  We use the tip of an atomic force microscope (AFM) to charge floating
metallic gates defined on the surface of a Si/SiGe heterostructure. The AFM tip
serves as an ideal and movable cryogenic switch, allowing us to bias a floating
gate to a specific voltage and then lock the charge on the gate by withdrawing
the tip. Biasing with an AFM tip allows us to reduce the size of a quantum dot
floating gate electrode down to $\sim100~\mathrm{nm}$. Measurements of the
conductance through a quantum dot formed beneath the floating gate indicate
that its charge changes in discrete steps. From the statistics of the
single-electron leakage events, we determine the floating gate leakage
resistance $R \sim 10^{19}~ \mathrm{Ohm}$ - a value immeasurable by
conventional means.
