--- _id: '12109' abstract: - lang: eng text: Kelvin probe force microscopy (KPFM) is a powerful tool for studying contact electrification (CE) at the nanoscale, but converting KPFM voltage maps to charge density maps is nontrivial due to long-range forces and complex system geometry. Here we present a strategy using finite-element method (FEM) simulations to determine the Green's function of the KPFM probe/insulator/ground system, which allows us to quantitatively extract surface charge. Testing our approach with synthetic data, we find that accounting for the atomic force microscope (AFM) tip, cone, and cantilever is necessary to recover a known input and that existing methods lead to gross miscalculation or even the incorrect sign of the underlying charge. Applying it to experimental data, we demonstrate its capacity to extract realistic surface charge densities and fine details from contact-charged surfaces. Our method gives a straightforward recipe to convert qualitative KPFM voltage data into quantitative charge data over a range of experimental conditions, enabling quantitative CE at the nanoscale. acknowledged_ssus: - _id: M-Shop - _id: NanoFab - _id: ScienComp acknowledgement: "This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement\r\nNo. 949120). This research was supported by the Scientific Service Units of the Institute of Science and Technology Austria (ISTA) through resources provided by the Miba Machine\r\nShop, the Nanofabrication Facility, and the Scientific Computing Facility. We thank F. Stumpf from Park Systems for useful discussions and support with scanning probe microscopy.\r\nF.P. and J.C.S. contributed equally to this work." article_number: '125605' article_processing_charge: No article_type: original author: - first_name: Felix full_name: Pertl, Felix id: 6313aec0-15b2-11ec-abd3-ed67d16139af last_name: Pertl - first_name: Juan Carlos A full_name: Sobarzo Ponce, Juan Carlos A id: 4B807D68-AE37-11E9-AC72-31CAE5697425 last_name: Sobarzo Ponce - first_name: Lubuna B full_name: Shafeek, Lubuna B id: 3CD37A82-F248-11E8-B48F-1D18A9856A87 last_name: Shafeek orcid: 0000-0001-7180-6050 - first_name: Tobias full_name: Cramer, Tobias last_name: Cramer - first_name: Scott R full_name: Waitukaitis, Scott R id: 3A1FFC16-F248-11E8-B48F-1D18A9856A87 last_name: Waitukaitis orcid: 0000-0002-2299-3176 citation: ama: Pertl F, Sobarzo Ponce JCA, Shafeek LB, Cramer T, Waitukaitis SR. Quantifying nanoscale charge density features of contact-charged surfaces with an FEM/KPFM-hybrid approach. Physical Review Materials. 2022;6(12). doi:10.1103/PhysRevMaterials.6.125605 apa: Pertl, F., Sobarzo Ponce, J. C. A., Shafeek, L. B., Cramer, T., & Waitukaitis, S. R. (2022). Quantifying nanoscale charge density features of contact-charged surfaces with an FEM/KPFM-hybrid approach. Physical Review Materials. American Physical Society. https://doi.org/10.1103/PhysRevMaterials.6.125605 chicago: Pertl, Felix, Juan Carlos A Sobarzo Ponce, Lubuna B Shafeek, Tobias Cramer, and Scott R Waitukaitis. “Quantifying Nanoscale Charge Density Features of Contact-Charged Surfaces with an FEM/KPFM-Hybrid Approach.” Physical Review Materials. American Physical Society, 2022. https://doi.org/10.1103/PhysRevMaterials.6.125605. ieee: F. Pertl, J. C. A. Sobarzo Ponce, L. B. Shafeek, T. Cramer, and S. R. Waitukaitis, “Quantifying nanoscale charge density features of contact-charged surfaces with an FEM/KPFM-hybrid approach,” Physical Review Materials, vol. 6, no. 12. American Physical Society, 2022. ista: Pertl F, Sobarzo Ponce JCA, Shafeek LB, Cramer T, Waitukaitis SR. 2022. Quantifying nanoscale charge density features of contact-charged surfaces with an FEM/KPFM-hybrid approach. Physical Review Materials. 6(12), 125605. mla: Pertl, Felix, et al. “Quantifying Nanoscale Charge Density Features of Contact-Charged Surfaces with an FEM/KPFM-Hybrid Approach.” Physical Review Materials, vol. 6, no. 12, 125605, American Physical Society, 2022, doi:10.1103/PhysRevMaterials.6.125605. short: F. Pertl, J.C.A. Sobarzo Ponce, L.B. Shafeek, T. Cramer, S.R. Waitukaitis, Physical Review Materials 6 (2022). date_created: 2023-01-08T23:00:53Z date_published: 2022-12-29T00:00:00Z date_updated: 2023-08-03T14:11:29Z day: '29' department: - _id: ScWa - _id: NanoFab doi: 10.1103/PhysRevMaterials.6.125605 ec_funded: 1 external_id: arxiv: - '2209.01889' isi: - '000908384800001' intvolume: ' 6' isi: 1 issue: '12' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.2209.01889' month: '12' oa: 1 oa_version: Preprint project: - _id: 0aa60e99-070f-11eb-9043-a6de6bdc3afa call_identifier: H2020 grant_number: '949120' name: 'Tribocharge: a multi-scale approach to an enduring problem in physics' publication: Physical Review Materials publication_identifier: eissn: - 2475-9953 publication_status: published publisher: American Physical Society quality_controlled: '1' scopus_import: '1' status: public title: Quantifying nanoscale charge density features of contact-charged surfaces with an FEM/KPFM-hybrid approach type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 6 year: '2022' ...