Exponential Correlation Function Research Articles

Statistical fluctuation of universal mobility curves in sub‐100 nm MOSFETs due to random oxide interface

AbstractWe explore the behavior of universal mobility in sub‐100 nm Si MOSFETs, using a novel 3D statistical simulation approach. Our approach is based on 3D Brownian dynamics in devices with realistic Si/SiO2 interfaces reconstructed from a Gaussian or exponential correlation function. In this approach carrier trajectories in the bulk are treated via 3D Brownian dynamics, while the carrier‐interface roughness scattering is treated using a novel empirical model. Owing to the high efficiency of the transport kernel, effective mobility in 3D MOSFETs with realistic Si/SiO2 can be simulated in a statistical manner. We first demonstrate a practical calibration procedure for the interface mobility and affirm the universal behaviour in the long channel limit, using single atomic steps and a correlation length of 6 nm. Next, effective mobility in ensembles of MOSFETs with gate length down to 10 nm is investigated. It is found that random‐discrete nature of the Si/SiO2 interface leads to a distribution of carrier mobility below the interface, which can deviate considerably from universal mobility curves when Lgate < 6Λ, where Λ is the correlation length for the SiO2 interface. Based on recent data Λ = 2.8 nm, our simulations indicate that universal‐mobility curves should be reliable for MOSFET designs down to a gate length of 17 nm. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Spontaneous emission and elastic scattering of light from quantum-well excitons in a Fabry-Perot microcavity

A theory of spontaneous emission and elastic light scattering by quasi-two-dimensional excitons in a quantum well placed in a Fabry-Perot microcavity is developed. The problem is solved by means of electrodynamic Green’s functions with inclusion of fluctuations of the quantum-well width and cavity wall shape treated as a perturbation. General expressions are found in a zero approximation of perturbation theory (plane interfaces) for the radiative decay rates of quasi-two-dimensional excitons and for their energy shifts in the cavity. The boundary conditions for the electromagnetic field are taken into account through the coefficients of inward light reflection from the cavity walls. Resonance contributions to the scattering cross sections, which differ in the polarizations (p or s) of the incident and scattered waves, are derived in the lowest (Born) approximation in quantum-well width fluctuations. The spectral and angular dependences of elastic light scattering are studied numerically for Gaussian and exponential correlation functions. It is shown that the contribution from quantum-well width fluctuations to light scattering exceeds that due to single interfaces (surfaces) of a heterostructure by two orders of magnitude.

Non-Local Mean Field Dynamo Theory and Magnetic Fronts in Galaxies

In this article we address the problem of magnetic field generation and front propagation in turbulent electrically conducting fluids, involving the velocity with finite correlations times and small magnetic diffusivity. We suggest an integro-differential dynamo equation which involves the non-local terms for both the dynamo source α-term and turbulent transport of the mean magnetic field. We derive a set of formulas which allows us to determine the rate of magnetic front propagation in galaxies valid for arbitrary memory kernels. We illustrate the general results through the use of the exponential correlation functions for memory kernels and 'no-z' approximation. We find that the memory effects have strong influence on for both the growth rate and propagation speed. We perform numerical simulations of exterior front speed, and find that the transport memory essentially decreases the propagation rate.

Influence of the Parameters of a Random Medium on the Characteristics of Transient Reflections

Based on the invariant imbedding method, we study numerically the statistical characteristics of the kernel of the backscattering operator in the case of normal incidence of a plane wave on a one-dimensional random medium with strong fluctuation intensities and various correlation radii of the irregularities. The local reflection coefficient of the medium is modelled by a centered Gaussian process with an exponential correlation function. The first eight one-point cumulants and the correlation functions of delta-pulse reflection are considered and the fluctuation phenomena are analyzed. The transition to the diffusion scattering regime is studded, and the numerical results are compared with the known analytical solutions.

Exact Averaging of Stochastic Equations for Transport in Random Velocity Field

We present new examples of exactly averaged multi-dimensional equation of transport of a conservative solute in a time-dependent random flow velocity field. The functional approach and a technique for decoupling the correlations are used. In general, the averaged equation is non-local. We study the special cases where the averaged equation can be localized and reduced to a differential equation of finite-order, where the problem of evolution of the initial plume (Cauchy problem) can be solved exactly. We present in detail the results of the analyses of two cases of exactly averaged problems for Gaussian and telegraph random velocity with an identical exponential correlation function, which are informative and convenient models for continuous and discontinuous random functions. The problems in which the field has sources of solute and boundaries are also examined. We study the behavior of different initial plumes for all times (evolutions and convergence) and show the manner in which they approach the same asymptotic limit for two stochastic distributions of flow-velocity. A comparison between exact solutions and solutions derived by the method of perturbation is also discussed.

