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Ali Shakouri

Publications and source records attributed to Ali Shakouri.

27 records · Page 2Linked to original sources
arXiv2014

Spatiotemporal flux memory in nondiffusive transport

Anomalous diffusion constitutes a relation between tracer flux and tracer density gradient that is inherently nonlocal in space and/or time. Previous studies emphasize the non-Gaussian character of the tracer distribution that arises from adjusted constitutive relations but did not investigate the flux-gradient memory itself. Here, we present a universal analytic framework that enables systematic characterisation of nonlocality in a wide variety of transport regimes. A generalised diffusivity kernel $D^{\ast}$ fully embodies the spatiotemporal flux memory with respect to the gradient. An extension of the flux-gradient relation for subdiffusive transport is also proposed. Several conservation and invariance properties can be deduced, including that Poissonian flight processes have no flux memory in time while fractional time diffusion has no flux memory in space. We derive analytical expressions for $D^{\ast}(x,t)$ in several types of anomalous transport dynamics that are commonly encountered in practice, being fractional diffusion equations, tempered Lévy superdiffusion, and tempered fractional time diffusion. This detailed knowledge of the shape and nature of the flux memory, and the corresponding length and time scales over which nonlocal effects are physically important, remain completely hidden in conventional analyses based on tracer distributions or flux-gradient diagrams. Practical capabilities include the interpretation of microscale heat superdiffusion experiments. Overall, the theory can serve as a valuable framework for anomalous transport dynamics across multiple disciplines.

cond-mat.stat-mech↗
arXiv2014

Superdiffusive heat conduction in semiconductor alloys -- I. Theoretical foundations

Semiconductor alloys exhibit a strong dependence of effective thermal conductivity on measurement frequency. So far this quasi-ballistic behaviour has only been interpreted phenomenologically, providing limited insight into the underlying thermal transport dynamics. Here, we show that quasi-ballistic heat conduction in semiconductor alloys is governed by Lévy superdiffusion. By solving the Boltzmann transport equation (BTE) with ab initio phonon dispersions and scattering rates, we reveal a transport regime with fractal space dimension $1 < α< 2$ and superlinear time evolution of mean square energy displacement $σ^2(t) \sim t^β (1 < β< 2)$. The characteristic exponents are directly interconnected with the order $n$ of the dominant phonon scattering mechanism $τ\sim ω^{-n} (n>3)$ and cumulative conductivity spectra $κ_Σ(τ;Λ)\sim (τ;Λ)^γ$ resolved for relaxation times or mean free paths through simple relations $α= 3-β= 1 + 3/n = 2 - γ$. The quasi-ballistic transport inside alloys is no longer governed by Brownian motion, but instead dominated by Lévy dynamics. This has important implications for the interpretation of thermoreflectance (TR) measurements with modified Fourier theory. Experimental $α$ values for InGaAs and SiGe, determined through TR analysis with a novel Lévy heat formalism, match ab initio BTE predictions within a few percent. Our findings lead to a deeper and more accurate quantitative understanding of the physics of nanoscale heat flow experiments.

cond-mat.mtrl-sci↗
arXiv2014

Superdiffusive heat conduction in semiconductor alloys -- II. Truncated Lévy formalism for experimental analysis

Nearly all experimental observations of quasi-ballistic heat flow are interpreted using Fourier theory with modified thermal conductivity. Detailed Boltzmann transport equation (BTE) analysis, however, reveals that the quasi-ballistic motion of thermal energy in semiconductor alloys is no longer Brownian but instead exhibits Lévy dynamics with fractal dimension $α< 2$. Here, we present a framework that enables full 3D experimental analysis by retaining all essential physics of the quasi-ballistic BTE dynamics phenomenologically. A stochastic process with just two fitting parameters describes the transition from pure Lévy superdiffusion as short length and time scales to regular Fourier diffusion. The model provides accurate fits to time domain thermoreflectance raw experimental data over the full modulation frequency range without requiring any `effective' thermal parameters and without any a priori knowledge of microscopic phonon scattering mechanisms. Identified $α$ values for InGaAs and SiGe match ab initio BTE predictions within a few percent. Our results provide experimental evidence of fractal Lévy heat conduction in semiconductor alloys. The formalism additionally indicates that the transient temperature inside the material differs significantly from Fourier theory and can lead to improved thermal characterization of nanoscale devices and material interfaces.

