Nonparabolic multivalley balance-equation approach to impact ionization: Application to wurtzite GaN

Extended nonparabolic multivalley balance equations including impact ionization (II) process are presented and are applied to study electron transport and impact ionization in wurtzite-phase GaN with a , L-M, and conduction band structure at high electric field up to 1000kV/cm. Hot-electron transport properties and impact ionization coefficient are calculated taking account of the scatterings from ionized impurity, polar optical, deformation potential, and intervalley interactions. It is shown that, for wurtzite GaN when the electric field approximately equals 530kV/cm, the II process begins to contribute to electron transport and results in an increase of the electron velocity and a decrease of the electron temperature, in comparison with the case without the II process. Similar calculations for GaAs are also carried out and quantitative agreement is obtained between the calculated II coefficients by this present approach and the experimental data. Relative to GaAs, GaN has a higher threshold electric field for II and a smaller II coefficient. Received: 27 April 1998 / Revised: 17 July 1998 / Accepted: 13 August 1998     

流注放电低温等离子体中电子输运系数计算的蒙特卡罗模型

流体或者粒子-流体混合数值仿真是研究流注放电基本物理机制的常用手段,而精确的电子输运系数是保证其仿真正确性的必要前提.鉴于现有电子输运系数求解工具存在一定缺陷,本文开发了采用蒙特卡罗方法求解低温等离子体中电子输运系数的仿真工具,测试表明其准确性和精确度均较高.研究了氮氧气体混合比及大气压下三体碰撞吸附对电子输运系数的影响.氮气中流注放电仿真表明,流体仿真中采用本模型改进后的电子输运系数可显著改善流注通道内部的等离子体参数分布.     

Monte Carlo simulation of mini TEPC microdosimetric spectra: Influence of low energy electrons

In the past few years, miniaturized tissue-equivalent gas detectors (mini TEPCs) have been developed for application of microdosimetry in radiotherapy. These mini-TEPCs are characterised by millimetric dimensions. They are equipped neither with an internal calibration source nor with electric field tubes, which would properly define the sensitive volume hence the simulated site size. In spite of these lacks, mini TEPCs working in gas flow conditions have proven to be precise and reliable detectors. However, for future therapeutic plans including microdosimetric data, consistency between experimental and calculated data is important. Existing general-purpose Monte Carlo codes have proven to be very useful to calculate the energy deposition due to ionization in macroscopic targets, even in various complex radiation fields. However, theoretical models implemented in these codes for simulating electron transport and straggling are valid only for energies above a few keV. This restricts their applicability for simulating radiation transport at a micrometric level, where low-energy electrons play a dominant role. In this work, we calculate frequency distributions of deposited energy in a mini TEPC (with sizes equivalent to 1 and 2 μm) due to photons using the Monte Carlo code FLUKA. Comparisons between simulated and experimental data show a rather good agreement. Differences due to different FLUKA settings are discussed.     

Observation of the transition from impact-ionization-dominated to field-ionization-dominated impurity breakdown in silicon

It is shown that by measuring the genration rate vs stepped voltage amplitude it is possible to separate the impurity impact ionization from the pure field ionization. Also, the phosphorus impact ionization coefficient in silicon at high electric fields was measured and compared with the Monte Carlo calculations.     

Pressure ionization in laser-fusion target simulation

Accurate simulation of high density target implosion requires material properties (ionization, pressure, energy, opacity and transport coefficients) at densities where bound electrons are significantly perturbed by neighboring atoms. In modern laser-fusion simulation codes, this data is supplied by tables and/or calculated from a Stromgren model for ionization equilibrium. Improvements have been made in the Stromgren average-atom model which aim at assuring thermodynamic consistency and obtaining better agreement with more elaborate calculations. Arbitrary degeneracy is allowed for the free electrons. Consistent Coulomb contributions to pressure and continuum lowering are obtained. A new pressure ionization scheme merges bound electrons into the continuum as a smooth function of density and the corresponding contribution to pressure is calculated. Results are shown for aluminum.     

