Mean Switching Time Research Articles

Proton and <formula formulatype="inline"><tex Notation="TeX">$\gamma$</tex> </formula>-Rays Irradiation-Induced Dark Current Random Telegraph Signal in a 0.18-<formula formulatype="inline"><tex Notation="TeX">$\mu{\hbox{m}}$</tex> </formula> CMOS Image Sensor

The dark current random telegraph signal (RTS) behavior has been studied in a five-transistor-per-pixel (5T) pinned photodiode 0.18-μm COTS active pixel sensor (APS). Several devices, irradiated using protons and gamma rays, have been studied in order to assess the ionizing and displacement damage effects. The influence of the proton energy, fluence, ionizing dose and applied bias during irradiation on the number of RTS pixels, the number of discrete levels, maximum transition amplitude, and mean switching time constants is investigated.

Spin-transfer torque magnetization reversal in uniaxial nanomagnets with thermal noise

We consider the general Landau-Lifshitz-Gilbert (LLG) dynamical theory underlying the magnetization switching rates of a thin film uniaxial magnet subject to spin-torque effects and thermal fluctuations. After discussing the various dynamical regimes governing the switching phenomena, we present analytical results for the mean switching time behavior. Our approach, based on explicitly solving the first passage time problem, allows for a straightforward analysis of the thermally assisted, low spin-torque, switching asymptotics of thin film magnets. To verify our theory, we have developed an efficient Graphics Processing Unit (GPU)-based micromagnetic code to simulate the stochastic LLG dynamics out to millisecond timescales. We explore the effects of geometrical tilts between the spin-current and uniaxial anisotropy axes on the thermally assisted dynamics. We find that even in the absence of axial symmetry, the switching times can be functionally described in a form virtually identical to the collinear case.

Thermally-Assisted Spin-Transfer Torque Magnetization Reversal of Uniaxial Nanomagnets in Energy Space

The asymptotic behavior of switching time as a function of current for a uniaxial macrospin under the effects of both spin-torque and thermal noise is explored analytically by focusing on its diffusive energy space dynamics. The scaling dependence ($I\rightarrow 0$, $<\tau\propto\exp(-\xi(1-I)^2)$) is shown to confirm recent literature results. The analysis shows the mean switching time to be functionally independent of the angle between the spin current and magnet's uniaxial axes. These results have important implications for modeling the energetics of thermally assisted magnetization reversal of spin transfer magnetic random access memory bit cells.

Extrinsic Noise Enhances Switching in Models of Cellular Decision Making

Numerous biological processes do not follow deterministic rules, i.e., genetically identical cells can display different phenotypes even in identical environments. Such processes involve what is termed cellular decision making, where individual cells probabilistically make choices that determine their fate. One view of cellular decision making is that stochastic noise present in the biomolecular interaction networks responsible for the decisions is a major factor in their probabilistic nature. Most previous work has been focused on the intrinsic noise of these networks, but, especially for high copy-number biomolecules, extrinsic noise is likely much more significant. Here we present a theoretical study of switching in such networks and show that extrinsic noise can not only lower (often by multiple orders of magnitude) the escape time from a stable decision state, but can fundamentally change the process of escape.We first develop an analytical theory for studying how a simple self-regulating gene, which is bistable with hi and low states, is affected by extrinsic noise. Studying the system near bifurcation, we use Fokker-Planck and WKB theory along with a novel formulation of the extrinsic noise to predict the deviation in mean switching time due to the extrinsic noise. We use computational simulations to validate our theory and then to study a more relevant biological system, namely the lac genetic switch.The white noise and weak, adiabatic noise regimes are well described by a barrier-crossing model with corrections. In the strong, adiabatic noise regime, however, extrinsic noise changes the behavior of stochastic switching. A large contribution to switching in this regime originates from movement of the dynamical system in parameter space, which changes the number and location of fixed points. These results have implications for studying natural cellular processes and for engineering complex genetic programs.

