Nonequilibrium Electron Distribution Function Research Articles

Nonequilibrium electron distribution functions in a semiconductor plasma irradiated with fast ions

A kinetic equation for the electrons scattered by acoustic phonons in a solid is derived, and relationships between power-law asymptotic solutions and the particle and energy fluxes in phase space are established. The dependence of the nonextensivity parameter on the intensity of the particle flow in phase space is determined for a nonequilibrium solid-state plasma with sources and sinks. The formation of a steady-state nonequilibrium electron distribution function in a semiconductor with a source and a sink in phase space is numerically simulated using the Landau and Fokker-Planck collision integrals. The nonequilibrium electron distributions formed in the solid-state plasmas of semiconductors and of a Sb/Cs cathode are studied experimentally. It is shown that, within the electron energy range of 5–100 eV, the electron distribution functions decrease with energy according to a power law.

Resonant three-wave interaction in the presence of suprathermal electron fluxes

Abstract. A theoretical and numerical model is presented which describes the nonlinear interaction of lower hybrid waves with a non-equilibrium electron distribution function in a magnetized plasma. The paper presents some relevant examples of numerical simulations which show the nonlinear evolution of a set of three waves interacting at various resonance velocities with a flux of electrons presenting some anisotropy in the parallel velocity distribution (suprathermal tail); in particular, the case when the interactions between the waves are neglected (for sufficiently small waves' amplitudes) is compared to the case when the three waves follow a resonant decay process. A competition between excitation (due to the fan instability with tail electrons or to the bump-in-tail instability at the Landau resonances) and damping processes (involving bulk electrons at the Landau resonances) takes place for each wave, depending on the strength of the wave-wave coupling, on the linear growth rates of the waves and on the modifications of the particles' distribution resulting from the linear and nonlinear wave-particle interactions. It is shown that the energy carried by the suprathermal electron tail is more effectively transfered to lower energy electrons in the presence of wave-wave interactions.

Interaction of suprathermal electron fluxes with lower hybrid waves

Several in situ measurements performed in the terrestrial magnetosphere and in the solar wind have evidenced the simultaneous presence of whistlers or lower hybrid waves with suprathermal fluxes or beams of electrons. The so-called fan instability, which can be driven by an anisotropy of the energetic electron velocity distribution along the ambient magnetic field, can play an essential role in space plasmas where energetic electron fluxes are ubiquitous. By destabilizing waves at the anomalous cyclotron resonance, this instability can modify drastically the shape of the parallel velocity distribution and give rise to bumps in the tail. This paper presents a new theoretical model which allows one to describe the nonlinear interaction of a packet of lower hybrid waves with a nonequilibrium electron distribution function. This Hamiltonian self-consistent model, which is based on a semianalytical approach, provides an efficient and original tool to point out new physical features, especially in what concerns the nonlinear stage of the fan instability and its implications for space physics.

Electron-phonon drag in degenerate conductors in a magnetic field

Mutual drag of electrons and phonons in degenerate conductors in classical magnetic fields is considered. It is shown that the coupled kinetic equations for nonequilibrium electron and phonon distribution functions can be transformed into a system of Volterra’s inhomogeneous integral equations. A solution is found to the system of integral equations with inclusion of all terms yielding contributions linear in the degeneracy parameter. An analysis is made of the effect of a magnetic field on momentum relaxation in an electron-phonon system.

Methods of calculating the band structure and low-energy secondary electron spectroscopy of iridium

A theoretical interpretation is put forward for the fine structure of the secondary electron emission spectra of Ir normal to the (111) surface and the total current spectrum of an Ir polycrystal. The calculations took into account the energy dependence of the broadening of the energy band levels, the electron-electron and electron-plasmon contributions to the nonequilibrium electron distribution function, and the isotropic component of the current from the electrons scattered at the surface. It is shown that the fine structure of the secondary electron emission spectrum and the total current spectrum is mainly attributable to the electron structure of the final states into which the electrons enter or from which they are emitted so that the characteristics of the band configuration in the energy band structure can be reconstructed directly from the experimental data. This method can be used to separate bulk effects from surface effects in the secondary electron emission and total current spectra. It is confirmed that the fine structure of the secondary electron emission and total current spectra depends on the geometric structure and the degree of ordering of the crystals. A reduction in the intensity of the fine structure serves as a measure of the defect structure in the surface region of the sample which can be successfully used to monitor the surface state during treatment.

High-field miniband transport in semiconductor superlattices under the influence of a transverse magnetic field

The miniband transport in semiconductor superlattices under the influence of high electric and magnetic fields aligned parallel to the superlattice axis is treated within a rigorous quantum-mechanical approach. Intra-collisional field effects due to the electric and magnetic field are taken into account. Pronounced resonances are predicted to occur in the current density due to Landau and Wannier–Stark quantization of the electronic states and due to their scattering on polar-optical phonons. The combined electric and magnetic field effects are treated by a non-equilibrium lateral electron distribution function, which is the solution of a quantum-kinetic equation. The field-dependent coupling between longitudinal and transverse degrees of freedom via the lateral distribution function leads to a non-separable dependence of the current on the electric and magnetic fields. Wannier–Stark current oscillations are strongly enhanced by high magnetic fields. The experimentally detected crossover in the temperature dependence of the current is reproduced. Finally, the influence of an electric field on magneto-phonon resonances is studied.

Numerical Simulation of Heat Removalfrom Low Dimensional Nanostructures

The acoustic phonon radiation patterns and acoustic phonon spectra due to electron acoustic phonon interaction in double barrier quantum well have been investigated by solving both the kinetic equations for electrons and phonons. The acoustic phonon radiation patterns have strongly pronounced maximum in the directions close to the perpendicular to the quantum well direction. The radiation pattern anisotropy is explained in terms of possible electron transitions, nonequilibrium electron distribution function, and the Hamiltonian of electron‐phonon interactions.