Multicomponent transport algorithms for partially ionized mixtures

We investigate iterative methods for solving linear systems arising from the kinetic theory of gases and providing multicomponent transport coefficients of partially ionized plasmas. We consider the situations of weak and strong magnetic fields as well as electron temperature nonequilibrium and the linear systems are investigated in their natural constrained singular symmetric form. Stationary iterative techniques are considered with new more singular formulations of the transport linear systems as well as orthogonal residuals algorithms. The new formulations are derived by considering generalized inverses with nullspaces of increasing dimension. Numerical tests are performed with high temperature air and iterative techniques lead to fast and accurate evaluation of the transport coefficients for all ionization levels and magnetic field intensities.     

Impact ionization and electroluminescence in single barrier tunnelling structures

At high electric fields, hot electrons injected into the undoped regions of n-i-n structures can give rise to impact ionization of the host lattice and electron-hole pair production. The holes created by impact ionization recombine with majority carrier electrons, leading to electroluminescence (EL) from the device at fields in excess of 10⁵V/cm. In the present work, we show that the study of such EL in GaAs/AlGaAs/GaAs single barrier tunnelling structures provides a simple and effective quantitative method to determine impact ionization coefficients in GaAs. Structures with undoped regions of length 100, 150 and 200nm are shown to give very similar results for the impact ionization coefficient. The values obtained for the impact ionization coefficient are shown to be consistent with those obtained by carrier multiplication methods.     

Prediction of electron and ion concentrations in low-pressure premixed acetylene and ethylene flames

Flame stabilisation and extinction in a number of different flows can be affected by application of electric fields. Electrons and ions are present in flames, and because of charge separation, weak electric fields can also be generated even when there is no externally applied electric field. In this work, a numerical model incorporating ambipolar diffusion and plasma kinetics has been developed to predict gas temperature, species, and ion and electron concentrations in laminar premixed flames without applied electric fields. This goal has been achieved by combining the existing CHEMKIN-based PREMIX code with a recently developed methodology for the solution of electron temperature and transport properties that uses a plasma kinetics model and a Boltzmann equation solver. A chemical reaction set has been compiled from seven sources and includes chemiionisation, ion-molecule, and dissociative–recombination reactions. The numerical results from the modified PREMIX code (such as peak number densities of positive ions) display good agreement with previously published experimental data for fuel-rich, non-sooting, low-pressure acetylene and ethylene flames without applied electric fields.     

Electron lucky-drift impact ionization coefficients of ZnS : Mn

Fit of the experimental data of ZnS : Mn by a modified lucky-drift formula has been performed using the least square algorithm. The fit agrees well with the experimental data only at high field. The best fitting parameters at high field are the mean free path of order 102.74 Å and Keldysh factor,p ₀ = 0.0138. A generalized Keldysh formula has been used, due to introduction of a soft threshold factor. The soft lucky-drift theory can also be used to calculate the impact ionization coefficients of high electron energy of ZnS : Mn without losing its physical significance compared to full band-structure Monte Carlo calculation with a remarkably reduced amount of computer resources. The curvature on semi-log plot of experimental impact ionization coefficient against the inverse of electric field is different from what is observed for other materials at low electric fields due to impact ionization of deep level impurities.     

Nonlocal analysis to study of the impact ionization and avalanche characteristics of deep submicron Si devices

In this paper, we have presented electric field dependence of the electron and hole impact ionization coefficients and threshold energies in submicron Si diodes with intrinsic region thicknesses down to 31 nm. To do so, we have used a nonlocal analysis, in order to take the effects of arbitrary distribution of ionization events in both space and time domains and the effects of enhancement in the average speed of those carriers which ionize early in their trajectories as well as nonuniform electric fields in the multiplication region and its surrounding ambient, carrier’s dead space history and its spatial ionization rate, into consideration all in one comprehensive analytic model.     

