Traditional extensions of the Nyquist-Johnson formula for thermal fluctuations in nonlinear dissipative elements have often led to thermodynamically inconsistent models and sparked long-standing debates about the proper interpretation of stochastic differential equations. In this work, we show that it is possible to derive, for each of the main stochastic interpretations, a Gaussian white-noise model for nonlinear dissipative elements at thermal equilibrium that fully complies with the fundamental principles of thermodynamics. The resulting models reproduce the Gibbs (Maxwell-Boltzmann) distribution and ensure zero-mean voltages and currents, thereby resolving the Brillouin paradox and maintaining consistency with the second law of thermodynamics. Furthermore, we demonstrate that these models satisfy additional thermodynamic requirements, including positive entropy production during transients and zero net heat exchange between dissipative elements at equilibrium.

Stability of ultra-low-voltage SRAM bitcells in retention mode is threatened by two types of uncertainty: process variability and intrinsic noise. While variability dominates the failure probability, noise-induced bit flips in weakened bitcells lead to dynamic instability. We study both effects jointly in a unified SPICE simulation framework. Starting from a synthetic representation of process variations introduced in a previous work, we identify the cases of poor noise immunity that require thorough noise analyses. Relying on a rigorous and systematic methodology, we simulate them in the time domain so as to emulate a true data retention operation. Short times to failure, unacceptable for a practical ultra-low-power memory system application, are recorded. The transient bit-flip mechanism is analyzed and a dynamic failure criterion involving the unstable steady state is established. We conclude that, beyond static variability, the dynamic noise inflates defectiveness among SRAM bitcells. Then, a stochastic nonlinear model, fully characterizable from conventional deterministic SPICE simulations, is presented. We then leverage it to efficiently and accurately predict the mean time to failure with an analytical Eyring-Kramers formula, recently extended to account for the varying-noise behavior of nonlinear systems.

The failure probabilities of industrial SRAM cells fall below the ppm (10−6) range, disqualifying the computational-intensive Monte-Carlo simulations for efficient robustness assessment. Starting from a novel two-dimensional threshold voltage imbalance representation, we propose a new methodology for fast and accurate prediction of the subthreshold SRAM hold stability failure rate. The probability is derived in a closed form which involves the transistor threshold-voltage standard deviations and only requires the two quick DC extractions of the worst- and best-case static noise margins. We validate our approach on a Six-Transistor (6T) bitcell in 28 nm Fully Depleted Silicon-On-Insulator (FD-SOI) CMOS technology. Our method turns out to be especially insightful for comparative and sensitivity analyses, for instance to study the effect of supply voltage downscaling or temperature variations. Finally, we show that the achieved accuracy and the capability of estimating extremely low failure probabilities (down to 10−9), combined with the important gain in simulation and post-processing cost, makes our methodology attractive compared to other recent modelling works.

Back-bias control is a new degree of freedom brought by fully-depleted silicon-on-insulator (FDSOI) CMOS technologies, which can be used to control the oscillation frequency of voltage-controlled ring oscillators (VCROs). The resulting VCRO architecture is called a back-bias-controlled oscillator (BBCO). This paper compares it with the conventional current-starved ring oscillator (CSRO) topology in terms of power consumption and phase noise figure-of-merit (FoM), while taking practical design constraints of process-voltage-temperature (PVT) robustness and frequency tuning range into account. The proposed comprehensive analysis takes advantage of relevant and compact analytical models, as well as extensive pre-layout simulation results. The comparison is made at four different target oscillation frequencies, which are representative of frequency synthesis for WiFi/Bluetooth/LPWAN wireless communications and of clock generation for smartphone/Internet-of-Things processors: 300 MHz, 868 MHz, 2.45 GHz, and 5.18 GHz. In 28-nm FDSOI technology, the results demonstrate that BBCOs can intrinsically reach 1.69 to$4.63\times $lower minimum power consumption and slightly better FoM values than CSROs.