Stationary Density Profile Research Articles

Fluctuation driven transport and stationary profiles

Transport equations for particles and energy can be derived when the fluctuations conserve adiabatic invariants. The transport equations determine both stationary density and pressure profiles and the direction of the turbulence-driven fluxes which can be inward or outward. An inward turbulent pinch is predicted which creates stationary profiles and reverses direction depending on the density and temperature gradients. The transport fluxes are independent of the underlying drive that leads to plasma turbulence. For low frequency turbulence, the formulation remains correct when the collisional time scale is faster than the confinement time scale.

An extinction-survival-type phase transition in the probabilistic cellular automaton p182–q200

We investigate the critical behaviour of a probabilistic mixture of cellular automata (CA) rules 182 and 200 (in Wolfram's enumeration scheme) by mean-field analysis and Monte Carlo simulations. We found that as we switch off one CA and switch on the other by the variation of the single parameter of the model, the probabilistic CA (PCA) goes through an extinction–survival-type phase transition, and the numerical data indicate that it belongs to the directed percolation universality class of critical behaviour. The PCA displays a characteristic stationary density profile and a slow, diffusive dynamics close to the pure CA 200 point that we discuss briefly. Remarks on an interesting related stochastic lattice gas are addressed in the conclusions.

Hot-carrier degradation caused interface state profile—Simulation versus experiment

Hot-carrier degradation is associated with the buildup of defects at or near the silicon/silicon dioxide interfaced of a metal-oxide-semiconductor transistor. However, the exact location of the defects, as well as their temporal buildup during stress, is rarely studied. In this work we directly compare the experimental interface state density profiles generated during hot-carrier stress with simulation results obtained by a hot-carrier degradation model. The developed model tries to capture the physical picture behind hot-carrier degradation in as much detail as feasible. The simulation framework includes a transport module, a module describing the microscopic mechanisms of defect generation, and a module responsible for the simulation of degraded devices. Due to the model complexity it is very important to perform a thorough check of the output data of each module before it is used as the input for the next module. In this context a comparison of the experimental interface state concentration observed by the charge-pumping technique with the simulated one is of great importance. Obtained results not only show a good agreement between experiment and theory but also allow us to draw some important conclusions. First, we demonstrate that the multiple-particle mechanism of Si–H bond breakage plays a significant role even in the case of a high-voltage device. Second, the absence of the lateral shift of the charge-pumping signal means that no bulk oxide charge buildup occurs. Finally, the peak of interface state density corresponds to the peak of the carrier acceleration integral and is markedly shifted from typical markers such as the maximum of the electric field or the carrier temperature. This is because the degradation is controlled by the carrier distribution function and simplified schemes of hot-carrier treatment (based on the mentioned quantities) fail to describe the matter.

Calculation of spatial distribution of optical escape factor and its application to He I collisional-radiative model

An integral analytical formula for a spatial distribution of the optical escape factor (OEF) in an infinite cylindrical plasma is derived as a function of an arbitrary upper state spatial density profile, the temperature ratio of the upper state to the lower state, and the optical depth of the corresponding transition. Test calculations are carried out for three different upper state profiles, i.e., uniform (rectangular), parabolic, and Gaussian upper state profiles. The OEF takes on negative values at the periphery of the parabolic and Gaussian upper state profiles. These characteristics cannot be expressed by the conventional OEF formulas derived for the center of the plasma, even though the optical depth is increased. In addition to the analytical derivation of the formula, two practical formulas are proposed: an empirical formula of the spatial distribution of the OEF for the Gaussian upper state density profile and a linear formula of the OEF distribution for upper state profiles that are expressed as linear combinations. These formulas enable us to calculate the spatial distribution of the OEF for the multiple-Gaussian upper state profile without the need for time-consuming integral calculations.