Breakdown of universal mobility curves in sub-100-nm MOSFETs

We explore the breakdown of universal mobility behavior in sub-100-nm Si MOSFETs, using a novel three-dimensional (3-D) statistical simulation approach. In this approach, carrier trajectories in the bulk are treated via 3-D Brownian dynamics, while the carrier-interface roughness scattering is treated using a novel empirical model. Owing to the high efficiency of the transport kernel, effective mobility in 3-D MOSFETs with realistic Si-SiO/sub 2/ interfaces reconstructed from a Gaussian or exponential correlation function can be simulated in a statistical manner. We first demonstrate a practical calibration procedure for the interface mobility and affirm the universal behavior in the long channel limit. Next, effective mobility in ensembles of MOSFETs with a gate length down to 10 nm is investigated. It is found that the random-discrete nature of the Si-SiO/sub 2/ interface leads to a distribution of carrier mobility below the interface, which can deviate considerably from universal mobility curves when L/sub gate/<6/spl Lambda/, where /spl Lambda/ is the correlation length for the SiO/sub 2/ interface.

Scattering coefficient forSwave incident in a random medium characterized by exponential correlation function

Summary Analytical expressions for scattering coefficients for S-wave incidence have been derived for the medium defined by the exponential correlation function. Low- and high-frequency asymptotic characteristics of the total scattering coefficients have also been investigated. The scattered energy of the converted waves reaches a maximum value in the high-frequency range for the case of an exponential correlation function. The meridional component of the scattered energy for common-mode scattering has a second-power frequency dependence for the high-frequency range, while the latitude component of the scattered energy for common-mode scattering has a fourth-power frequency dependence for the high-frequency range. A comparison of the scattering coefficient for P- and S-wave incidence is also discussed. Mode-conversion for P-wave incidence is greater than that for S-wave incidence. On the other hand, for the common-mode case the scattered energy for S-wave incidence is greater than that for P-wave incidence.

Relationship between the transverse NMR decay and the dipolar interaction in elastomers: a comparison of two models

The analysis of the transverse magnetization decay is a well-established method to obtain information about network parameters of elastomers or polymeric melts. The starting point is the scaling concept introduced by Cohen-Addad, which reduces the detailed description of the atomic bond-vector motion to that of a larger scaled subchain motion. When considering polymer networks some simplifications in the calculation of the NMR response are widely used. In the frozen bond assumption all the crosslink positions in a network are taken to be at fixed points, with the intercrosslink network end-to-end vectors having a Gaussian distribution. In the second moment approximation it is assumed that there is a Gaussian distribution of dipolar interactions, and additionally an exponential correlation function of the motion is used. Both models are able to explain the non-exponential magnetization decay (FID of a Hahn-echo NMR experiment). We will compare these different starting points to give some relations between them. Both models are tested by a NMR-relaxation experiment.

A predictability analysis of network traffic

This paper assesses the predictability of network traffic by considering two metrics: (1) how far into the future a traffic rate process can be predicted with bounded error; (2) what the minimum prediction error is over a specified prediction time interval. The assessment is based on two stationary traffic models: the auto-regressive moving average and the Markov-modulated poisson process. In this paper, we do not aim to propose the best traffic (prediction) model, which is obviously a hard and arguable issue. Instead, we focus on the constrained predictability estimation with assumption and discussion about the modeling accuracy. The specific time scale or bandwidth utilization target of a predictive network control actually forms the constraint. We argue that the two models, though both short-range dependent, can capture statistics of (self-similar) traffic quite accurately for the limited time scales of interests in measurement-based traffic management. This argument, in mathematical terms, simply reflects the fact that the summarized exponential (correlation) functions may approximate a hyperbolical one very well. Our study reveals that the applicability of traffic prediction is limited by the deteriorating prediction accuracy with increasing prediction interval. From both analytical and numerical studies, we explore the different roles of traffic statistics, either at the 1st-order or the 2nd-order, in traffic predictability. Particularly, the statistical multiplexing and proper measurement (e.g. sampling/filtering) of traffic show positive effects. Experimental results suggest promising backbone traffic prediction, and generally enhanced predictability if small time-scale traffic variations, which are usually of less importance to bandwidth allocation and call admission control, have been filtered out. The numerical results in the paper provide quantized reference to the optimal online traffic predictability for network control purposes.

A generalized power law spectrum and its applications to the backscattering of soil surfaces based on the integral equation model

A generalized power law spectrum is proposed to describe the random rough surfaces in this paper. The parameters of the spectrum are related to the traditional physical parameters of root mean square (rms) height and correlation length. It can naturally reduce to the spectra of Gaussian and exponential correlation functions. The corresponding correlation functions are also derived. It can provide wider range of spectra to describe the random rough surfaces than other spectra. Based on the proposed spectrum, backscattering of soil surfaces is studied by using the integral equation model (IEM). The simulation results are compared with the experimental measurements of real soil surfaces at L, C, and X bands for the different roughness scales and moisture conditions. The reasonably good agreements between the measurements and the simulations are observed for all three-frequency bands and different incidence angles with the same sets of the physical roughness parameters.

