We have examined the structure of Cu filaments in Cu/amorphous-Ta2O5 (a-Ta2O5)/Pt atomic switch from first principles. We have found that the Cu single atomic chains are unstable during the molecular dynamics (MD) simulation and thus cannot work as conduction paths. On the other hand, Cu nanowires with various diameters are stable and can form conductive paths. In this case, the Cu-Cu bonding mainly contributes to the conductive, delocalized defect state. These make a sharp contrast with the case of single Cu chains in crystalline Ta2O5, which can be conductive paths through the alternant Cu-Ta bonding structure. A series of MD simulations suggest that even Cu nanowires with a diameter of 0.24 nm can work as conduction paths. The calculations of the transport properties of Cu/a-Ta2O5/Pt heterostructures with Cu nanowires between two electrodes further confirm the conductive nature of the Cu nanowires in the a-Ta2O5.