# Charging of highly resistive granular metal films

## TL;DR

This study uses scanning Kelvin probe microscopy to investigate slow charging and relaxation processes in highly resistive granular metal films, revealing logarithmic relaxation behaviors explained by a hopping percolation model.

## Contribution

It demonstrates the effectiveness of Kelvin probe microscopy in analyzing slow charge dynamics in resistive granular films and introduces a hopping percolation model to explain the observed phenomena.

## Key findings

- Charging times are exponentially distributed over a wide range.
- Relaxation to equilibrium follows a logarithmic pattern.
- Hopping percolation explains the slow charge dynamics.

## Abstract

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.