Traps that are located in the gate oxide of MOSFETs have been established as a cause of low-frequency noise phenomena. Analysis of such noise is usually based on frequency domain, stationary models. It has been shown that such simplistic models produce erroneous results for circuits with time-varying bias conditions. Tian et al. proposed an idealized trap model with the goal of capturing the nonstationary behavior of oxide traps, and were able to elucidate the experimentally observed large noise power reduction in switched MOSFET circuits which eluded any explanation obtainable with legacy stationary models. In this paper, we build on their seminal work and first identify an oversight in their model derivation which had produced an incorrect expression for the single trap noise spectrum. We next derive the correct spectrum expression, verify it against detailed idealized trap simulations and discuss its implications. The idealized trap model is amenable to analytical derivations and useful as a first stage in understanding nonstationary trap noise. We then demonstrate that noise simulations based on a detailed trap description implemented in a compact MOSFET model in a circuit simulator are needed for an accurate characterization of low-frequency noise in switched MOSFET circuits that matches experimental results.Index Terms-Low-frequency noise, noise analysis, nonstationary noise, RTS noise.

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Modeling and analysis of low frequency noise in circuit simulators with time-varying bias conditions is a long-standing open problem. In this paper, we offer a definite solution for this problem and present a model for low-frequency noise that captures the internal, stochastic dynamics of the individual noise sources via dedicated internal pseudo nodes that are coupled with the rest of the circuit. Our method correctly incorporates the inherent nonstationarity of low-frequency noise into the device model and the circuit simulator. It is based on a probabilistic description of oxide traps in nano-scale devices that individually cause the so-called random telegraph signal (RTS) noise, and, en masse, are believed to be the culprits of other low-frequency noise phenomena, such as 1/f and burst noise. Our model captures the dependence of noise characteristics on the state variables of the circuit.Its simple yet precise mathematical formulation allows the utilization of well-established, non Monte Carlo techniques for nonstationary noise analysis. In one embodiment that we present in this paper, the proposed noise model is used to perform frequency-domain, non Monte Carlo, semi-analytical noise evaluation for circuits under periodic large-signal excitations. For this case, we verify that the computed noise spectral densities match the ones obtained via spectral estimation from timedomain Monte Carlo noise simulation data.

Defects or traps in semiconductors and nano devices that randomly capture and emit charge carriers result in lowfrequency noise, such as burst and 1/f noise, which are important concerns in the design of both analog and digital circuits. The capture and emission rates of these traps are functions of the time-varying voltages across the device, resulting in nonstationary noise characteristics. Modeling of low-frequency, nonstationary noise in circuit simulators is a long-standing open problem. It has been realized that the low-frequency noise models in circuit simulators were the culprits that produced erroneous noise performance results for circuits under strongly time-varying bias conditions. In this paper, we present two fully nonstationary models for traps, a fine-grained Markov chain model and a coarsegrained Langevin model based on similar models for ion channels in neurons. The nonstationary trap models we present subsume and unify all of the work that has been done recently in the device modeling and circuit design literature on modeling nonstationary trap noise. We provide a detailed explication of these models with regard to their stochastic properties and develop carefully crafted circuit simulation techniques that are stochastically correct. We have implemented the proposed techniques in a Matlab ® based circuit simulator, by expanding the industry standard compact MOSFET model PSP to include a nonstationary description of oxide traps. We present results obtained by this extended model and the proposed simulation techniques for the low-frequency noise characterization of a common source amplifier and the phase jitter of a ring oscillator.