We report on the fabrication and electrical characterization of functionalized solid-state nanopores in low stress silicon nitride membranes. First, a pore of approximately 50 nm diameter was drilled using a focused ion beam technique, followed by the local deposition of silicon dioxide. A low-energy electron beam induced the decomposition of adsorbed tetraethyl orthosilicate resulting in site-selective functionalization of the nanopore by the formation of highly insulating silicon oxide. The deposition occurs monolayer by monolayer, which allows for control of the final diameter with subnanometer accuracy. Changes in the pore diameter could be monitored in real time by scanning electron microscopy. Recorded ion currents flowing through a single nanopore revealed asymmetry in the ion conduction properties with the sign of the applied potential. The low-frequency excess noise observed at negative voltage originated from stepwise conductance fluctuations of the open pore.