Electron transport in semiconductors in the presence of impact ionization

The development of impact ionization in semiconductors has been considered. A transport equation for the electron distribution function in the presence of impact ionization has been derived. It has been found that the collison integral of this equation is nonlinear with respect to the distribution function. The relation between the solutions of this equation and the usual Boltzmann equation have been determined. A Monte Carlo method for numerical calculations in the presence of impact ionization has been developed. The results of numerical calculations carried out using a simplified model of indium antimonide are presented.     

Increase in the accuracy of approximating the profile of the erosion zone in planar magnetrons

It has been shown that the use of the survival function of the Weibull distribution shifted along the ordinate axis allows one to increase the accuracy of the approximation of the normalized profile of an erosion zone in the area from the axis to the maximum sputtering region compared with the previously suggested distribution function of the extremum values. The survival function of the Weibull distribution is used in the area from the maximum to the outer boundary of an erosion zone. The major advantage of using the new approximation is observed for magnetrons with a large central nonsputtered spot and for magnetrons with substantial sputtering in the paraxial zone.

     

Third adiabatic invariant and the collisionless distribution function of particles in a tokamak

It has been shown that the distribution function of an ensemble of particles with a given energy in a collisionless regime in a tokamak is formed as a function primarily of the third adiabatic invariant, particularly in the near-axis region. In the periphery of the plasma column, the contribution of the toroidal component of the canonical momentum/longitudinal adiabatic invariant to the distribution function becomes noticeable. The coordinate dependence of the ensemble distribution function in the velocity space is determined predominantly by the trajectories of charged particles.     

The dependence of the electron distribution function on the discharge current in Ne and Ne-He discharge

The dependence of the shape of the electron distribution function on discharge current has been found in Ne and Ne-He low-pressure discharge by means of experimental set-up which makes possible direct record of the electron distribution function.The authors desire to acknowledge the support offered them by Professor Dr. V. Kunzl.     

On the electron equilibrium distribution function in the kinetic theory of electron cyclotron maser

The problems concerning the specification of electron equilibrium distribution function for the kinetic theory of ECRM are investigated in this paper. After detailed analysis of the published equilibium distribution functions, several conclusion have been achieved.     

The crossover from classical to quantum regime in the problem of the decay of the metastable state

The probability of the decay of the metastable state has been found as a function of viscosity and temperature. At low temperatures, a classical overbarrier transition changes to the quantum tunneling. At low viscosity in classical and transitive semiquantum region of temperatures a depopulation of the distribution function is significant. The distribution function is shown to satisfy the integral kinetic equation, the kernel of which equals the transition probability. The probability of transitions, induced by the red noise, with the frequency comparable to the transition frequency, is found.     

Angular distribution of magnetic particles in particulate tapes

The distribution functions of magnetic recording particulate tapes were studied by the measurements of magnetoremanence. For fitting distribution function, cosines series function such as Legendre polynomial has been popularly used, however, Gaussian function is found to be preferable for sharp or wide distributions. Audio metal tape has the sharpest distribution function among the seven tapes.     

Investigation of cubic non-linearity-driven electrostatic structures in the presence of double spectral index distribution function

In this article, modified Korteweg-de Vries equation (which involves cubic non-linearity) was derived to study non-linear ion acoustic waves in a plasma in which electrons follow the double spectral index distribution function. The double spectral index distribution successfully apes the distribution functions that have been frequently observed in space plasmas. The spectral index r moulds the distribution function at low energy and by increasing its value, flatness of the distribution enhances. The spectral index r can also have negative values due to which distribution becomes spiky at low energies. The index q , on the other hand, controls the shape of the tail of distribution function. It has been shown that propagation of the solitary structures gets significantly altered by the choice of the double spectral indices, namely, r and q . A comparison was also made, using the parameters of the auroral zone, between the quadratic and cubic non-linearities-driven non-linear structures and it was shown that the solitary structures form on a much shorter scale for cubic non-linearity compared to their quadratic counterpart.     

On the acoustic wave attenuation in a turbulent medium

The equation for the mean acoustic field has been obtained for a random turbulent medium using the Green function approach. The correlation function was described by the Karman distribution with the index n=2 approximately≃11/6. Applying Bourret's approximation, the exact expression for the mass operator has been calculated analytically. The frequency dependence of the scattering coefficient of the mean field has been derived. Conditions of Cherenkov radiation are discussed.     

Electronic band structure and distribution of excited electrons in the conduction band of anatase doped with boron, nitrogen, and carbon

A method for calculating the distribution of excited electrons in the conduction band of semiconductors has been proposed. This method takes into account both the excitation of electrons by means of an external light source and the transitions to the bottom of the conduction band due to the electron-phonon interaction. The interaction of electrons with the light field has been calculated from first principles in the dipole approximation using the linear muffin-tin orbital method. The electron-phonon interaction has been calculated in terms of the density functional perturbation theory. The method has been applied to the calculation of the quasi-steady-state distribution function of excited electrons in anatase doped with boron, nitrogen, and carbon. The correlations of the distribution function with the photocatalytic activity of doped anatase have been discussed.     