On the Breakdown of Universal Mobility Curves: A Brownian 3D Simulation Framework

We present an efficient simulation approach to study the universal mobility behaviour in Si MOS structures with random Si/SiO2 interfaces. Our approach is based on 3D Brownian dynamics in devices with realistic Si/SiO2 interfaces reconstructed from a Gaussian or exponential correlation function. The carrier-interface roughness scattering is treated ab-initio in our simulations and it results in correct velocity and real space distributions. The method is efficient and capable of 3D simulation of the interface roughness limited mobility in small MOSFETs in a statistical manner. After a careful calibration procedure, we reproduce the effective field dependence of interface mobility for μBulk = 1100 cm2/Vs using a random interface with single atomic steps and a correlation length of 6 nm.

The Influence of the Initial-Signal Duration on Nonstationary Reflections in a Random Medium

Using the invariant imbedding method, we study numerically the statistical characteristics of backscattering of plane-wave pulses incident normally on a random one-dimensional medium. The local reflection coefficient of the medium is simulated by a centered Gaussian process with an exponential correlation function. We consider the time dependences of the average intensity and the kurtosis coefficient of reflections for various durations and carrier frequencies of the initial signal. It is shown that the attenuation and fluctuations of reflections increase with the initial-signal duration normalized to the time scale of the medium irregularities and depend on the signal carrier. Numerical results for the average intensity are compared with previously obtained analytical solutions. We discuss the appearance conditions of a wave stochastic resonance in nonstationary reflections.

The Effect of Spatial Autocorrelation on the Error Rates of the Linear Discriminant Functions

The problem of classification of the realization of the intrinsically stationary multivariate Gaussian random field into one of two populations with different means and factorized covariance matrices is considered. Unknown means and the common covariance matrix of the feature vector components are estimated from the spatially correlated training samples assuming spatial correlations to be known. Two plug‐in linear discriminant functions (DF) are considered. The first linear DF uses the maximum likelihood (ML) estimators of means and the bias‐adjusted ML estimator of covariance. The second one uses usual sample means and bias‐adjusted sample covariance. The first‐order asymptotic expansions with respect to the inverses of training sample sizes of the expected error rate associated with two plug‐in DF's are presented. The numerical results obtained allow us to compare the performance of the suggested DF's. The numerical calculations are done for the exponential spatial correlation function.

Statistical modelling of the backscattered field in a one-dimensional non-stationary stochastic problem

Within the framework of an exact wave approach in the spatial-time domain, the one-dimensional stochastic problem of sound pulse scattering by a layered random medium is considered. On the basis of a unification of methods which has been developed by the authors, previously applied to the investigation of non-stationary deterministic wave problems and stochastic stationary wave problems, an analytical-numerical simulation of the behaviour of the backscattered field stochastic characteristics was carried out. Several forms of incident pulses and signals are analysed. We assume that random fluctuations of a medium are described by virtue of the Gaussian Markov process with an exponential correlation function. The most important parameters appearing in the problem are discussed; namely, the time scales of diffusion, pulse durations, the medium layer thickness or the largest observation time scale in comparison with the time scale of one correlation length for the case of a half-space. An exact pattern of the pulse backscattering processes is obtained. It is illustrated by the behaviour of the backscattered field statistical moments for all observation times which are of interest. It is shown that during the time interval when the main part of the pulse energy leaves the medium, the backscattered field is a substantially non-stationary process, having a non-zero mean value and an average intensity that decays according to a power law. There are various power indices for the different duration incident pulses, however, they are not the same as those of previous papers, which were obtained on the basis of an approximate and asymptotic analysis. We have also verified that the Gaussian law is valid for the probability density function of the backscattered field in the case of any incident pulse duration.

Markov models of non-Gaussian exponentially correlated processes and their applications.

We consider three different methods of generating non-Gaussian Markov processes with given probability density functions and exponential correlation functions. All models are based on stochastic differential equations. A number of analytically treatable examples are considered. The results obtained can be used in different areas such as telecommunications and neurobiology.

