In this work, we propose an intuitive and easily implementable approach to model and interpret scanning Kelvin probe microscopy images of insulating samples with localized charges. The method, based on the image charges method, has been validated by a systematic comparison of its predictions with experimental measurements performed on charge domains of different sizes, injected in polymethyl methacrylate discontinuous films. The agreement between predictions and experimental lateral profiles, as well as with spectroscopy tip-sample distance curves, supports its consistency. The proposed procedure allows obtaining quantitative information such as total charge and the size of a charge domain and allows estimating the most adequate measurement parameters.
We have used the Scanning Kelvin probe microscopy technique to monitor the charging process of highly resistive granular thin films. The sample is connected to two leads and is separated by an insulator layer from a gate electrode. When a gate voltage is applied, charges enter from the leads and rearrange across the sample. We find very slow processes with characteristic charging times exponentially distributed over a wide range of values, resulting in a logarithmic relaxation to equilibrium. After the gate voltage has been switched off, the system again relaxes logarithmically slowly to the new equilibrium. The results cannot be explained with diffusion models, but most of them can be understood with a hopping percolation model, in which the localization length is shorter than the typical site separation. The technique is very promising for the study of slow phenomena in highly resistive systems and will be able to estimate the conductance of these systems when direct macroscopic measurement techniques are not sensitive enough.
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