LAUSR

Electrical scanning probe microscopies (SPM) use ultrasharp metallic tips to obtain nanometer spatial resolution and are a key tool for characterizing nanoscale semiconducting materials and systems. However, these tips are not passive probes; their high work functions can induce local band bending whose effects depend sensitively on the local geometry and material properties and thus are inherently difficult to quantify. We use sequential finite element simulations to first explore the magnitude and spatial distribution of charge reorganization due to tip-induced band bending (TIBB) for planar and nanostructured geometries. We demonstrate that tip-induced depletion and accumulation of carriers can be significantly modified in confined geometries such as nanowires compared to a bulk planar response. This charge reorganization is due to finite size effects that arise as the nanostructure size approaches the Debye length, with significant implications for a range of SPM techniques. We then use the reorganized charge distribution from our model to describe experimentally measured quantities, using in operando scanning microwave impedance microscopy measurements on axial p-i-n silicon nanowire devices as a specific example. By incorporating TIBB, we reveal that our experimentally observed enhancement (absence) of contrast at the p-i (i-n) junction is explained by the tip-induced accumulation (depletion) of carriers at the interface. Our results demonstrate that the inclusion of TIBB is critical for an accurate interpretation of electrical SPM measurements, and is especially important for weakly screening or low-doped materials, as well as the complex doping patterns and confined geometries commonly encountered in nanoscale systems.