## 1 Introduction  
The growth of global energy consumption requires the development of effective energy conversion methods. Solid oxide fuel cells (SOFCs) are promising devices for the conversion of fuel energy to electricity with high efficiency and low environmental pollution [1; 2]. SOFCs based on proton-conducting electrolytes offer significant advantages compared to those using oxygen ion conducting electrolytes. Among these benefits, a lower operating temperature due to an acceptable conductivity in the proton-conducting oxides at intermediate temperatures, and the ability to produce pure hydrogen on the hydrogen electrode avoiding the problem of fuel dilution by mixing with water, appear to be the most important ones. Reducing the operating temperature lowers the cost and enhances the durability and reliability of SOFCs [2; 3]. A further enhancement of SOFC performance can be achieved through a decrease in electrolyte thickness. Nowadays, the application of thin-film membranes for the development of portable powering microdevices is considered a significant part of an upcoming nanoionics revolution [4; 5]. The high performance of SOFCs with a thin-film electrolyte was demonstrated in [6; 7; 8; 9; 10; 11; 12; 13; 14]. However, thin-film SOFC efficiency was reported to be sensitive to the diffusional interaction between the electrolyte and the electrodes [4; 15; 16; 17; 18; 19]. Thin films usually exhibit a non-zeroingd structure, which enhances the effect of material interaction as diffusion along the grain boundaries is much faster than in the grain bulk [16; 19; 20]. The diffusion of metal ions from the supporting electrode into the electrolyte film during processing can entail an increase of the electronic conductivity and therefore a decrease in the power generation efficiency and overall lifespan of the membrane [18]. Besides, in the extreme operating conditions of SOFC, phase stability degradation of a thin-film electrolyte can proceed faster compared to a bulk electrolyte because of a large ratio of surface to volume [21]. For these reasons, the problem of material selection and processing for the SOFCs with a thin-film membrane is expected to be more significant than for the electrolyte-supported SOFCs. Among different families of proton-conducting oxides, perovskite-type acceptor-doped strontium zirconate is likely to be an appropriate material for a thin-film membrane for SOFCs since it was reported to exhibit both proton conductivity and high chemical stability required for the long-term performance [22; 23; 24; 25; 26; 27]. Undoped strontium zirconate exhibits rather low conductivity, however, the substitution of acceptor ions (Y, Dy, Yb, etc.) at Zr positions enhances conductivity due to increasing oxygen vacancies concentration [22; 23; 24; 25; 26]. Acceptor-doped SrZrO\({}_{3}\) was shown to possess almost pure protonic conduction in a hydrogen atmosphere, whereas in wet oxidizing atmospheres it is a mixed proton and electron-hole conductor [22]. Besides, a small strontium deficiency was shown to improve the conductivity of SrZrO\({}_{3}\)-based electrolytes due to an increase in the oxygen vacancy concentration [23; 28]. In our previous study, we found that Sr\({}_{0.98}\)Zr\({}_{0.95}\)Y\({}_{0.05}\)O\({}_{3-\delta}\) composition possessed the highest conductivity (\(\sim\)10\({}^{-3}\) S cm\({}^{-1}\) at 800 \({}^{\circ}\)C) among Sr\({}_{x}\)Zr\({}_{0.95}\)Y\({}_{0.05}\)O\({}_{3-\delta}\) (0.94 \(<\) x \(<\) 1.02) ceramic samples [28]. That is why this composition was chosen for investigation in the present research. The main objective of the present research is to study the charge transport properties of a thin electrode-supported Sr\({}_{0.98}\)Zr\({}_{0.95}\)Y\({}_{0.05}\)O\({}_{3-\delta}\) (SZY) film.