Stretched-exponential Behavior Research Articles

Long-lived, pulse-induced transient absorption inLiNb1-x Ta x O3 (0≤x≤1) solid solutions: the case of three intrinsic defect sites for electron localization with strong coupling

Abstract Femto-/nanosecond pulse-induced, red and near-infrared absorption is studied in LiNb1-x Ta x O3 (0≤x≤1, LNT) solid solutions with the aim of studying transient optical nonlinearities associated with the formation, transport and recombination of optically generated small bound electron polarons with strong coupling to the lattice. As a result, a pronounced, long-lived transient absorption is uncovered for LNT which exceed lifetimes and starting amplitudes of LiNbO3 (LN) and LiTaO3 (LT) by a factor of up to 100 and 10, respectively. The transients reveal a stretched-exponential decay behavior and a thermally activated process which provide strong evidence for an underlying hopping transport mechanism of small bound polarons. All findings are discussed in comparison to the model systems LN and LT within the framework of appropriate band models and optical generation of polarons via two-photon excitation. To explain the significant differences, the simultaneous presence of Nb5+ Li , Ta5+ Li antisites, and Ta5+ V interstitial defects, i.e. a mixture of the intrinsic defects widely established for LN and LT, is assumed for LNT.

Effect of Back-Channel Surface on Reliability of Solution-Processed In0.51Ga0.15Zn0.34O Thin-Film Transistors with Thin Active Layer.

We have investigated the degradation mechanism of solution-processed indium-gallium-zinc-oxide (IGZO) thin-film transistors. The threshold voltage shift (ΔVth) followed a linear function under negative gate bias stress (NBS), while it showed a stretched-exponential behavior under positive gate bias stress. The slope of ΔVth for stress time was rarely changed with variations below 0.3 mV/s. The thickness of the fabricated IGZO layer (In0.51Ga0.15Zn0.34O) was approximately 10 nm. The Debye length (LD) was larger than IGZO thickness (tIGZO) due to the fully depleted active layer under NBS. Therefore, the degradation phenomenon under NBS was related to the adsorption at back-channel surface. The back-channel surface could be affected by the gate bias under NBS, and the molecules adsorbed at the IGZO layer were positively charged and induced extra electrons by NBS. We verified that the number of positively charged adsorbates had a proportional relationship with the ΔVth based on the two-dimensional technology computer-aided design (TCAD) simulation. Furthermore, we investigated the degradation phenomenon with the ΔVth equation regarding the adsorbates, and the result confirmed that the adsorption process could cause the linear ΔVth. We experimentally confirmed the effect of back-channel surface by comparing the ΔVth between different atmospheric conditions and LD. Consequently, the reaction at the back-channel surface should be considered to develop the metal-oxide semiconductor devices.

Pattern-Avoiding Ascent Sequences of Length 3

Pattern-avoiding ascent sequences have recently been related to set-partition problems and stack-sorting problems. While the generating functions for several length-3 pattern-avoiding ascent sequences are known, those avoiding 000, 100, 110, 120 are not known. We have generated extensive series expansions for these four cases, and analysed them in order to conjecture the asymptotic behaviour.
 We provide polynomial time algorithms for the $000$ and $110$ cases, and exponential time algorithms for the $100$ and $120$ cases. We also describe how the $000$ polynomial time algorithm was detected somewhat mechanically given an exponential time algorithm.
 For 120-avoiding ascent sequences we find that the generating function has stretched-exponential behaviour and prove that the growth constant is the same as that for 201-avoiding ascent sequences, which is known.
 The other three generating functions have zero radius of convergence, which we also prove. For 000-avoiding ascent sequences we give what we believe to be the exact growth constant. We give the conjectured asymptotic behaviour for all four cases.

NMR 1H-1H Dipole Relaxation in Fluids: Relaxation of Individual 1H-1H Pairs versus Relaxation of Molecular Modes.

