Conduction through thin titanium dioxide films

Conduction through TiO₂ films of thickness 100 to 450 Å have been investigated. The samples were prepared by either anodization of Ti evaporation of TiO₂, with Au or Al evaporated for contacts. The anodized samples exhibited considerable hysteresis due to electrical forming, however it was possible to avoid this problem with the evaporated samples from which complete sets of experimental results were obtained and used in the analysis. Electrical measurements included: the dependence of current and capacitance on dc voltage and temperature; the dependence of capacitance and conductance on frequency and temperature; and transient measurements of current and capacitance. A thick (3000 Å) evaporated TiO₂ film was used for measuring the dielectric constant (27.5) and the optical dispersion, the latter being similar to that for rutile. An electron transmission diffraction pattern of a evaporated film indicated an essentially amorphous structure with a short range order that could be related to rutile. Photoresponse measurements indicated the same band gap of about 3 ev for anodized and evaporated films and reduced rutile crystals and gave the barrier energies at the contacts.

The results are interpreted in a self consistent manner by considering the effect of a large impurity concentration in the films and a correspondingly large ionic space charge. The resulting potential profile in the oxide film leads to a thermally assisted tunneling process between the contacts and the interior of the oxide. A general relation is derived for the steady state current through structures of this kind. This in turn is expressed quantitatively for each of two possible limiting types of impurity distributions, where one type gives barriers of an exponential shape and leads to quantitative predictions in c lose agreement with the experimental results. For films somewhat greater than 100 Å, the theory is formulated essentially in terms of only the independently measured barrier energies and a characteristic parameter of the oxide that depends primarily on the maximum impurity concentration at the contacts. A single value of this parameter gives consistent agreement with the experimentally observed dependence of both current and capacitance on dc voltage and temperature, with the maximum impurity concentration found to be approximately the saturation concentration quoted for rutile. This explains the relative insensitivity of the electrical properties of the films on the exact conditions of formation.