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.