Collective Poisson process with periodic rates: applications in physics from micro-to nanodevices

Continuous reductions in the dimensions of semiconductor devices have led to an increasing number of noise sources, including random telegraph signals (RTS) due to the capture and emission of electrons by traps at random positions between oxide and semiconductor. The models traditionally used for microscopic devices become of limited validity in nano- and mesoscale systems since, in such systems, distributed quantities such as electron and trap densities, and concepts like electron mobility, become inadequate to model electrical behaviour. In addition, current experimental works have shown that RTS in semiconductor devices based on carbon nanotubes lead to giant current fluctuations. Therefore, the physics of this phenomenon and techniques to decrease the amplitudes of RTS need to be better understood. This problem can be described as a collective Poisson process under different, but time-independent, rates, τ(c) and τ(e), that control the capture and emission of electrons by traps distributed over the oxide. Thus, models that consider calculations performed under time-dependent periodic capture and emission rates should be of interest in order to model more efficient devices. We show a complete theoretical description of a model that is capable of showing a noise reduction of current fluctuations in the time domain, and a reduction of the power spectral density in the frequency domain, in semiconductor devices as predicted by previous experimental work. We do so through numerical integrations and a novel Monte Carlo Markov chain (MCMC) algorithm based on microscopic discrete values. The proposed model also handles the ballistic regime, relevant in nano- and mesoscale devices. Finally, we show that the ballistic regime leads to nonlinearity in the electrical behaviour.