Abstract
Electrostatic forces are among the most common interactions in nature and omnipresent at the nanoscale. Scanning probe methods represent a formidable approach to study these interactions locally. The lateral resolution of such images is, however, often limited as they are based on measuring the force (gradient) due to the entire tip interacting with the entire surface. Recently, we developed scanning quantum dot microscopy (SQDM), a new technique for the imaging and quantification of surface potentials which is based on the gating of a nanometer-size tip-attached quantum dot by the local surface potential and the detection of charge state changes via non-contact atomic force microscopy. Here, we present a rigorous formalism in the framework of which SQDM can be understood and interpreted quantitatively. In particular, we present a general theory of SQDM based on the classical boundary value problem of electrostatics, which is applicable to the full range of sample properties (conductive versus insulating, nanostructured versus homogeneously covered). We elaborate the general theory into a formalism suited for the quantitative analysis of images of nanostructured but predominantly flat and conductive samples.
Highlights
Introduction to scanning quantum dot microscopy (SQDM)1.1 Electrostatic potentials at the nanoscale and their measurementElectrostatic forces are among the most common interactions in nature
The working principle of SQDM is based on the gating of a QD which is mechanically strongly but electronically weakly coupled to the conductive tip of a non-contact atomic force microscope
The potential difference between the QD and the tip is influenced by the potential and the shape of the surfaces of tip and sample
Summary
Electrostatic forces are among the most common interactions in nature While they appear in the macroscopic world only when excess charges are present, they are omnipresent at the nanoscale because the constituents of matter, electrons and nuclei, carry discrete charges. A rather recent development in this direction is the passivation of a standard metal probe with a single CO molecule [15, 16] At these small distances additional effects besides the contact potential difference appear and hamper the quantitative interpretation of the data. We elaborate the general theory into a formalism suited for the quantitative analysis of images of nanostructured but predominantly flat and conductive samples This formalism is applicable to, e.g., atomically ordered metal surfaces with point or line defects, including adsorbates such as isolated molecules, molecular films or 2D materials
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