Band offsets and band bending at heterovalent semiconductor interfaces

We present a comprehensive study of band offsets and band bending at heterovalent semiconductor heterointerfaces. A perfectly abrupt heterovalent interface is usually thermodynamically unstable, and atomic intermixing of materials with different numbers of valence electrons causes large variations in band offsets and local doping density, depending on the spatial arrangement of atoms at the interface. The studied prototypical II-VI/III-V semiconductor interfaces are $n$-doped ZnSe/GaAs (001) heterostructures with varied composition profiles close to the interface, which were realized by molecular-beam epitaxy with different amounts of Zn or Se predeposited on $n$-GaAs prior to $n$-ZnSe layer growth. The samples are characterized by temperature-dependent electrical transport across the interface, electrochemical capacitance-voltage profiling, Raman spectroscopy, and high-resolution x-ray diffraction. We find that the potential barrier in the conduction band at a Zn-rich $n$-ZnSe/$n$-GaAs interface is as high as 550 meV and it gradually decreases with Se predeposition down to about 70 meV. A large depletion region at the heterointerface, about 50 nm wide, is assigned to significant intermixing of acceptor-type atoms, resulting in an effective electron deficit of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }{\text{cm}}^{\ensuremath{-}2}$. The depletion width and the acceptor density around the interface are nearly independent from the growth start procedure. Se predeposition, however, partially shifts the depletion region at the heterointerface from GaAs into ZnSe, compared to Zn predeposition. The results are discussed on the basis of a band-bending model accounting for variable band offsets, interface state density and atomic interdiffusion profiles depending on growth start.

Stationary density profiles in the Levitated Dipole Experiment: toward fusion without tritium fuel

The Levitated Dipole Experiment (LDX) is used to study high-temperature plasma confined by the magnetic field produced by a high-current superconducting ring. Multiple-frequency electron cyclotron resonance heating (ECRH) heats and sustains plasma discharges for long, quasi-steady periods, and conditions of high plasma beta are reached by adjusting the rate of neutral fueling. When the superconducting ring is levitated by attraction to a coil located above the vacuum chamber, cross-field transport becomes the main loss channel for plasma particles and energy. We find operation with a levitated dipole always leads to centrally peaked density profiles, even when the plasma ionization source occurs near the plasma edge. In recent experiments, we also observe the normalized gradient, or shape, of the density profile to be ‘stationary’ while the ECRH heating power and gas fueling rates are strongly modulated. Theoretically, stationary profiles result in an energy confinement time (of the thermal plasma) that greatly exceeds the particle confinement time. This condition, along with high-beta plasma stability, is a necessary condition for utilizing advanced fuels in a fusion power source.

Effect of interface states on sub-threshold response of III–V MOSFETs, MOS HEMTs and tunnel FETs

The effect of interface states on the current–voltage characteristics in the sub-threshold region of three different types of III–V based transistor architectures has been studied using a drift–diffusion based numerical simulator. Experimentally extracted interface state density profile is included in the simulation to analyze their effect on the sub-threshold response of InGaAs based MOSFETs, MOS HEMTs and tunnel FETs. Based on the Fermi-level position at the oxide/semiconductor interface and the corresponding interface state density ( D it), the sub-threshold response for the three devices can vary, with tunnel FETs having the least sub-threshold degradation due to D it.

Electrical characterization and device characterization of ZnO microring shaped films by sol–gel method

Zinc oxide microrings formed nanoparticles were prepared on n-type silicon substrate by sol–gel method. The structure of ZnO film is confirmed by XRD analysis and ZnO film exhibits a polycrystalline grown with a hexagonal wurtzite-type. The optical band gap of the ZnO film deposited on silicon substrate was determined using the reflectance spectra by means of Kubelka-Munk formula and was found to be 3.22 eV. The structural properties of the ZnO film were investigated by atomic force microscopy. The AFM results indicate that the ZnO film is consisted of microrings with nanoparticles. A single phase of ZnO microring with outer diameter is ranging from 2.2 μm to 1.72 μm and inner diameters ranging from 125 nm to 470 nm was obtained. A Schottky diode having Au/n-type ZnO plus n-type silicon structure was fabricated. The current–voltage and impedance spectroscopy properties of the diode have been investigated. The barrier height ϕ b and ideality factor n values for the diode were found to be 0.80 eV and 2.01, respectively. The series resistance for the diode was calculated from the admittance behavior in accumulation region. The interface state density profile for the diode was obtained. The obtained results indicate that the electric parameters of the diode are affected by structural properties of ZnO film.

