The surface charge decay: A theoretical and experimental analysis

The ability to retain localized charges at the surface or interface of dielectric materials is a universal property that applies to many different fields such as tribocharging, charge nanopatterning, nanoxerography, etc. Once the surface is charged, its stability and subsequent discharging rate will determine the potential applications of a given system. This decay rate is properly defined by the macroscopic equations which depend on dielectric constants and conductivities of the two media. Here, we derive the equations to model the decay of charge distributions localized at the surface/interface of materials and solve them avoiding additional approximations made so far. Addressing the problem in the Fourier space, we arrive to a compact generic equation which provides a useful tool to determine both the bulk and surface conductivities of a material. Furthermore, we show that Kelvin Probe Force Microscopy (KPFM) is a particularly suited method to exploit this tool. Monitoring the charge decay of previously injected charge patches on silicon dioxide (SiO2), together with an appropriated data analysis, we verify the behavior predicted by our equations. This allows us to characterize the surface and bulk conductivities of SiO2 layers as well as its dependence with the relative humidity.