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We studied the electrical properties of a carbon nanotube (CNT) via interconnect fabricated by a novel damascene process which is mostly compatible with conventional Cu interconnects. It was found that the resistance of 60-nm-height vias was independent of temperatures as high as 423 K, which suggests that the carrier transport is ballistic. The obtained resistance of 0.05 Omega for 2.8-mum-diameter vias is the lowest value ever reported. From the via height dependence of the resistance, the electron mean free path was estimated to be about 80 nm, which is similar to the via height predicted for 32-nm technology node (year 2013). This indicates that it will be possible to realize CNT vias with ballistic transport for 32-nm technology node and below.