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# Quantitative imaging of electric surface potentials with single-atom sensitivity

## Abstract

Because materials consist of positive nuclei and negative electrons, electric potentials are omnipresent at the atomic scale. However, due to the long range of the Coulomb interaction, large-scale structures completely outshine small ones. This makes the isolation and quantification of the electric potentials that originate from nanoscale objects such as atoms or molecules very challenging. Here we report a non-contact scanning probe technique that addresses this challenge. It exploits a quantum dot sensor and the joint electrostatic screening by tip and surface, thus enabling quantitative surface potential imaging across all relevant length scales down to single atoms. We apply the technique to the characterization of a nanostructured surface, thereby extracting workfunction changes and dipole moments for important reference systems. This authenticates the method as a versatile tool to study the building blocks of materials and devices down to the atomic scale.

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## Code availability

The custom code that was used for the deconvolution in this study is available from the corresponding author upon reasonable request.

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## Acknowledgements

C.W. acknowledges funding through the European Research Council (ERC-StG 757634 ‘CM3’). A.T. and N.F. acknowledge funding by DFG-SFB 951 (project A10). F.S.T. acknowledges funding by DFG-SFB 1083 (project A12).

## Author information

Authors

### Contributions

C.W., R.T. and F.S.T. conceived and designed this research. M.F.B.G., P.L., T.E., N.Fr. and M.M. performed the experiments, C.W. and M.F.B.G. analysed the data. M.M. and R.F. designed and provided the feedback controller, N.Fe. and A.T. conducted the DFT simulations. C.W. and F.S.T. interpreted the data, developed the theory of SQDM imaging and wrote the paper.

### Corresponding author

Correspondence to Christian Wagner.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

Supplementary Figs. 1,2, Supplementary references 1,2

## Rights and permissions

Reprints and Permissions

Wagner, C., Green, M.F.B., Maiworm, M. et al. Quantitative imaging of electric surface potentials with single-atom sensitivity. Nat. Mater. 18, 853–859 (2019). https://doi.org/10.1038/s41563-019-0382-8

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• ### Electric potentials at the atomic scale

Nature Materials (2019)