Thermally assisted spin-transfer torque magnetization reversal in uniaxial nanomagnets

We simulate the stochastic Landau-Lifshitz-Gilbert dynamics of a uniaxial nanomagnet out to sub-millisecond timescales using a graphical processing unit based micromagnetic code and determine the effect of geometrical tilts between the spin-current and uniaxial anisotropy axes on the thermally assisted reversal dynamics. The asymptotic behavior of the switching time (I→0, 〈τ〉∝exp(−ξ(1−I)2)) is approached gradually, indicating a broad crossover regime between the ballistic and thermally assisted spin transfer reversal. Interestingly, the functional form of the mean switching time is shown to be independent of the angle between the spin current and magnet's uniaxial axes. These results have important implications for modeling the energetics of thermally assisted magnetization reversal of spin transfer magnetic random access memory bit cells.

Determining the Stability of Genetic Switches: Explicitly Accounting for mRNA Noise

Cells use genetic switches to shift between alternate gene-expression states, e.g., to adapt to new environments or to follow a developmental pathway. Here, we study the dynamics of switching in a generic-feedback on-off switch. Unlike protein-only models, we explicitly account for stochastic fluctuations of mRNA, which have a dramatic impact on switch dynamics. Employing the WKB theory to treat the underlying chemical master equations, we obtain accurate results for the quasistationary distributions of mRNA and protein copy numbers and for the mean switching time, starting from either state. Our analytical results agree well with Monte Carlo simulations. Importantly, one can use the approach to study the effect of varying biological parameters on switch stability.

Noise-induced effects in magnetization reversal and chirality control of circular array of single-domained nanomagnets

The effect of noise on the process of high-speed remagnetization of vortex state of a pentagonal array of five circular magnetic nanoparticles is studied by means of computer simulation of Landau–Lifshits model. The mean switching time (MST) and its standard deviation (SD) of the reversal between the counterclockwise and clockwise vorticities have been computed. It has been demonstrated that with the reversal by the pulse with sinusoidal shape, the optimal pulse duration exists, which minimizes both the MST and the SD. Besides, both MST and SD significantly depend on the angle between the reversal magnetic field and pentagon edge, and the optimal angle roughly equals 10°. Also, it is demonstrated that the optimization of the angle, duration and the amplitude of the driving field leads to significant decrease in both MST and SD. In particular, for the considered parameters, the MST can be decreased from 60 ns to 2–3 ns. Such a chain of magnetic nanoparticles can effectively be used as an element of magnetoresistive memory, and at the temperature 300 K the stable operation of the element is observed up to rather small size of nanoparticles with the radius of 20 nm.

Reconfigurable CMOS Oscillator Based on Multifrequency AlN Contour-Mode MEMS Resonators

This paper reports on the first demonstration of a reconfigurable complementary-metal-oxide-semiconductor (CMOS) oscillator based on microelectromechanical system (MEMS) resonators operating at four different frequencies (268, 483, 690, and 785 MHz). A bank of multifrequency switchable AlN contour-mode MEMS resonators was connected to a single CMOS oscillator circuit that can be configured to selectively operate in four different states with distinct oscillation frequencies. The phase noise (PN) of the reconfigurable oscillator was measured for each of the four different frequencies of operation, showing values between -94 and - 70 dBc/Hz at a 1-kHz offset and PN floor values as low as -165 dBc/Hz at a 1-MHz offset. Jitter values as low as a 114-fs root mean square (integrated 12 kHz-20 MHz) and switching times as fast as 20 μs were measured. This first prototype represents a miniaturized solution (30 times smaller) over commercially available voltage-controlled surface-acoustic-wave oscillators and potentially has the advantage of generating multiple stable frequencies without the need of cumbersome and power-consuming phase-locked-loop circuits.

