Multiple modulation SPM is a general term for a strategy that extracts information about a surface or nanostructure by combining various signals on samples and tips, using multiple frequencies to distinguish them and accessing multiple harmonics in detection. In addition to the usual conductance, capacitance, surface potential, this approach yields electronic structure, trap state lifetimes, and local dielectric function. Scanning Impedance Microscopy, the first SPM technique to exploit frequency dependence, and its variants will be described. In applications to nanostructure devices, intrinsically higher spatial resolution with respect to scanning gate microscopy is demonstrated, valence band energies of individual defects are quantified, and density of states derived from quantum capacitance extracted. At atomic interfaces in an oxide, local transport anomalies are associated with structurally trapped electrons and associated electric fields are found to cause an unexpected localized phase transition.
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