  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.
