resonances along the molecular backbone. We suggest that extended molecules on MoS$_2$ can be used as a sensor for the shape of the electrostatic potential of arbitrary tips.