Electron transfer (ET) phenomena at and near semiconductor/molecule interfaces are of fundamental significance for applications involving liquid-junction photovoltaics, organic photovoltaics, and electrochemical heterogeneous catalysis. To probe mechanisms of electron delivery through barrier layers at such interfaces, we make use of atomic layer deposition to deposit ultrathin films of TiO2 conformally onto SnO2 electrodes. In the presence of TiO2 films (i.e., barrier layers) up to 10 angstrom thick, electrons are delivered from the electrode to molecules, in solution by tunneling through the layers, as evidenced, in part, by an exponential decrease in ET rate with layer thickness. For films thicker than 10 angstrom, there is little change in ET rate as a function of TiO2 thickness. To our surprise, thermally annealing a 55 angstrom layer of TiO2 on SnO2, yielded a 10-fold decrease in ET rate compared to that imposed by the as-deposited layer. At applied potentials near the conduction-band edge of SnO2, and significantly below the band edge of TiO2, electrochemical impedance spectroscopy with nominally flat, as-deposited TiO2 indicates the presence of nearly twice the density of electronic states as found with air-annealed samples. These and related observations point to a barrier-layer-thickness-dependent change in the mechanism of electron delivery, from the underlying electrode to solution species, from one based on tunneling to one entailing trap-facilitated hopping. The findings have design implications for the application of interfacial barrier layers to electrochemical and photoelectrochemical problems.