A Diffusive System Driven by a Battery or by a Smoothly Varying Field

We consider the steady state of a one dimensional diffusive system, such as the symmetric simple exclusion process (SSEP) on a ring, driven by a battery at the origin or by a smoothly varying field along the ring. The battery appears as the limiting case of a smoothly varying field, when the field becomes a delta function at the origin. We find that in the scaling limit, the long range pair correlation functions of the system driven by a battery turn out to be very different from the ones known in the steady state of the SSEP maintained out of equilibrium by contact with two reservoirs, even when the steady state density profiles are identical in both models.

BCS–BEC crossover in a trapped Fermi super-fluid using a density-functional equation

We derive a generalized time-dependent Galilean-invariant density-functional (DF) equation appropriate to study the stationary and non-stationary properties of a trapped Fermi super-fluid in the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover. This equation is equivalent to a quantum hydrodynamical equation for a Fermi super-fluid. The bulk chemical potential of this equation has the proper (model-independent) dependence on the Fermi–Fermi scattering length in the BCS and BEC limits. We apply this DF equation to the study of the stationary density profile and size of a cigar-shaped Fermi super-fluid of 6Li atoms, and the results are in good agreement with the experiment of Bartenstein et al in the BCS–BEC crossover. We also apply the DF equation to the study of axial and radial breathing oscillation and our results for these frequencies are in good agreement with experiments in the BCS–BEC crossover.

Asymmetric exclusion processes on [formula omitted]-input [formula omitted]-output junctions with parallel update

In this paper, we investigate totally asymmetric exclusion processes (TASEPs) on lattices with an m -input n -output junction in parallel update. A general theoretical solution for traffic dynamics of TASEPs with a junction is developed. More interestingly, m -input n -output junctions can be classified by a parameter, λ = m / n . The junctions with the same λ exhibit the same dynamic properties (e.g., phase diagrams, stationary currents, and density profiles). When the number of m and/or n changes, the low-density and high-density regions can be measured qualitatively and quantitatively. The phase diagram is obtained from a simple mean-field approximation and supported by computer simulations. Stationary current and density profiles are calculated which show good agreement with computer simulations.

Theory of charged impurity scattering in two-dimensional graphene

We review the physics of charged impurities in the vicinity of graphene. The long-range nature of Coulomb impurities affects both the nature of the ground state density profile and graphene’s transport properties. We discuss the screening of a single Coulomb impurity and the ensemble averaged density profile of graphene in the presence of many randomly distributed impurities. Finally, we discuss graphene’s transport properties due to scattering off charged impurities both at low and high carrier density.

The influence of series resistance and interface states on intersecting behavior of I–V characteristics of Al/TiO2/p-Si (MIS) structures at low temperatures

In this study, we have investigated the intersection behavior of the forward bias current–voltage (I–V) characteristics of the Al/TiO2/p-Si (MIS) structures in the temperature range of 100–300 K. The intersection behavior of the I–V curves appears as an abnormality when compared to the conventional behavior of ideal Schottky diodes and MIS structures. This behavior is attributed to the lack of free charge at a low temperature and in the temperature region, where there is no carrier freezing out, which is non-negligible at low temperatures, in particular. The values calculated from the temperature-dependent forward bias I–V data exhibit unusual behavior, where the zero-bias barrier height (ϕb0) and the series resistance (Rs) increase with increasing temperature. Such temperature dependence of ϕb0 and Rs is in obvious disagreement with the reported negative temperature coefficient. An apparent increase in the ideality factor (n) and a decrease in the ϕb0 at low temperatures can be attributed to the inhomogeneities of the barrier height, the thickness of the insulator layer and non-uniformity of the interfacial charges. The temperature dependence of the experimental I–V data of the Al/TiO2/p-Si (MIS) structures has revealed the existence of a double Gaussian distribution with mean barrier height values () of 1.108 eV and 0.649 eV, and standard deviations (σs) of 0.137 V and 0.077 V, respectively. Furthermore, the temperature dependence of the energy distribution of interface state density (Nss) profiles has been determined from forward bias I–V measurements by taking into account the bias dependence of the effective barrier height (ϕe) and n. The fact that the values of Nss increase with increasing temperature has been attributed to the molecular restructuring and reordering at the metal/semiconductor interface under the effect of temperature.

