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Charge carrier transport through the probe-sample junction can have substantial consequences for outcomes of electrical and electromechanical atomic-force-microscopy (AFM) measurements. For understanding physical processes under the probe, we carried out conductive-AFM (C-AFM) measurements of local current-voltage (I-V) curves as well as their derivatives on samples of a mixed ionic-electronic conductor Li1-xMn2O4 and developed an analytical framework for the data analysis. The implemented approach discriminates between contributions the highly resistive sample surface layer and the bulk with the account of ion redistribution in the field of the probe. It was found that, with increasing probe voltage, the conductance mechanism in the surface layer transforms from Pool-Frenkel to space-charge-limited current. The surface layer significantly alters the ion dynamics in the sample bulk under the probe, which leads, in particular, to a decrease of the effective electromechanical AFM signal associated with the ionic motion in the sample. The framework can be applied for the analysis of electronic transport mechanisms across the probe/sample interface as well as to uncover the role of the charge transport in the electric field distribution, mechanical, and other responses in AFM measurements of a broad spectrum of conducting materials. © 2020 Elsevier B.V. more...