Mechanically flexible mobile phones have been long anticipated due to the rapid development of thin-film electronics in the last couple of decades. However, to date, no such phone has been developed, largely due to a lack of flexible electronic components that are fast enough for the required wireless communications, in particular the speed-demanding front-end rectifiers. Here Schottky diodes based on amorphous indium-gallium-zinc-oxide (IGZO) are fabricated on flexible plastic substrates. Using suitable radio-frequency mesa structures, a range of IGZO thicknesses and diode sizes have been studied. The results have revealed an unexpected dependence of the diode speed on the IGZO thickness. The findings enable the best optimized flexible diodes to reach 6.3 GHz at zero bias, which is beyond the critical benchmark speed of 2.45 GHz to satisfy the principal frequency bands of smart phones such as those for cellular communication, Bluetooth, Wi-Fi and global satellite positioning.