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The mechanism of charge carrier transport in the indium tin oxide (ITO)/polymer/Cu structure is studied, where thin films of copoly(arylene ether ketone) with cardo fluorene moieties are used. This copoly(arylene ether ketone) is non-conjugated polymer which has the properties of electronic switching from the insulating to the highly conductive state. The dependence on the polymer film thickness of such parameters as the potential barrier at the ITO/polymer interface, the concentration of charge carriers, and their mobility in the polymer is studied for the first time. The study of this system is of interest due to the proven potential of using the synthesized polymer in the contact system of a silicon solar cell with an ITO top layer. The parameters of charge carriers and ITO/polymer barrier are evaluated based on the analysis of current–voltage characteristics of ITO/polymer/Cu structure within the injection current models and the Schottky model. The thickness of the polymer layer varies from 50 nm to 2.1 µm. The concentration of intrinsic charge carriers increases when decreasing the polymer film thickness. The charge carrier mobility depends irregularly on the thickness, showing a maximum of 9.3 × 10⁻⁴ cm²/V s at 210 nm and a minimum of 4.7 × 10⁻¹¹ cm²/V s at 50 nm. The conductivity of polymer films first increases with a decrease in thickness from 2.1 µm to 210 nm, but then begins to decrease upon transition to the globular structure of the films at smaller thicknesses. The dependence of the barrier height on polymer thickness has a minimum of 0.28 eV for films 100–210 nm thick. The influence of the supramolecular structure and surface charge field of thin polymer films on the transport of charge carriers is discussed. Full article