A common complaint from users of device models is that the “better” the model, the longer it takes to simulate. Modelling based on interpolation between sampled data points is attractive in this context because it offers low model evaluation times. Although such “table-based” modelling has a long history, important conceptual and implementation issues have been obscure in the literature. These issues include: separating the algebraic (“DC”) and dynamic (“charge/flux”) components properly; extrapolation outside sampled regions; smoothness; accuracy vs. computation vs. memory tradeoffs; and suitability of the table-based model for various analyses (such as DC, AC, transient, RF, etc., analyses). In this paper, we clarify precisely what functions should be sampled for a table-based device model to work properly in any analysis. We re-visit interpolation, showing that well-implemented cubic splines provide excellent smoothness and arbitrarily great accuracy at low, almost-constant evaluation cost. However, memory requirements increase with accuracy. We present a novel extrapolation scheme using passivity concepts that aids convergence. Using Berkeley MAPP, we demonstrate speedups of 150× in core BSIM model evaluations (translating to overall simulation speedups of 6-18×) with relative errors of 0.001%. Our approach can convert any existing device model to a smooth/accurate table-based model with small, fixed evaluation cost. Unlike previous work, our code will be released as open source, serving as a platform for the community to evaluate and experiment with table-based models quickly and conveniently.

Modeling and analysis of low-frequency noise, such as 1/f and burst noise, with time-varying bias conditions is a long-standing open problem in circuit simulation. In this paper, we offer a solution for this problem and present a computational model for low-frequency noise. The merits of our model are twofold. First, it is fully nonstationary. It can represent noise processes with time-varying statistics that are tightly coupled to the circuit variables in a stochastically correct manner. Second, its mathematical structure allows the utilization of well-established, non-Monte Carlo noise analysis techniques which are orders of magnitude faster than their Monte Carlo counterparts. We first provide an overview of our noise model along with the legacy modeling techniques. We verify that, when used with fast non-Monte Carlo analysis methods, our noise model produces results with the same accuracy as computationally laborious Monte Carlo simulations. We then proceed to contrast our nonstationary noise model with the legacy modulated stationary model. As a typical instance, where the results produced by these two models differ significantly due to intricate nonstationary behavior, we analyze the switched biasing technique that was proposed in order to reduce low-frequency noise. As a case study, we examine the 1/f noise behavior in the previously proposed coupled sawtooth oscillator circuit and show that, whereas simulations conducted with the legacy modulated stationary model suggest that no noise reduction is obtainable with switched biasing, our nonstationary noise model predicts the correct amount of noise reduction observed in previously published experimental data.

Defects or traps in semiconductors and nano devices that randomly capture and emit charge carriers result in low-frequency 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 coarse-grained 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.

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 low-frequency noise, such as burst and 1/f noise, that are great 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 longstanding 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 first identify an almost perfect analogy between trap noise in nano devices and the so-called ion channel noise in biological nerve cells, and propose a new approach to modeling and analysis of low-frequency noise that is founded on this connection. We derive two fully nonstationary models for traps, a fine-grained Markov chain model based on recent previous work and a completely novel coarse-grained Langevin model based on similar models for ion channels in neurons. The nonstationary trap models we derive 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 also describe joint noise analysis paradigms for a nonlinear circuit and a number of traps. 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.