Beyond the dynamic density functional theory for steady currents: Application to driven colloidal particles in a channel

Motivated by recent studies on the dynamics of colloidal solutions in narrow channels, we consider the steady state properties of an assembly of noninteracting particles subject to the action of a traveling potential moving at a constant speed, while the solvent is modeled by a heat bath at rest in the laboratory frame. Here, since the description we propose takes into account the inertia of the colloidal particles, it is necessary to consider the evolution of both positions and momenta and study the governing equation for the one-particle phase-space distribution. First, we derive the asymptotic form of its solutions as an expansion in Hermite polynomials and their generic properties, such as the force and energy balance, and then we particularize our study to the case of an inverted parabolic potential barrier. We numerically obtain the steady state density and temperature profile and show that the expansion is rapidly convergent for large values of the friction constant and small drifting velocities. On the one hand, the present results confirm the previous studies based on the dynamic density functional theory (DDFT): On the other hand, when the friction constant is large, it display effects such as the presence of a wake behind the barrier and a strong inhomogeneity in the temperature field which are beyond the DDFT description.

Numerical study of one-dimensional and interacting Bose–Einstein condensates in a random potential

We present a detailed numerical study of the effect of a disordered potential on a confined one-dimensional Bose–Einstein condensate, in the framework of a mean-field description, using a highly efficient and fast converging numerical scheme. For repulsive interactions, we consider the Thomas–Fermi and Gaussian limits and for attractive interactions the behaviour of soliton solutions. We find that the average spatial extension of the stationary density profile decreases with an increasing disorder strength both for repulsive and attractive interactions among bosons. In the Thomas–Fermi limit, a strong localization of the bosons is obtained in momentum space around the state k = 0. The time-dependent density differs considerably in the cases we have considered. For attractive and disordered Bose–Einstein condensates, we show evidence of a bright soliton with an overall unchanged shape, but a disorder-dependent width. For weak disorder, the soliton is delocalized and for stronger disorder, it bounces back and forth between high potential barriers.

Bimodality and hysteresis in systems driven by confined Lévy flights

We demonstrate the occurrence of bimodality and dynamical hysteresis in a system describing an overdamped quartic oscillator perturbed by additive white and asymmetric Lévy noise. Investigated estimators of the stationary probability density profiles display not only a turnover from unimodal to bimodal character but also a change in a relative stability of stationary states that depends on the asymmetry parameter of the underlying noise term. When varying the asymmetry parameter cyclically, the system exhibits a hysteresis in the occupation of a chosen stationary state.

Weakly coupled, antiparallel, totally asymmetric simple exclusion processes

We study a system composed of two parallel totally asymmetric simple exclusion processes with open boundaries, where the particles move in the two lanes in opposite directions and are allowed to jump to the other lane with rates inversely proportional to the length of the system. Stationary density profiles are determined and the phase diagram of the model is constructed in the hydrodynamic limit, by solving the differential equations describing the steady state of the system, analytically for vanishing total current and numerically for nonzero total current. The system possesses phases with a localized shock in the density profile in one of the lanes, similarly to exclusion processes endowed with nonconserving kinetics in the bulk. Besides, the system undergoes a discontinuous phase transition, where coherently moving delocalized shocks emerge in both lanes and the fluctuation of the global density is described by an unbiased random walk. This phenomenon is analogous to the phase coexistence observed at the coexistence line of the totally asymmetric simple exclusion process, however, as a consequence of the interaction between lanes, the density profiles are deformed and in the case of asymmetric lane change, the motion of the shocks is confined to a limited domain.

