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P. Balaya, J. Jamnik, J. Fleig, J. Maier:
"Mesoscopic hole conduction in nanocrystalline SrTiO₃: A detailed analysis by impedance spectroscopy";
Journal of the Electrochemical Society, 154 (2007), P69 - P76.

In the context of the search for fundamental size effects regarding electrical conduction, we analyze the transition from semi-infinite or isolated to overlapped depletion layers in appreciably dense nanocrystalline SrTiO3 ceramics occurring if the grain size becomes smaller than ~100 nm. At these small grain sizes, the bulk impedance signal that is seen clearly for microcrystalline samples disappears, leaving only one impedance response, which can be attributed to the space-charge zones. Space-charge potentials and Mott-Schottky lengths are calculated and shown to be consistent with the assumption of the mesoscopic condition. In accordance with the increased homogeneity of the mesoscopic situation in an 80 nm sample, and unlike for microcrystalline samples, the impedance response is characterized by almost an ideal capacitance that no longer originates from space-charge polarization. These conclusions are corroborated by detailed numerical calculations using linear irreversible thermodynamics.

http://dx.doi.org/10.1149/1.2716555