The intramolecular 1H NMR dipole-dipole relaxation of molecular fluids has traditionally been interpreted within the Bloembergen-Purcell-Pound (BPP) theory of NMR intramolecular relaxation. The BPP theory draws upon Debye's theory for describing the rotational diffusion of the 1H-1H pair and predicts a monoexponential decay of the 1H-1H dipole-dipole autocorrelation function between distinct spin pairs. Using molecular dynamics (MD) simulations, we show that for both n-heptane and water this is not the case. In particular, the autocorrelation function of individual 1H-1H intramolecular pairs itself evinces a rich stretched-exponential behavior, implying a distribution in rotational correlation times. However, for the high-symmetry molecule neopentane, the individual 1H-1H intramolecular pairs do conform to the BPP description, suggesting an important role of molecular symmetry in aiding agreement with the BPP model. The intermolecular autocorrelation functions for n-heptane, water, and neopentane also do not admit a monoexponential behavior of individual 1H-1H intermolecular pairs at distinct initial separations. We suggest expanding the autocorrelation function in terms of modes, provisionally termed molecular modes, that do have an exponential relaxation behavior. With care, the resulting Fredholm integral equation of the first kind can be inverted to recover the probability distribution of the molecular modes. The advantages and limitations of this approach are noted.

Degradation of a-IGZO Thin-Film Transistors Under Negative Bias and Illumination Stress in the Time Span of a Few Seconds

This letter investigated the time response behavior of amorphous indium–gallium–zinc oxide (a-IGZO) thin-film transistors (TFTs) under negative gate bias and illumination stress (NBIS) in sub-seconds. For the first time, significant degradation even in periods as short as sub-seconds under NBIS was observed. The stretched-exponential behavior of threshold voltage shift ( $\Delta $ Vth) revealed similar mechanisms for short- and long-term NBIS. As a-IGZO TFTs operate at a very high speed, the non-negligible $\Delta $ Vth owing to the influence of fast oxygen vacancy needs to be considered to ensure a-IGZO TFT circuits function well in real applications.

Glass-like stress relaxation of a permanent gelatin network as a signature of pretransitional helix-coil fluctuations.

The stress response of permanently crosslinked gelatin gels was recently observed to display glass-like features, namely, a stretched-exponential behavior terminated by an exponential decay, the characteristic time scales of which increase dramatically with decreasing temperature. This phenomenon is studied here using a model of flexible polymer gel network where relaxation proceeds via elementary monomer exchanges between helix and coil segments. The relaxation dynamics of a full network simulation is found to be nearly identical to that of a model of independent strands, which shows that for flexible polymer gels in the range of elastic moduli of interest, both strand contour length disorder and elastic couplings are irrelevant. We thus focus on the independent strand model and find it not only to explain the observed functional form of the stress relaxation curves but also to yield predictions that match very satisfactorily the experimental measurements of final relaxation time and total stress drop. The system under study thus constitutes a rare case where the origin of glass-like behavior can be unambiguously identified, namely, as the signature of the enhancement of helix content fluctuations when approaching from above the mean-field helix-coil transition of strands.

Direct link between boson-peak modes and dielectric α-relaxation in glasses.

We compute the dielectric response of glasses starting from a microscopic system-bath Hamiltonian of the Zwanzig-Caldeira-Leggett type and using an ansatz from kinetic theory for the memory function in the resulting generalized Langevin equation. The resulting framework requires the knowledge of the vibrational density of states (DOS) as input, which we take from numerical evaluation of a marginally stable harmonic disordered lattice, featuring a strong boson peak (excess of soft modes over Debye ∼ω_{p}^{2} law). The dielectric function calculated based on this ansatz is compared with experimental data for the paradigmatic case of glycerol at T≲T_{g}. Good agreement is found for both the reactive (real) part of the response and for the α-relaxation peak in the imaginary part, with a significant improvement over earlier theoretical approaches. On the low-frequency side of the α peak, the fitting supports the presence of ∼ω_{p}^{4} modes at vanishing eigenfrequency as recently shown [E. Lerner, G. During, and E. Bouchbinder, Phys. Rev. Lett. 117, 035501 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.035501]. α-wing asymmetry and stretched-exponential behavior are recovered by our framework, which shows that these features are, to a large extent, caused by the soft boson-peak modes in the DOS.

