Low frequency resistance fluctuations in an ionic liquid gated channel probed by cross-correlation noise spectroscopy

A system in equilibrium keeps ``exploring" nearby states in the phase space and consequently, fluctuations can contain information, that the mean value does not. However, such measurements involve a fairly complex interplay of effects arising in the device and measurement electronics, that are non-trivial to disentangle. In this paper, we briefly analyse some of these issues and show the relevance of a two-amplifier cross-correlation technique for semiconductors and thin films commonly encountered. We show that by using home-built amplifiers costing less than $10$ USD/piece one can measure spectral densities as low as $\sim 10^{-18}-10^{-19}~ {\rm {V^2}{Hz^{-1}}}$. We apply this method to an ionic liquid gated Ga:ZnO channel and show that the glass transition of the ionic liquid brings about a change in the exponent of the low frequency resistance fluctuations. Our analysis suggests that a log-normal distribution of the Debye relaxation times of the fluctuations and an increased weight of the long timescale relaxations can give a semi-quantitative explanation of the observed change in the exponent.