cond-mat.mtrl-sci↗
arXiv2010

Transient Energy and Heat Transport in Metals: Effect of the Discrete Character of the Lattice

A recently developed Shastry's formalism for energy transport is used to analyze the temporal and spatial behaviors of the energy and heat transport in metals under delta function excitation at the surface. Comparison with Cattaneo's model is performed. Both models show the transition between nonthermal (ballistic) and thermal (ballistic-diffusive) regimes. Furthermore, because the new model considers the discrete character of the lattice, it highlights some new phenomena such as damped oscillations in the energy transport both in time and space. The energy relaxation of the conduction band electrons in metals is considered to be governed by the electron-phonon scattering, and the scattering time is taken to be averaged over the Fermi surface. Using the new formalism, one can quantify the transfer from nonthermal modes to thermal ones as energy propagates in the material and it is transformed into heat. While the thermal contribution shows a wave-front and an almost exponentially decaying behavior with time, the nonthermal part shows a wave-front and a damped oscillating behavior. Two superimposed oscillations are identified; a fast oscillation that is attributed to the nonthermal nature of energy transport at very short time scales and a slow oscillation that describes the nature of the transition from the nonthermal regime to the thermal regime of energy transport.

cond-mat.mes-hall↗
arXiv2007

Study of Phonon Modes in Germanium Nanowires

The observation of pure phonon confinement effect in germanium nanowires is limited due to the illumination sensitivity of Raman spectra. In this paper we measured Raman spectra for different size germanium nanowires with different excitation laser powers and wavelengths. By eliminating the local heating effect, the phonon confinement effect for small size nanowires was clearly identified. We have also fitted the Raman feature changes to estimate the size distribution of nanowires for the first time.

quant-ph↗
arXiv2006

Monte Carlo Simulation of Electron Transport in Degenerate Semiconductors

A modified algorithm is proposed to include Pauli exclusion principle in Monte-Carlo simulations. This algorithm has significant advantages to implement in terms of simplicity, speed and memory storage. We show that even in moderately high applied fields, one can estimate electronic distribution with a shifted Fermi sphere without introducing significant errors. Furthermore, the free-flights must be coupled to state availability constraints; this leads to substantial decrease in carrier heating at high fields. We give the correct definition for electronic temperature and show that in high applied fields, the quasi Fermi level is valley dependent. The effect of including Pauli exclusion principle on the band profile; electronic temperature and quasi Fermi level for inhomogeneous case of a single barrier heterostructure is illustrated.

cond-mat.mtrl-sci↗
arXiv2006

Thermoelectric transport perpendicular to thin film heterostructures using Monte Carlo technique

The Monte Carlo technique is used to calculate electrical as well as thermoelectric transport properties across thin film heterostructures. We study a thin InGaAsP barrier layer sandwiched between two InGaAs contact layers, when the barrier thickness is in 50nm-2000nm range. We found that with decreasing size, the effective Seebeck coefficient is increased substantially. The transition between pure ballistic thermionic transport and fully diffusive thermoelectric transport is also described.

cond-mat.mtrl-sci↗
arXiv2005

Thermoelectric properties of a nanocontact

Thermoelectric properties of a nanocontact made of two capped single wall nanotubes (SWNT) are calculated within the tight-binding approximation and Green's function method. It is found that semiconducting nanotubes can have high Seebeck coefficient very near the actual Fermi energy. This in turn leads to very high figures of merit easily exceeding one. Modifying the properties by shifting the chemical potential can be achieved by doping or application of a (nano-)gate voltage. The presence of impurities near the contact also strongly modify the properties and this can be taken advantage of, in order to design devices with high thermopower and figures of merit.

cond-mat.mtrl-sci↗