<p>Films of aligned semiconducting carbon nanotubes could be used to build complementary metal–oxide–semiconductor field-effect transistors for digital integrated circuits and radio-frequency transistors for terahertz analogue integrated circuits. However, the operating frequencies of such devices remains too low for potential application in the sixth generation of wireless communications. Here we report metal–oxide–semiconductor field-effect transistors that are based on aligned carbon nanotube films and have a cut-off frequency beyond 1 THz. By optimizing gate structures and fabrication processes, we create devices with a gate length of 80 nm that have a carrier mobility of over 3,000 cm² V⁻¹ s⁻¹, as well as an on-state current of 3.02 mA µm⁻¹, a peak transconductance of 1.71 mS μm⁻¹ at a bias of −1 V, and a saturation velocity of 3.5 × 10⁷ cm s⁻¹. By introducing a Y-shaped gate, we also create devices with gate lengths of 35 nm that have an extrinsic cut-off frequency (<i>f</i>_T) of up to 551 GHz and a maximum oscillation frequency (<i>f</i>_max) of 1,024 GHz. Finally, we use devices with a gate length of 50 nm to fabricate mmWave-band (30 GHz) radio-frequency amplifiers that have a gain of up to 21.4 dB.</p>