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

Abstract

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, t c and t 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.

A Stand-Alone, Physics-Based, Measurement-Driven Model and Simulation Tool for Random Telegraph Signals Originating From Experimentally Identified MOS Gate-Oxide Defects

“…Areal trap density is provided to the RTSSIM to compute the number of active traps. The number of traps active in a specific device follows a Poisson distribution [1], [35], [36], and the trap density as a function of energy is taken as a U-shaped distribution in the Si bandgap [13], [37]. From these, the total number of traps (N t A active , N t AA active , and N t D active ) active in that specific device is calculated.…”

Stochastic model of self-driven two-species objects inspired by particular aspects of a pedestrian dynamics

“…[2][3][4]), charge trapping phenomena (electron transport) in semiconductor devices (see for example Refs. [5][6][7][8][9][10][11]), and transport of molecules (chromatography) in chemistry [12][13][14].…”

“…A large number of stochastic phenomena in literature are related to the passage of particles through random media generated, for example, by imperfections of the environment. Examples can be found as disordered linear chains generated by arbitrary mass and springconstants 1 , random walks in random environments and diffusion (see for example [2][3][4] , charge trapping phenomena (electron transport) in semiconductor devices (see for example [6][7][8][9][10][11] ), and transport of molecules (chromatography) in Chemistry ( [12][13][14] ).…”

Estimating time constants of the RTS noise in semiconductor devices: a complete description of the observation window in the time domain

“…are here translated as averaged capture time (τ c ), and averaged emission time (τ e ) respectively. Although many works consider the analysis in the frequency domain of RTS (to cite a few ones [5,6,7,8,9,10]), on the other hand, time-domain analysis (see for example [11,12,13,14]) deserves more attention from researchers in this kind of modeling. Time-domain analysis is important for example to understand the degradation phenomena in semiconductor devices from experimental [15], and theoretical point of view [16].…”