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Resistive switching characteristics are investigated for Al/TiOx/Al devices, particularly for the structural effects in crossbar and via-hole-type devices. The via-hole structure shows more reliable switching characteristics than the crossbar structure, owing to the elimination of possible edge effects. The asymmetric switching behavior is analyzed with top Al/TiOx, and bottom Al/TiOx interfaces. A trap-controlled space-charge- limited-current model is proposed as a possible switching mechanism, and it is verified that switching mainly occurs on the top electrode/TiOx, interface side.