Large deviations theory for noisy nonlinear electronics: CMOS inverter as a case study

Abstract

The latest generations of transistors are nanoscale devices whose performance and reliability are limited by thermal noise in low-power applications. Therefore, developing efficient methods to compute the voltage and current fluctuations in such nonlinear electronic circuits is essential. Traditional approaches commonly rely on adding Gaussian white noise to the macroscopic dynamical circuit laws, but do not capture rare fluctuations and lead to thermodynamic inconsistencies. A correct and thermodynamically consistent approach can be achieved by describing single-electron transfers as Poisson jump processes accounting for charging effects. But such descriptions can be computationally demanding. To address this issue, we consider the macroscopic limit, which corresponds to scaling up the physical dimensions of the transistor and resulting in an increase of the number of electrons on the conductors. In this limit, the thermal fluctuations satisfy a "large deviations principle", which we show is also remarkably precise in settings involving only a few tens of electrons, by comparing our results with Gillespie simulations and spectral methods. Traditional approaches are recovered by resorting to an ad hoc diffusive approximation introducing inconsistencies. To illustrate these findings, we consider a low-power CMOS inverter, or NOT gate, which is a basic primitive in electronic design. Voltage (resp. current) fluctuations are obtained analytically (semi-analytically) and reveal interesting features.

Investigation of Temperature and Channel Dimension Effects on CMOS Circuit Performance

“…Elevated temperatures can result in increased leakage currents in transistors, reducing efficiency and potentially compromising reliability [16]. Conversely, low temperatures can decelerate transistor response times [17]. To mitigate these effects, CMOS engineers must diligently implement thermal management techniques to ensure devices function within designated temperature ranges [18][19].…”

Laser-induced ultrafast spin-transfer processes in non-linear zigzag carbon chain systems

“…Complementary metal-oxide semiconductors (CMOS) [1][2][3] applications have been effectively downscaled to boost integrated circuits (ICs) [4][5][6] speed and accuracy at a reduced cost. Nevertheless, the miniaturization of CMOS logic circuits today comes up against increasingly penalizing leakage currents and other fundamental limitations.…”

“…1 (t 1 is the end time of the first pulse, and o i is the energy of state |C i i at t 1 ) is formed after the influence of the first pulse (the coherent superposition is mainly contributed by the initial and the target states in the present scenario). The optimized parameters of the double…”