Modeling and analysis of (nonstationary) low frequency noise in nano devices: A synergistic approach based on stochastic chemical kinetics

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.