The Stretched Exponential Behavior and Its Underlying Dynamics. The Phenomenological Approach

AbstractWe show that the anomalous diffusion equations with a fractional spatial derivative in the Caputo or Riesz sense are strictly related to the special convolution properties of the Lévy stable distributions which stem from the evolution properties of stretched or compressed exponential function. The formal solutions of these fractional differential equations are found by using the evolution operator method where the evolution is conceived as integral transform whose kernel is the Green function. Exact and explicit examples of the solutions are reported and studied for various fractional order of derivatives and for different initial conditions.

The relation between stretched-exponential relaxation and the vibrational density of states in glassy disordered systems

Amorphous solids or glasses are known to exhibit stretched-exponential decay over broad time intervals in several of their macroscopic observables: intermediate scattering function, dielectric relaxation modulus, time-dependent elastic modulus, etc. This behaviour is prominent especially near the glass transition. In this Letter we show, on the example of dielectric relaxation, that stretched-exponential relaxation is intimately related to the peculiar lattice dynamics of glasses. By reformulating the Lorentz model of dielectric matter in a more general form, we express the dielectric response as a function of the vibrational density of states (DOS) for a random assembly of spherical particles interacting harmonically with their nearest-neighbours. Surprisingly we find that near the glass transition for this system (which coincides with the Maxwell rigidity transition in this model), the dielectric relaxation is perfectly consistent with stretched-exponential behaviour with Kohlrausch exponents 0.56<β<0.65, which is the range where exponents are measured in most experimental systems. Crucially, the root cause of stretched-exponential relaxation can be traced back to soft modes (boson-peak) in the DOS.

Cellular Automata Modelling of Photo-Induced Oxidation Processes in Molecularly Doped Polymers

The possibility of employing cellular automata (CA) to model photo-induced oxidation processes in molecularly doped polymers is explored. It is demonstrated that the oxidation dynamics generated using CA models exhibit stretched-exponential behavior. This dynamical characteristic is in general agreement with an alternative analysis conducted using standard rate equations provided the molecular doping levels are sufficiently low to prohibit the presence of safe-sites which are impenetrable to dissolved oxygen. The CA models therefore offer the advantage of exploring the effect of dopant agglomeration which is difficult to assess from standard rate equation solutions. The influence of UV-induced bleaching or darkening upon the resulting oxidation dynamics may also be easily incorporated into the CA models and these optical effects are investigated for various photo-oxidation product scenarios. Output from the CA models is evaluated for experimental photo-oxidation data obtained from a series of hydrazone-doped polymers.

Time-resolved analysis of the white photoluminescence from chemically synthesized SiCxOy thin films and nanowires

The study reported herein presents results on the room-temperature photoluminescence (PL) dynamics of chemically synthesized SiCxOy≤1.6 (0.19 &amp;lt; x &amp;lt; 0.6) thin films and corresponding nanowire (NW) arrays. The PL decay transients of the SiCxOy films/NWs are characterized by fast luminescence decay lifetimes that span in the range of 350–950 ps, as determined from their deconvoluted PL decay spectra and their stretched-exponential recombination behavior. Complementary steady-state PL emission peak position studies for SiCxOy thin films with varying C content showed similar characteristics pertaining to the variation of their emission peak position with respect to the excitation photon energy. A nearly monotonic increase in the PL energy emission peak, before reaching an energy plateau, was observed with increasing excitation energy. This behavior suggests that band-tail states, related to C-Si/Si-O-C bonding, play a prominent role in the recombination of photo-generated carriers in SiCxOy. Furthermore, the PL lifetime behavior of the SiCxOy thin films and their NWs was analyzed with respect to their luminescence emission energy. An emission-energy-dependent lifetime was observed, as a result of the modulation of their band-tail states statistics with varying C content and with the reduced dimensionality of the NWs.

Time-resolved photoluminescence spectroscopy ofNbNb4+andO−polarons inLiNbO3single crystals

We probe here the optical relaxation properties of Mg-doped wide-band-gap ${\mathrm{LiNbO}}_{3}$ single crystals with both a high spectral and temporal resolution at cryogenic temperatures. Surprisingly, we observe the photoluminescence to decay in a two-step process: a fast relaxation and a slower one centered around an energy ${E}_{max}$ = 2.62 $\ifmmode\pm\else\textpm\fi{}0.05$ eV. Both decays fit well to the stretched-exponential behavior. Moreover, we are able to associate these energies to the recombination of light-induced ${\mathrm{Nb}}_{\text{Nb}}^{4+}$ and ${\mathrm{O}}^{\ensuremath{-}}$ small polarons. Also, we checked the stability of our findings by using ${\mathrm{LiNbO}}_{3}$ single crystals that show on-purpose modified radiative recombination processes, i.e., with a Mg doping both above and below the optical damage resistance threshold, as well as with different poling histories of inverted domains.

