In order to clarify the physics of the gating of solids by ionic liquids (ILs) we have gated lightly doped $p$-Si, which is so well studied that it can be called the “hydrogen atom of solid state physics” and can be used as a test bed for ionic liquids. We explore the case where the concentration of induced holes at the Si surface is below ${10}^{12}{\text{cm}}^{-2}$, hundreds of times smaller than record values. We find that in this case an excess negative ion binds a hole on the interface between the IL and Si becoming a surface acceptor. We study the surface conductance of holes hopping between such nearest neighbor acceptors. Analyzing the acceptor concentration dependence of this conductivity, we find that the localization length of a hole is in reasonable agreement with our direct variational calculation of its binding energy. The observed hopping conductivity resembles that of well studied ${\text{Na}}^{+}$ implanted Si MOSFETs.

• Received 6 May 2015
• Revised 21 July 2015

DOI:https://doi.org/10.1103/PhysRevB.92.085424