Numerous efforts have been undertaken to develop rectifying antennas operating at high frequencies, especially dedicated to light harvesting and photodetection applications. However, the development of efficient high frequency rectifying antennas has been a major technological challenge both due to a lack of comprehension of the underlying physics and limitations in the fabrication techniques. Various rectification strategies have been implemented, including metal-insulator-metal traveling-wave diodes, plasmonic nanogap optical antennas, and whisker diodes, although all show limited high-frequency operation and modest conversion efficiencies. Here a new type of rectifying antenna based on plasmonic carrier generation is demonstrated. The proposed structure consists of a resonant metallic conical nano-antenna tip in contact with the oxide surface of an oxide/metal bilayer. The conical shape allows for an improved current generation based on plasmon-mediated electromagnetic-to-electron conversion, an effect exploiting the nanoscale-tip contact of the rectifying antenna, and proportional to the antenna resonance and to the surface-electron scattering. Importantly, this solution provides rectification operation at 280 THz (1064 nm) with a 100-fold increase in efficiency compared to previously reported results. Finally, the conical rectifying antenna is also demonstrated to operate at 384 THz (780 nm), hence paving a way toward efficient rectennas toward the visible range.