The barrier height distribution in identically prepared Al/p-Si Schottky diodes with the native interfacial insulator layer (SiO 2)

The Al/p-Si Schottky diodes (33 dots) with the native interfacial insulator layer (SiO 2) were fabricated on the same quarter Si wafer. The Schottky barrier height (SBH), ideality factor ( n), interface state densities ( N ss) and series resistance ( R s) of these diodes have been calculated from their experimental forward bias current–voltage ( I– V), reverse bias capacitance–voltage ( C– V) and conductance–voltage ( G/ ω– V) measurements. Even though they are identically performed on the same quarter Si wafer, the calculated values of SBH have ranged from 0.680 to 0.736 eV, and ideality factor n from 1.62 to 2.87, and interface state densities N ss from 0.395×10 13 to 1.2×10 13 eV −1 cm −2 and series resistance R s from 623 to 4900 Ω. It was found that the values of barrier height Φ B obtained from C– V characteristics is larger than that of the value from I– V characteristics. The energy distribution of surface state density profiles for the selected six samples Al/p-Si Schottky diodes was determined from forward bias I– V characteristics by taking the bias dependence of the effective barrier height into account at room temperature. The experimental values of SBHs distributions obtained from the I– V and C −2– V characteristics have been fitted by a Gaussian function, and their mean values of SBHs have been calculated to be 0.708 and 0.810 eV, respectively. Experimental results show that the interface states at a native insulator layer between metal and semiconductor play an important role in the value of the SBH, ideality factor, series resistance and the other main electrical parameters of Schottky diodes.

Electrical transport characteristics of Sn/p-Si schottky contacts revealed from I– V– T and C– V– T measurements

The current–voltage ( I– V) and capacitance–voltage ( C– V) characteristics of metal–semiconductor (Sn/p-Si) Schottky contacts were measured in the temperature range 150–400 K. The effect of the temperature on the series resistances R S, ideality factors n, the barrier height Φ b and interface state density N SS obtained from the I– V and C– V characteristics were investigated. The n, Φ b, R S, and N SS values were seen to be strongly temperature dependent. The ideality factors, series resistances and interface state densities decreased with increasing temperature for all diodes and the values of n, R S, and N SS obtained from I– V and C– V measurements were found in the ranges of 2.024–1.108, 2.083–1.121; 79.508–33.397 Ω; and 2.14×10 13–0.216×10 13 cm 2 eV −1, 2.277×10 13–0.254×10 13 cm 2 eV −1, respectively. The temperature dependence of energy distribution of interface state density ( N SS) profiles has been determined from I– V measurements by taking into account the bias dependence of the effective barrier height and ideality factor.

Current transport mechanism in Al/Si 3N 4/p-Si (MIS) Schottky barrier diodes at low temperatures

The current–voltage ( I– V) and capacitance–voltage ( C– V) characteristics of metal–insulator–semiconductor (Al/Si 3N 4/p-Si) Schottky barrier diodes (SBDs) were measured in the temperature range of 80–300 K. By using the thermionic emission (TE) theory, the zero-bias barrier height Φ B0 calculated from I– V characteristics was found to increase with increasing temperature. Such temperature dependence is an obvious disagreement with the negative temperature coefficient of the barrier height calculated from C– V characteristics. Also, the ideality factor decreases with increasing temperature, and especially the activation energy plot is nonlinear at low temperatures. Such behaviour is attributed to Schottky barrier inhomogeneties by assuming a Gaussian distribution of barrier heights (BHs) at interface. We attempted to draw a Φ B0 versus q/2 kT plot to obtain evidence of a Gaussian distribution of the BHs, and the values of Φ Bo = 0.826 eV and α o = 0.091 V for the mean barrier height and standard deviation at zero-bias, respectively, have been obtained from this plot. Thus, a modified ln( I o/ T 2) − q 2 σ o 2/2( kT) 2 versus q/ kT plot gives Φ B0 and Richardson constant A * as 0.820 eV and 30.273 A/cm 2 K 2, respectively, without using the temperature coefficient of the barrier height. This value of the Richardson constant 30.273 A/cm 2 K 2 is very close to the theoretical value of 32 A/cm 2 K 2 for p-type Si. Hence, it has been concluded that the temperature dependence of the forward I– V characteristics of the Al/Si 3N 4/p-Si Schottky barrier diodes can be successfully explained on the basis of TE mechanism with a Gaussian distribution of the barrier heights. In addition, the temperature dependence of energy distribution of interface state density ( N SS) profiles was determined from the forward I– V measurements by taking into account the bias dependence of the effective barrier height and ideality factor.