Stochastic dynamics of phase-slip trains and superconductive-resistive switching in current-biased nanowires

Superconducting nanowires fabricated via carbon-nanotube-templating can be used to realize and study quasi-one-dimensional superconductors. However, measurement of the linear resistance of these nanowires have been inconclusive in determining the low-temperature behavior of phase-slip fluctuations, both quantal and thermal. Thus, we are motivated to study the nonlinear current-voltage characteristics in current-biased nanowires and the stochastic dynamics of superconductive-resistive switching, as a way of probing phase-slip events. In particular, we address the question: Can a single phase-slip event occurring somewhere along the wire--during which the order-parameter fluctuates to zero--induce switching, via the local heating it causes? We explore this and related issues by constructing a stochastic model for the time-evolution of the temperature in a nanowire whose ends are maintained at a fixed temperature. We derive the corresponding master equation as tool for evaluating and analyzing the mean switching time at a given value of current. The model indicates that although, in general, several phase-slip events are necessary to induce switching via a thermal runaway, there is indeed a regime of temperatures and currents in which a single event is sufficient. We carry out a detailed comparison of the results of the model with experimental measurements of the distribution of switching currents, and provide an explanation for the counter-intuitive broadening of the distribution width that is observed upon lowering the temperature. Moreover, we identify a regime in which the experiments are probing individual phase-slip events, and thus offer a way for exploring the physics of nanoscale quantum tunneling of the superconducting order parameter.

Inherent Stochasticity of Superconductor-Resistor Switching Behavior in Nanowires

We study the stochastic dynamics of superconductive-resistive switching in hysteretic current-biased superconducting nanowires undergoing phase-slip fluctuations. We evaluate the mean switching time using the master-equation formalism, and hence obtain the distribution of switching currents. We find that as the temperature is reduced this distribution initially broadens; only at lower temperatures does it show the narrowing with cooling naively expected for phase slips that are thermally activated. We also find that although several phase-slip events are generally necessary to induce switching, there is an experimentally accessible regime of temperatures and currents for which just one single phase-slip event is sufficient to induce switching, via the local heating it causes.

NOISE INDUCED PHENOMENA IN POINT JOSEPHSON JUNCTIONS

We present the analysis of the mean switching time and its standard deviation of short overdamped Josephson junctions, driven by a direct current and a periodic signal. The effect of noise enhanced stability is investigated. It is shown that fluctuations may both decrease and increase the switching time.

EFFECTS OF COLORED NOISE IN SHORT OVERDAMPED JOSEPHSON JUNCTION

We investigate the transient dynamics of a short overdamped Josephson junction with a periodic driving signal in the presence of colored noise. We analyze noise induced phenomena, specifically resonant activation and noise enhanced stability. We find that the positions both of the minimum of RA and maximum of NES depend on the value of the noise correlation time τc. Moreover, in the range where RA is observed, we find a non-monotonic behavior of the mean switching time as a function of τc.

Micromagnetic Study on Thermally Induced Magnetization Reversal of a Coupled Spin Chain System

We performed numerical studies of the dynamics of thermally induced magnetization reversal of a coupled Heisenberg spin chain, based on the stochastic Landau-Lifshitz-Gilbert equation. Special attention is given to characterizing the transitions between different switching mechanisms (e.g., coherent rotation, soliton, and multidroplet reversals), as the chain length L is increased. Our calculations reveal that the switching time, switching time distribution, and the time evolution behavior of magnetization reversal display nontrivial dependence on the chain length L, and undergo distinct transitions as a function of L. In particular, we found that the switching time distribution is an important determinant of thermal stability, in addition to the mean switching time

Coarse-grained analysis of stochasticity-induced switching between collective motion states.

A single animal group can display different types of collective motion at different times. For a one-dimensional individual-based model of self-organizing group formation, we show that repeated switching between distinct ordered collective states can occur entirely because of stochastic effects. We introduce a framework for the coarse-grained, computer-assisted analysis of such stochasticity-induced switching in animal groups. This involves the characterization of the behavior of the system with a single dynamically meaningful "coarse observable" whose dynamics are described by an effective Fokker-Planck equation. A "lifting" procedure is presented, which enables efficient estimation of the necessary macroscopic quantities for this description through short bursts of appropriately initialized computations. This leads to the construction of an effective potential, which is used to locate metastable collective states, and their parametric dependence, as well as estimate mean switching times.