Random-walk annihilation process of photo-induced neutral-ionic domain walls in TTF-CA

The charge and lattice dynamics at the neutral-ionic phase transition in the organic mixed-stack compound TTF-CA were measured by time-resolved Fourier-transform infrared spectroscopy and modeled by Monte Carlo simulations on a one-dimensional chain. After photoexcitation in the ionic state, we observe transient changes in reflectivity, which follow a stretched-exponential behavior on a microsecond time scale. This implies that the dimerization between the TTF and CA molecules vanishes, creating metastable domains. The time, temperature and intensity dependences can be modeled by a diffusion-annihilation process of neutral-ionic domain walls. Their random walk explains the relaxation process and its characteristic decay with time.

Exploring diffusion across permeable barriers at high gradients. II. Localization regime

We present an analytical solution of the one-dimensional Bloch–Torrey equation for diffusion across multiple semi-permeable barrier. This solution generalizes the seminal work by Stoller, Happer, and Dyson, in which the non-Gaussian stretched-exponential behavior of the pulsed-gradient spin-echo (PGSE) signal was first predicted at high gradients in the so-called localization regime. We investigate how the diffusive exchange across a semi-permeable barrier modifies this asymptotic behavior, and explore the transition between the localization regime at low permeability and the Gaussian regime at high permeability. High gradients are suitable to spatially localize the contribution of the nuclei near the barrier and to enhance the sensitivity of the PGSE signal to the barrier permeability. The emergence of the localization regime for three-dimensional domains is discussed.

Direct observation of a single nanoparticle–ubiquitin corona formation

The advancement of nanomedicine and the increasing applications of nanoparticles in consumer products have led to administered biological exposure and unintentional environmental accumulation of nanoparticles, causing concerns over the biocompatibility and sustainability of nanotechnology. Upon entering physiological environments, nanoparticles readily assume the form of a nanoparticle-protein corona that dictates their biological identity. Consequently, understanding the structure and dynamics of a nanoparticle-protein corona is essential for predicting the fate, transport, and toxicity of nanomaterials in living systems and for enabling the vast applications of nanomedicine. Here we combined multiscale molecular dynamics simulations and complementary experiments to characterize the silver nanoparticle-ubiquitin corona formation. Notably, ubiquitins competed with citrates for the nanoparticle surface, governed by specific electrostatic interactions. Under a high protein/nanoparticle stoichiometry, ubiquitins formed a multi-layer corona on the particle surface. The binding exhibited an unusual stretched-exponential behavior, suggesting a rich binding kinetics. Furthermore, the binding destabilized the α-helices while increasing the β-sheet content of the proteins. This study revealed the atomic and molecular details of the structural and dynamic characteristics of nanoparticle-protein corona formation.

Stretched-exponential behavior and random walks on diluted hypercubic lattices

Diffusion on a diluted hypercube has been proposed as a model for glassy relaxation and is an example of the more general class of stochastic processes on graphs. In this article we determine numerically through large-scale simulations the eigenvalue spectra for this stochastic process and calculate explicitly the time evolution for the autocorrelation function and for the return probability, all at criticality, with hypercube dimensions N up to N=28. We show that at long times both relaxation functions can be described by stretched exponentials with exponent 1/3 and a characteristic relaxation time which grows exponentially with dimension N. The numerical eigenvalue spectra are consistent with analytic predictions for a generic sparse network model.