Fractional Brownian Motions and Enhanced Diffusion in a Unidirectional Wave-Like Turbulence

We study transport in random undirectional wave-like velocity fields with nonlinear dispersion relations. For this simple model, we have several interesting findings: (1) In the absence of molecular diffusion the entire family of fractional Brownian motions (FBMs), persistent or anti-persistent, can arise in the scaling limit. (2) The infrared cutoff may alter the scaling limit depending on whether the cutoff exceeds certain critical value or not. (3) Small, but nonzero, molecular diffusion can drastically change the scaling limit. As a result, some regimes stay intact; some (persistent) FBM regimes become non-Gaussian and some other FBM regimes become Brownian motions with enhanced diffusion coefficients. Moreover, in the particular regime where the scaling limit is a Brownian motion in the absence of molecular diffusion, the vanishing molecular diffusion limit of the enhanced diffusion coefficient is strictly larger than the diffusion coefficient with zero molecular diffusion. This is the first such example that we are aware of to demonstrate rigorously a nonperturbative effect of vanishing molecular diffusion on turbulent diffusion coefficient.     

Effect of electric field on diffusion in disordered materials

The effect of electric field on diffusion of charge carriers in disordered materials is studied by Monte Carlo computer simulations and analytical calculations. It is shown how an electric field enhances the diffusion coefficient in the hopping transport mode. The enhancement essentially depends on the temperature and on the energy scale of the disorder potential. It is shown that in one‐dimensional hopping the diffusion coefficient depends linearly on the electric field, while for hopping in three dimensions the dependence is quadratic.     

Electron swarm coefficients in 1,1,1,2 tetrafluoroethane (R134a) and its mixtures with Ar

Using a pulsed Townsend technique, we have measured the drift velocity, the longitudinal diffusion coefficient and the effective ionisation coefficient of electrons in R134a and R134a-Ar over a wide range of the density-reduced electric field intensity, E/N. Regarding the measurement of the electron drift velocities and of the effective ionization coefficients, we have covered a wider range than that hitherto achieved for pure R134a. Both the electron drift velocity and the effective ionisation coefficient have been found in very good agreement with those published in the literature, covering a shorter range of E/N. On the other hand, the swarm coefficients on R134a-Ar are, to the best of our knowledge, the first to be published. It is hoped that these data will be of interest for the test/derivation of electron collision cross sections for this important hydrofluorocarbon gas, which is nowadays of great use in gaseous detectors.     

A Survey of the Electron and Ion Transport Properties of SF6

A compilation of the available data on some of the basic transport properties of sulfur hexafluoride (SF6) is presented. The properties considered are a) electron ionization, attachment, detachment and diffusion coefficients, and electron drift velocity; b) positive and negative ion mobilities, negative ion diffusion, and ion-ion recombination coefficients; and c) secondary ionization coefficients. Approximate analytical representations of the data are also given.     

The electrical breakdown of gases in the presence of crossed electric and magnetic fields

The breakdown characteristics of a gas in the presence of crossed electric and magnetic fields are discussed in terms of the Townsend ionization coefficients. The “equivalent pressure” concept is used to assess the effect of a transverse magnetic field on the first Townsend coefficient and the objections which have been raised to the application of this approach to breakdown potentials are shown to be removed by a consideration of the dependence of the second Townsend coefficient upon electric and magnetic field strengths.     

First-principle calculation for the high-temperature diffusion coefficients of small pairs: the H–Ar Case

Argon has been widely used as a diluent for high-temperature reacting flow experiments. Numerical simulation of such process requires accurate diffusion coefficients for the H–Ar pair. All available potential energy functions for the H–Ar system have been empirically extrapolated in the repulsive region and are probably not reliable for prediction of H–Ar binary diffusion coefficient at high temperatures. We perform calculations using the restricted coupled cluster theory with single and double excitation (plus triple corrections) [RCCSD(T)] and suitable basis sets to obtain accurate potential energies. The calculated potential energy function is corrected for basis set superposition error and is validated against molecular beam scattering data. Comparisons with previous literature potential functions are also made. Using the Chapman–Enskog theory we carried out first-principle calculation of high-temperature diffusion coefficients by direct numerical integration of the collision integrals using the RCCSD(T) potential function. The computed diffusion coefficients are validated against available experimental data. Comparisons are also made with results obtained from transport compilations and packages commonly used in combustion simulation.     