Intensity distribution of electromagnetic radiation in one-dimensional superstructures

Distribution function of density of particles in one-dimensional sample with weak disorder has been found using Berezinsky diagram technique. For open systems, when a particle having reached the end of the sample can leave it, logarithmically normal distribution for density of particles has been obtained. It has been shown that the function obtaineddescribes radiation intensity distribution in weakly disordered superlattice.     

Electronic method for direct display of the electron energy distributions in plasma

Direct display of the electron energy distribution function has been performed with the aid of the analog computer MEDA 41 TA.     

Combined energy–power action on a source in the constant Mach number regime with the given external force

Combined action on a source that flows into a submerged area or vacuum in the constant Mach number regime has been studied. The action by an external force has been defined with a constant distribution function (the force is given per unit volume) and with a distribution function proportional to the gas density (the force is given per unit mass). The investigations have been carried out for cylindrical and spherical sources. Similarity and differences, advantages and drawbacks of the above-mentioned cases and variants have been analyzed. It has been shown that the enthalpy increases significantly in subsonic flow (for the Mach number smaller than unity) by several times in the cylindrical source and by more than an order of magnitude in the spherical source. The total enthalpy increment increases with the length of the action zone or with the coordinate of the closing section.     

Approximation of the erosion zone profile in planar magnetrons with a disk cathode

We have proposed a universal approximation of the normalized erosion zone profile of planar magnetrons with a disk cathode by a composite function that includes the probability density function for the minimal distribution of extremal values for the region from the center of the disk cathode to the maximum of the erosion zone and the survival Weibull distribution function (from the maximum to the outer boundary of the sputtering zone). The accuracy of the approximation has been verified for six magnetrons differing in the cathode size or in the design of the magnetic systems. In all cases, good agreement has been observed between the approximation and experimentally measured values. The results reported here can be used to analyze processes that occur on the cathode during sputtering and to refine the calculations of coating profiles.     

Dielectric losses in statistical mixtures

The specific features of the dielectric spectra of statistical mixtures in the form of heterogeneous systems with spherical particles chaotically arranged in the space have been investigated. The distribution function of relaxation times f(τ) has been restored. It has been established that the relaxation times are continuously distributed within a wide interval [τ₁, τ₂]. Different methods for broadening the relaxation time distribution interval and approximating the relaxation time distribution function f(τ) have been analyzed. It has been demonstrated that f(τ) is a nonmonotonic function with two maxima at the boundaries and a minimum in the vicinity of the midpoint of the interval [τ₁, τ₂]. These features of the relaxation time distribution function are responsible for the large difference between the average relaxation frequencies of the permittivity and the dielectric loss (electrical conductivity).     

Transition from a state with a certain momentum into a state with a certain parameter of spinless particle escape in the external field

A distribution function on the parameter of escape of particle B with the amplitude of process A → B in the external stationary field is investigated in this work. This distribution function is directly related to the form factor of the external-field source. By way of illustration consideration has been given to a hydrogen-like atom. It is shown that the distribution into the forward hemisphere comprises information on the spatial structure of an electron cloud, while the distribution into the backward hemisphere reproduces a spatial structure in the vicinity of a nucleus.     

19F+93Nb耗散反应的相互作用时间

测量了¹⁹F+⁹³Nb耗散反应产物的激发函数与角分布.从角分布的斜率提取的该反应系统的平均寿命在对称性较大的入射系统中反映了系统中耗散产物的特征时间;通过能量自关联函数方法从激发函数提取的反应时间不论在对称的还是在非对称的入射系统中都反映了耗散产物的特征时间.能量自关联函数还可以给出双核系统的转动角速度以及表征转动阻尼的退相干宽度,更好地描述双核系统随时间的整个演化过程.     

Nonlinear distribution functions for the Vlasov-Poisson system

The nonlinear distribution function introduced by Allis has been used to investigate the stability of the solution of Vlasov-Poisson’s equations. The ‘average’ Lagrangian is calculated on the basis of this distribution function, and the ‘average’ variational principle of Witham is applied to discuss modulational stability. It is found that the distribution function of Allis exactly gives rise to the Lighthill’s stability condition of non-linear waves.     

Energy distribution function in counter beam instability

A study has been made of the energy distribution function related to the instability in counter electron beams with different velocities. Two or more peaks were observed in the distribution function when the oscillation set up standing waves in the system.     

On the acoustic wave attenuation in a turbulent medium

Abstract

The equation for the mean acoustic field has been obtained for a random turbulent medium using the Green function approach. The correlation function was described by the Karman distribution with the index n=2 approximately?11/6. Applying Bourret's approximation, the exact expression for the mass operator has been calculated analytically. The frequency dependence of the scattering coefficient of the mean field has been derived. Conditions of Cherenkov radiation are discussed.