Modeling and analysis of nonstationary low-frequency noise in circuit simulators: enabling non monte carlo techniques

Abstract

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 time-domain Monte Carlo noise simulation data.