Single-parameter expression for ions reflection from surfaces

Based on a detailed analysis of the Boltzmann equation for ion transport in solids, it has been shown that for low-energy ions incident on a heavy element target the distribution function of the ions can be determined by one single parameter, called the scaled transport cross-section, which was defined earlier [1]. This means that the transport quantities of different ion-target-energy combinations should be similar only when their scaled transport cross-section is the same. To test this significant conclusion, we undertook a set of systematic and extensive calculations of reflection coefficients using the improved bipartition model of ion transport. The systematic calculations include 3410 ion-target-energy combinations, namely H, D, T, He, Li, B, C, N, O, Ne ions with energy ranges from 10 eV to 1 MeV normally incident to C, Al, Cu, Mo, Ag, W, Au, Pb, U targets. The only restrictions isM ₁/M ₂<1/6. The calculations verify that particle and energy reflection coefficients present an excellent one-to-one correspondence to the scaled transport cross-section. Furthermore, based on the calculations, universal expressions for both particle reflection coefficients and energy reflection coefficients for normal ion incidence have been obtained by fitting the numerical data. By comparing the results calculated by the universal expressions with experimental and Monte Carlo data, it is shown that the expression can describe reflection coefficients well.     

Transport Coefficients for Inelastic Maxwell Mixtures

The Boltzmann equation for inelastic Maxwell models (IMM) is used to determine the Navier–Stokes transport coefficients of a granular binary mixture in d-dimensions. The Chapman–Enskog method is applied to solve the Boltzmann equation for states near the (local) homogeneous cooling state. The mass, heat, and momentum fluxes are obtained to first order in the spatial gradients of the hydrodynamic fields, and the corresponding transport coefficients are identified. There are seven relevant transport coefficients: the mutual diffusion, the pressure diffusion, the thermal diffusion, the shear viscosity, the Dufour coefficient, the pressure energy coefficient, and the thermal conductivity. All these coefficients are exactly obtained in terms of the coefficients of restitution and the ratios of mass, concentration, and particle sizes. The results are compared with known transport coefficients of inelastic hard spheres (IHS) obtained analytically in the leading Sonine approximation and by means of Monte Carlo simulations. The comparison shows a reasonably good agreement between both interaction models for not too strong dissipation, especially in the case of the transport coefficients associated with the mass flux     

Investigation of the Soret effect in binary liquid mixtures by thermal-diffusion-forced Rayleigh scattering (contribution to the benchmark test)

Within the framework of an international benchmark test we have performed measurements of the transport coefficients S T (Soret coefficient), D (mutual diffusion coefficient) and D T (thermal diffusion coefficient) on the three binary organic liquid mixtures 1,2,3,4-tetrahydronaphthalene- n -dodecane, 1,2,3,4-tetra- hydronaphthalene-isobutylbenzene and isobutylbenzene- n -dodecane with the weight fraction c = 0.5 at T = 298.15 K by means of thermal-diffusion-forced Rayleigh scattering (TDFRS) for benchmarking purposes. Our results for the coefficients are in good agreement with those obtained by annular and parallelepipedic thermogravitational columns and by other benchmark tests which also apply TDFRS measurements.     

Diffusion coefficient distribution from NMR-DOSY experiments using Hopfield neural network

Diffusion ordered spectroscopy (DOSY) is a powerful two-dimensional NMR method to study molecular translation in various systems. The diffusion coefficients are usually retrieved, at each frequency, from a fit procedure on the experimental data, considering a unique coefficient for each molecule or mixture. However, the fit can be improved if one regards the decaying curve as a multiexponential function and the diffusion coefficient as a distribution. This work presents a computer code based on the Hopfield neural network to invert the data. One small-molecule binary mixture with close diffusion coefficients is treated with this approach, demonstrating the effectiveness of the method.