Carbon nanotube (CNT)-based electronics are a potential candidate to replace silicon complementary metal-oxide-semiconductor (CMOS) technology, which will soon meet its performance limit at the 7 or 5 nm technology node 1,2 . Prototype device studies using individual CNTs have shown that nanotube electronics have the potential to outperform Si CMOS technology in both performance and power consumption [3][4][5][6] , and are even close to the theoretical limits for all field-effect-transistor(FET)-based binary switches 7,8 . Recently, FETs were fabricated using aligned CNT arrays, and shown to have a higher channel conductance (at a lower bias) than that of Si CMOS FETs 9 . However, the key performance metrics reported for such CNT FETs, including on-state current density (I on ) and transconductance (g m ), are still substantially lower than those of conventional Si CMOS FETs at the same characteristic length [9][10][11][12][13] . The ideal material system for high-performance CNT electronics has been identified as a parallel array film of intrinsic pure semiconductor single-walled nanotubes of a single chirality with a diameter of approximately 1.3 nm and no defects, and a tube-tube spacing of 5-8 nm (ref. 14 ). Although such an ideal material system is yet to be realized, many breakthroughs in the purification and controlled synthesis of CNTs have been made in recent years [15][16][17][18][19] , suggesting the possibility of achieving the required nanotube purity and array density before 2020 14 . Using randomly oriented or aligned CNT array films, various types of CNT thin-film FETs have been fabricated [9][10][11][12][13] . However, hindered by the limited performance of nanotube FETs, the operation speed of CNT integrated circuits (ICs) 20-31 typically falls short of their expected terahertz potential, and that achieved by Si CMOS circuits (gigahertz), by several orders of magnitude. Notably, CNT-based ring oscillators (ROs) with an oscillation frequency (f o ) of 282 MHz have recently been reported 32 . However, CNT-thin-film-based ICs typically have a working frequency of less than 1 MHz, which might be useful for flexible electronics, but is not suitable for mainstream high-performance CMOS technology 33 . In this study, we used a randomly oriented CNT film to build CNT FETs and ICs, fabricating, in particular, five-stage ROs with f o of up to 5.54 GHz. The random CNT film is essentially the same as a network film, but here we used the term 'random film' to emphasize that our FETs are contact dominated and have a different transport mechanism to that of junction-dominated network-type FETs 34,35 . In principle, aligned CNT arrays would provide better device performance, but it remains a challenge to obtain wafer-scale aligned CNT arrays with high uniformity, high density and high semiconductor purity for constructing high-performance ICs. Although it is not the ideal scheme, the FET-and IC-based random CNT film can nevertheless provide a feasible demonstration to assess the floor-level performance (f...