Small-scale structure of lithosphere-asthenosphere beneath Gauribidanur Seismic array deduced from amplitude and phase fluctuations

The cross coherence function between log amplitude and phase (or travel time) has been analyzed along with the transverse coherence functions of log amplitude and phase in order to estimate the statistical distribution of heterogeneities beneath the Gauribidanur Seismic array (GBA). The power spectra of the P-wave velocity variations can be estimated under the array with the help of the transverse coherence functions (TCFs). The data of 72 earthquakes have been used to calculate the three TCFs (of phase, log amplitude and cross-coherence). The central frequency is 2 Hz. The measured root mean square (rms) log amplitude fluctuation is 0.40 and the rms phase fluctuation is 0.88. An overlapping two-layer model has been obtained for lithosphere and asthenosphere heterogeneities beneath GBA with different power law spectra. The upper layer, in which the heterogeneities are defined by Gaussian correlation function extends from the surface to about 160 km depth while the lower layer, in which the heterogeneities are defined by exponential correlation function extends from 16 to 280 km. The rms P-wave velocity variation has been estimated in the range of 0.3–1.5%. Clustering of cracks or intrusions may be responsible for the small-scale heterogeneities while temperature or compositional heterogeneities may be the cause of large-scale wave heterogeneities.

Model independent shape analysis of correlations in 1, 2 or 3 dimensions

A generic, model-independent method for the analysis of the two-particle short-range correlations is presented, that can be utilized to describe e.g. Bose–Einstein (HBT or GGLP), statistical, dynamical or other short-range correlation functions. The method is based on a data-motivated choice for the zeroth order approximation for the shape of the correlation function, and on a systematic determination of the correction terms with the help of complete orthonormal sets of functions. The Edgeworth expansion is obtained for approximately Gaussian, the Laguerre expansion for approximately exponential correlation functions. Multi-dimensional expansions are also introduced and discussed.

A BPP(Bloembergen-Purcell-Pound) model for nuclear spin relaxation dueto diffusion in disordered systems: combined barrier- andsite-energy disorder

Nuclear spin relaxation rates due to magnetic interactions betweendiffusing spins in ordered systems are often interpreted in terms ofan exponential correlation function (the BPP model). The commonextension of this to disordered systems is to average the relaxationrate for a jump rate with energy E over a distribution N(E) ofenergies in the disordered system. A more rigorous extension of theBPP model to disordered systems is described which incorporatessimultaneous barrier- and site-energy distributions. An efficientcomputational scheme is developed to evaluate the triple integralsrequired. Results are presented for the correlation functions andrelaxation rates for some typical values of parameters for both ofthe above extensions of the BPP model to disordered systems. Thereare significant differences between the results for the two models.The model presented here provides a means of analysing experimentalrelaxation data to deduce information about both barrier- andsite-energy distributions.

Quinolines: T1 NMR relaxation times of quinolines as a function of temperature in liquid and supercooled liquid state

The behaviour of the 13C spin-lattice relaxation time a function of temperature is reported for eight quinoline family compounds. For a set of compounds (ln T1−1) = f(T−1) is linear, for the other set (ln T1−1) = f(T−1) is best represented by two linear straight lines which intercept at a temperature Tt which depends upon the compound. For quinoline and lepidine the study has been also performed in the supercooled state. T1−1 shows a maximum for lepidine, and the relaxation time evolution as a function of T may be interpreted using a stretched exponential correlation function.

Thermal radiation properties of turbulent lean premixed methane air flames

Thermal radiation properties of turbulent premixed flames have received little attention in the past perhaps because of the lower radiative heat loss compared with that for non-premixed flames. However, the high-temperature sensitivity of NO kinetics and the importance of radiation in near-limit laminar premixed flames provide fundamental reasons for studies of radiation properties of turbulent premixed flames. Reduced cooling airflows in lean premixed combustors, miniaturization of combustors, and the possible use of radiation sensors in combustion control schemes are some of the practical reasons for studying radiation heat transfer in these flames. Motivated by this, we report the first (to our knowledge) study of spectral radiation properties of turbulent premixed flames. Measurements of mean, root mean square (rms) and probability density functions (PDFs) of spectral radiation intensities leaving diametric paths at five heights in two turbulent lean premixed methane/air jet flames stabilized using small H 2 /air pilot flames in a coflow of air were completed. Measurememts of spectral radiation intensities leaving three laminar flames were also completed These data were used to evaluate narrowband radiation calculations independent of the treatment of turbulent fluctuations. Stochastic spatial series analysis was used to estimate instantaneous distributions of temperature. The analysis requires the specification of mean and rms temperature distributions, integral length scale distributions, and an assumption of exponential spatial correlation function. We specified the mean and rms temperature distributions measured by calibrated narrowband thin filament pyrometry. A simple flame and mixing model was used to relate the concentrations of CO 2 and H 2 O to the temperature. We used scalar spatial series in conjunction with a radiation model to calculate the mean, rms, and PDFs of spectral radiation intensities. Overall, the model predictions are in reasonable agreement with the data. The only improvement needed is in the area of capturing correlated occurrences of high temperatures along the radiation path.