Theoretical and experimental analysis of electron transport across ultrathin, homogeneously disordered oxide layers is presented with particular regard to the question of how much the effects are universal. We show that (i) distribution of transparencies across dirty subnanometer-thick insulating films is bimodal and (ii) conductance-voltage characteristics of oxide layers with thicknesses increased up to several nanometers are power functions with an index near 1.3. The universality of transport properties is explained as an effect of strong local barrier-height fluctuations generated by the presence of oxygen vacancies.
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