Experimental study of stochastic resonance in a Chua’s circuit operating in a chaotic regime

We present results of an experimental study of stochastic resonance in an electronic Chua’s circuit whose dynamics switches between two different stable chaotic attractors when it is driven by a periodic signal and a Gaussian white noise. Due to the internal dynamics of the attractors the minimum amplitude for the external forcing to induce jumps strongly depends on the external frequency. We determine from the Fourier transform of the output signal the amplification factor of the input signal and study its dependence on the external frequency and the noise intensity. We show that the envelope of the distribution of switching times follows a gamma distribution, typical from bistable systems, and that the mean switching time decays exponentially with the noise intensity. We propose a simple method for obtaining the optimal noise intensity from the residence and switching times probability distributions and show that it coincides with the value obtained from the maximum of the amplification factor.

Decay of metastable current states in one-dimensional resonant tunneling devices

Current switching in a double-barrier resonant tunneling structure is studied in the regime where the current-voltage characteristic exhibits intrinsic bistability, so that in a certain range of bias two different steady states of current are possible. Near the upper boundary V_{th} of the bistable region the upper current state is metastable, and because of the shot noise it eventually decays to the stable lower current state. We find the time of this switching process in strip-shaped devices, with the width small compared to the length. As the bias V is tuned away from the boundary value V_{th} of the bistable region, the mean switching time \tau increases exponentially. We show that in long strips \ln\tau \propto (V_{th} -V)^{5/4}, whereas in short strips \ln\tau \propto (V_{th} -V)^{3/2}. The one-dimensional geometry of the problem enables us to obtain analytically exact expressions for both the exponential and the prefactor of \tau. Furthermore, we show that, depending on the parameters of the system, the switching can be initiated either inside the strip, or at its ends.

Gene regulatory networks: A coarse-grained, equation-free approach to multiscale computation

We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately initialized short bursts of stochastic simulations; the results of these are processed to estimate coarse-grained quantities of interest, such as mesoscopic transport coefficients. In particular, using a simple model of a genetic toggle switch, we illustrate the computation of an effective free energy Phi and of a state-dependent effective diffusion coefficient D that characterize an unavailable effective Fokker-Planck equation. Additionally we illustrate the linking of equation-free techniques with continuation methods for performing a form of stochastic "bifurcation analysis"; estimation of mean switching times in the case of a bistable switch is also implemented in this equation-free context. The accuracy of our methods is tested by direct comparison with long-time stochastic simulations. This type of equation-free analysis appears to be a promising approach to computing features of the long-time, coarse-grained behavior of certain classes of complex stochastic models of gene regulatory networks, circumventing the need for long Monte Carlo simulations.

Minimization of timing errors in reproduction of single flux quantum pulses

We present the analysis of the mean switching time and its standard deviation of an overdamped Josephson junction, driven by a direct current and a single flux quantum (SFQ) pulse. The performed analysis allows us to find the optimal value of the bias current of the clock generator, responsible for the shape of SFQ pulse, which minimizes noise-induced switching errors.

Stochastic current switching in bistable resonant tunneling systems

Current-voltage characteristics of resonant-tunneling structures often exhibit intrinsic bistabilities. In the bistable region of the I-V curve one of the two current states is metastable. The system switches from the metastable state to the stable one at a random moment in time. The mean switching time \tau depends exponentially on the bias measured from the boundary of the bistable region V_{th}. We find full expressions for \tau (including prefactors) as functions of bias, sample geometry, and in-plane conductivity. Our results take universal form upon appropriate renormalization of the threshold voltage V_{th}. We also show that in large samples the switching initiates inside, at the edge, or at a corner of the sample depending on the parameters of the system.

Suppression of Timing Errors in Short Overdamped Josephson Junctions

The influence of fluctuations and periodical driving on temporal characteristics of short overdamped Josephson junctions is analyzed. We obtain the standard deviation of the switching time in the presence of a dichotomous driving force for arbitrary noise intensity and in the frequency range of practical interest. For sinusoidal driving the resonant activation effect has been observed. The mean switching time and its standard deviation have a minimum as a function of driving frequency. As a consequence the optimization of the system for fast operation will simultaneously lead to the minimization of timing errors.