Conduction through TiO2 films of thickness 100 to 450 Åhave been investigated. The samples were prepared by eitheranodization of Ti evaporation of TiO2, with Au or Al evaporatedfor contacts. The anodized samples exhibited considerable hysteresis due to electrical forming, however it waspossible to avoid this problem with the evaporated samplesfrom which complete sets of experimental results were obtainedand used in the analysis. Electrical measurementsincluded: the dependence of current and capacitance on dcvoltage and temperature; the dependence of capacitance andconductance on frequency and temperature; and transientmeasurements of current and capacitance. A thick (3000 Å)evaporated TiO2 film was used for measuring the dielectricconstant (27.5) and the optical dispersion, the latter beingsimilar to that for rutile. An electron transmission diffractionpattern of a evaporated film indicated an essentiallyamorphous structure with a short range order that could berelated to rutile. Photoresponse measurements indicated thesame band gap of about 3 ev for anodized and evaporatedfilms and reduced rutile crystals and gave the barrier energiesat the contacts.
The results are interpreted in a self consistent mannerby considering the effect of a large impurity concentration inthe films and a correspondingly large ionic space charge.The resulting potential profile in the oxide film leads to athermally assisted tunneling process between the contacts andthe interior of the oxide. A general relation is derived forthe steady state current through structures of this kind. Thisin turn is expressed quantitatively for each of two possiblelimiting types of impurity distributions, where one type givesbarriers of an exponential shape and leads to quantitative predictionsin c lose agreement with the experimental results.For films somewhat greater than 100 Å, the theory is formulatedessentially in terms of only the independently measuredbarrier energies and a characteristic parameter of the oxidethat depends primarily on the maximum impurity concentrationat the contacts. A single value of this parameter gives consistentagreement with the experimentally observed dependenceof both current and capacitance on dc voltage and temperature,with the maximum impurity concentration found to be approximatelythe saturation concentration quoted for rutile. This explains the relative insensitivity of the electrical properties of the films on the exact conditions of formation.
