A duality between surface charge and work function in scanning Kelvin probe microscopy

Scanning Kelvin probe microscopy (SKPM) is a powerful technique for macroscopic imaging of the electrostatic potential above a surface. Though most often used to image work-function variations of conductive surfaces, it can also be used to probe the surface charge on insulating surfaces. In both cases, relating the measured potential to the underlying signal is non-trivial. Here, we derive general relationships between the measured SKPM voltage and the underlying source, revealing either can be cast as a convolution with an appropriately scaled point spread function (PSF). For charge that exists on a thin insulating layer above a conductor, the PSF has the same shape as what would occur from a work-function variation alone, differing by a simple scaling factor. We confirm this relationship by: (1) backing it out from finite-element simulations of work-function and charge signals, and (2) experimentally comparing the measured PSF from a small work-function target to that from a small charge spot. This scaling factor is further validated by comparing SKPM charge measurements with Faraday cup measurements for highly charged samples from contact-charging experiments. Our results highlight a hereto unappreciated connection between SKPM voltage and charge signals, offering a rigorous recipe to extract either from experimental data.