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 nontrivial to disentangle. In this paper, we briefly analyze 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 very low-cost amplifiers, one can measure spectral densities as low as approximately ${10}^{\ensuremath{-}18}$--${10}^{\ensuremath{-}19}\phantom{\rule{0.2em}{0ex}}{\mathrm{V}}^{2}\phantom{\rule{0.2em}{0ex}}\mathrm{H}{\mathrm{z}}^{\ensuremath{-}1}$. 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 of the conducting channel. The variation is absent in ungated devices. 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 phenomenological but quantitative explanation of the observed change in the exponent.