The growing demands of the IoT market call for novel ultra-low-cost RF semiconductor devices. Using GHz- frequency Schottky diodes fabricated on a wafer-scale, low-cost natively flexible rectennas and RF energy harvesters can be realized. This paper will present, for the first time, the non-linear model followed by antenna-circuit co-design for solution-processed Zinc-Oxide (ZnO) Schottky diodes. The rectifier equivalent circuit model is compared to experimental on-wafer characterization showing very good agreement up to 40 GHz. Using a complex-impedance source emulating a printable rectenna, the designed voltage doubler rectifier shows a power conversion efficiency up to 70% in the UHF RFID band (0.915 GHz). The optimum source and load impedance parameters for a single-series and voltage-doubler rectifier are finally presented, showing that ZnO nano-gap diodes can be adopted by future designers in rectennas and RF energy harvesting applications.