Low-frequency noise in downscaled silicon transistors: Trends, theory and practice

Abstract

By the continuing downscaling of sub-micron transistors in the range of few to one deca-nanometers, we focus on the increasing relative level of the low-frequency noise in these devices. Large amount of published data and models are reviewed and summarized, in order to capture the state-of-the-art, and to observe that the 1/area scaling of low-frequency noise holds even for carbon nanotube devices, but the noise becomes too large in order to have fully deterministic devices with area less than 10nm×10nm. The low-frequency noise models are discussed from the point of view that the noise can be both intrinsic and coupled to the charge transport in the devices, which provided a coherent picture, and more interestingly, showed that the models converge each to other, despite the many issues that one can find for the physical origin of each model. Several derivations are made to explain crossovers in noise spectra, variable random telegraph amplitudes, duality between energy and distance of charge traps, behaviors and trends for figures of merit by device downscaling, practical constraints for micropower amplifiers and dependence of phase noise on the harmonics in the oscillation signal, uncertainty and techniques of averaging by noise characterization. We have also shown how the unavoidable statistical variations by fabrication is embedded in the devices as a spatial “frozen noise”, which also follows 1/area scaling law and limits the production yield, from one side, and from other side, the “frozen noise” contributes generically to temporal 1/f noise by randomly probing the embedded variations during device operation, owing to the purely statistical accumulation of variance that follows from cause-consequence principle, and irrespectively of the actual physical process. The accumulation of variance is known as statistics of “innovation variance”, which explains the nearly log-normal distributions in the values for low-frequency noise parameters gathered from different devices, bias and other conditions, thus, the origin of geometric averaging in low-frequency noise characterizations. At present, the many models generally coincide each with other, and what makes the difference, are the values, which, however, scatter prominently in nanodevices. Perhaps, one should make some changes in the approach to the low-frequency noise in electronic devices, to emphasize the “statistics behind the numbers”, because the general physical assumptions in each model always fail at some point by the device downscaling, but irrespectively of that, the statistics works, since the low-frequency noise scales consistently with the 1/area law.