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A physics-based analytical model for the current-voltage (I-V) characteristics corresponding to the low and high resistive states in electroformed metal-insulator-metal structures with HfO2 layers is proposed. The model relies on the Landauer theory for the electron transport in mesoscopic systems. The switching phenomenon is ascribed to the modulation of the constriction's bottleneck cross-sectional area associated with atomic rearrangements within the confinement path. The extracted parameter values allow one to conclude that the length and radius of the region that controls the conduction characteristics are in the nanometer range.