Reconstruction of Kelvin probe force microscopy image with experimentally calibrated point spread function

Quantitative imaging of electric surface potentials with single-atom sensitivity

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.

Determination of tip transfer function for quantitative MFM using frequency domain filtering and least squares method

Magnetic force microscopy has unsurpassed capabilities in analysis of nanoscale and microscale magnetic samples and devices. Similar to other Scanning Probe Microscopy techniques, quantitative analysis remains a challenge. Despite large theoretical and practical progress in this area, present methods are seldom used due to their complexity and lack of systematic understanding of related uncertainties and recommended best practice. Use of the Tip Transfer Function (TTF) is a key concept in making Magnetic Force Microscopy measurements quantitative. We present a numerical study of several aspects of TTF reconstruction using multilayer samples with perpendicular magnetisation. We address the choice of numerical approach, impact of non-periodicity and windowing, suitable conventions for data normalisation and units, criteria for choice of regularisation parameter and experimental effects observed in real measurements. We present a simple regularisation parameter selection method based on TTF width and verify this approach via numerical experiments. Examples of TTF estimation are shown on both 2D and 3D experimental datasets. We give recommendations on best practices for robust TTF estimation, including the choice of windowing function, measurement strategy and dealing with experimental error sources. A method for synthetic MFM data generation, suitable for large scale numerical experiments is also presented.