Voltage Controlled Interfacial Layering in an Ionic Liquid on SrTiO$_3$

One prominent structural feature of ionic liquids near surfaces is formation of alternating layers of anions and cations. However, how this layering responds to applied potential is poorly understood. We focus on the structure of 1-butyl-1-methylpyrrolidinium tris(pentafluoroethyl) trifluorophosphate (BMPY-FAP) near the surface of a strontium titanate (SrTiO$_3$) electric double-layer transistor. Using x-ray reflectivity, we show that at positive bias, the individual layers in the ionic liquid double layer thicken and the layering persists further away from the interface. We model the reflectivity using a modified distorted crystal model with alternating cation and anion layers, which allows us to extract the charge density and the potential near the surface. We find that the charge density is strongly oscillatory with and without applied potential, and that with applied gate bias of 4.5 V the first two layers become significantly more cation rich than at zero bias, accumulating about $2.5 \times 10^{13}$ cm$^{-2}$ excess charge density.