Degradation Model of Self-Heating Effects in Silicon-on-Glass TFTs

This paper investigates the origin and reduction of self-heating effects in single-crystal silicon-on-glass (SiOG) thin-film transistors (TFTs). A hump forms in the transfer characteristics of p-channel SiOG TFTs when the temperature of the devices is increased either by direct heating or electrical biasing. The size of the hump proportionally scales with the channel width <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</i> , indicating that it is related to the bulk active-layer properties such as conduction through a backchannel. While the hump increases in the positive direction, the main transistor shifts in the negative direction with increasing self-heating stress time, supporting the exclusion of edge effects. The time dependence of the hump shift is well described by the stretched-exponential behavior, indicating that the backchannel is a result of electron trapping into the silica layer that is between the glass and silicon active layer. To mitigate this hump effect, we demonstrate in this paper that TFTs with an active layer divided into smaller parts along the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</i> direction (in order to increase heat dissipation) show better stability to self-heating stress (i.e., no hump formation) than TFTs with full active layers. Split devices have more channel edges, compared with those with a full active layer, supporting the idea that the hump is indeed not due to edge effects.

Anomalous diffusion in a space- and time-dependent energy landscape

We study the influence on diffusion in one dimension of a potential energy perturbation varying as apower in space and time. We concentrate on the case of a parabolic perturbation in space decaying ast − ω which shows a rich variety of scaling behaviours. Whenω = 1, the perturbation is truly marginal and leads to anomalous (super)diffusionwith a dynamical exponent varying continuously with the perturbationamplitude below some negative threshold value. For slower decay,ω < 1, the perturbation becomes relevant and the system is either subdiffusive for an attractivepotential or displays a stretched-exponential behaviour for a repulsive one. Exact resultsare obtained for the mean value and the variance of the position as well as for the survivingprobability.

An exponential law for stretching–relaxation properties of bone piezovoltages

An exponential law is presented for modeling piezoelectric behavior of bone tissues. The law is established based on experimental observation and existing empirical decay function. The model is then used to investigate the relaxation behavior of pizeovoltages induced by external load. Piezovoltages between the two opposing surfaces of bovine tibia bone samples under three point bending deformation are measured using an ultra high input impedance bioamplifier. The experimental results indicate that the pizeovoltages of bone show different relaxation behaviors during loading and unloading process. It is found that the piezovoltage decay follows a stretched exponential law when the load increases from zero to its maximum value, while it follows a typical relaxation exponential law when the load is kept its maximum value. The stretching-exponential behavior is independent of loading amplitude and rate. One possible reason for causing the stretched exponential behavior may be due to the triple helices structure of collagen fibrils distributed randomly in bone, which can experience relatively large deformation under external loads. The deformation process may include self-deformation and relative slipping between the molecule chains. The relative slipping movements may change the dielectric constants and resistances of bone, which can lead to multiple relaxation time behaviors during the deformation process of bone.

Comments on the electric modulus formalism model and superior alternatives to it for the analysis of the frequency response of ionic conductors

Because of the past and continuing wide usage of the 1973 original modulus formalism (OMF) model for analyzing dispersive frequency-response data of ion-conducting materials, it is important to discuss and demonstrate its theoretical and experimental inadequacies to help avoid its future use and to describe and illustrate important alternatives to it. The OMF fits data with a K1 response model alone, one indirectly derived from stretched-exponential temporal behavior, while the corrected modulus formalism (CMF) involves the composite CK1 model, one that includes in addition a separate free, parallel bulk dielectric parameter, ε D ∞. The crucial error of the OMF approach is its identification of a high-frequency-limiting dielectric constant intrinsic to K1 response and associated entirely with conductive effects, with the full high-frequency-limiting dielectric constant of the material, ε ∞, one that must include the non-ionic, primarily dipolar quantity ε D ∞. Comparison here of OMF fitting results with those of the CMF CK1 model for both an experimental data set and an exact one derived from it demonstrate the incorrectness of the OMF and the virtues of the CK1 alternative. The OMF fitting approach, but not the CMF one, leads to crucial inconsistency between the estimates of its β shape parameter for fits of the data expressed at all immittance levels except those of σ′ and ε″, where it yields the same results as the CK1. Its incorrect β estimates, extensively used in the Ngai coupling model and interpreted as being associated with ion–ion correlations, also lead to erroneous “excess wing” effects in plots of the imaginary part of the data and fit at the modulus level. Further, OMF modulus-level fits yield non-physical estimated values of the characteristic relaxation time of the K1 model. Finally, some possible alternatives to the CK1 model are discussed for situations involving dielectric-system dispersion.