Numerical Solution of the Quantum Landau Equation for Dense Plasmas

AbstractThe numerical solution of the quantum Landau kinetic equation for a dense electron gas is considered. Being one of the most simple kinetic equations, it still retains essential physical features of a correlated many‐particle system, such as selfconsistent static screening and Pauli blocking, and, at the same time, it is a good test case for the efficiency of numerical methods. Two schemes for the evaluation of the scattering rates and the collision integral are discussed. To illustrate our results, we present time‐dependent calculations i) for the relaxation of a nonequilibrium electron distribution function and ii) for the stopping of fast electrons.

On the Theory of Conduction of Antiferromagnetic Semiconductors

AbstractThe kinetic properties of an isotropic antiferromagnetic nondegenerate semiconductor in a high electric field are investigated theoretically. By solving a system of kinetic equations for electrons and magnons a nonequilibrium electron distribution function is found. It is shown that under certain conditions the volt–ampere characteristic calculated with the use of this function may have an N shape.

Numerical modeling of lower hybrid heating and current drive

The generation of currents in toroidal plasma by application of waves in the lower hybrid frequency range involves the interplay of several physical phenomena which include: wave propagation in toroidal geometry, absorption via wave-particle resonances, the quasilinear generation of strongly nonequilibrium electron and ion distribution functions, and the self-consistent evolution of the current density in such a nonequilibrium plasma. We describe a code, LHMOD, which we have developed to treat these aspects of current drive and heating in tokamaks. We present results obtained by applying the code to a computation of current ramp-up and to an investigation of the possible importance of minority hydrogen absorption in a deuterium plasma as the “density limit” to current drive is approached.

The Non‐Equilibrium Electron Distribution Function in the Electrical Resistance Problem for Potassium Metal Influence of N‐ and U‐Processes

AbstractThe angular and energy structures of the nonequilibrium electron distribution function for potassium at low temperatures are investigated. It is shown that the peculiarities in the δfk structure due to U‐processes are largely suppressed by interference between normal and U‐processes. Hence at the umklapp process freezing temperatures the value of resistivity is affected not only by U‐transitions from “hot spots” but equally by diffuse N‐transitions. The solution of Boltzmann equation by quadrature formulas is discussed.

Secondary radiation in impurity polar semiconductors

An expression is obtained for the secondary radiation section of polar semiconductors due to radiation trapping of electrons or holes at deep impurity levels with the participation of intermediate quasilocal states. The dependence of the section on the frequency of the exciting monochromatic wave is determined mainly by the nonequilibrium electron distribution function, which is a number of equidistant peaks. The spacing between adjacent peaks equals the frequency of the longitudinal optical (LO) phonon, while the peak width is determined by the dispersion of the LO phonons. The distinction between the radiation and Lorentz line shapes is also associated with the form of the electron distribution function.

Deviations form Matthiessen's Rule in Dilute Aluminum Alloys

The electrical resistivity of dilute alloys of aluminum with Mg, Si, Cu, Zn and Ag as solute, respectively, has been measured together with the resistivity of pure aluminum from 4.2 to 300 K as a function of the solute concentration (0.001∼1 at%), to determine the deviation Δ from Matthiessen's rule. At intermediate temperatures, the humps have been observed in the curves of Δ/ρ 0 (ρ 0 : residual resistivity) versus temperature. The hump moves toward lower temperature and becomes more sharp and higher as the solute content decreases. These behaviors can be explained in terms of the anisotropy of the nonequilibrium electron distribution function. At lower temperatures, Δ does not follow a well defined T n law and it is attributed to simultaneous scattering by at least two processes. At high temperatures above about 100 K, Δ increases or decreases linearly with temperature.

Anomalous Electron-Phonon Transport Properties of Impure Metals. I. The Electrical Resistivity

The electron-phonon contribution ${\ensuremath{\rho}}_{\mathrm{ep}}(T,c)$ to the resistivity of an impure metal, or dilute metal alloy, can be drastically different from that of the ideally pure metal, ${\ensuremath{\rho}}_{\mathrm{ep}}^{0}(T)$, if, in the region of the Fermi energy, the conduction-electron relaxation time ${\ensuremath{\tau}}_{0}(\ensuremath{\epsilon})$ for impurity scattering varies with energy $\ensuremath{\epsilon}$ on a scale comparable to or less than the Debye energy $\ensuremath{\hbar}{\ensuremath{\omega}}_{D}$ of the metal. This effect is a consequence of the sensitivity of the (inelastic) electron-phonon resistivity to any energy-dependent component in the nonequilibrium electron-distribution function. We present a working formula for the effect and indicate several important consequences for nontransitional metals containing magnetic or nonmagnetic transitional impurities. In the limit of small impurity concentrations $c$, the alloy and host electron-phonon resistivities are connected to the electron-diffusion thermopower $S(T,c)$ of the alloy via the simple relation ${\ensuremath{\rho}}_{\mathrm{ep}}(T,c)\ensuremath{\simeq}{\ensuremath{\rho}}_{\mathrm{ep}}^{0}(T) {1+{(\frac{\ensuremath{\hbar}{\ensuremath{\omega}}_{D}}{{\ensuremath{\epsilon}}_{F}})}^{2}{[\frac{S(T,c)}{{S}_{0}(T)}]}^{2}}$, where ${S}_{0}$ denotes the "free-electron" thermopower. More generally, ${\ensuremath{\rho}}_{\mathrm{ep}}(T,c)$, and also ${\ensuremath{\rho}}_{\mathrm{imp}}(T,c)$, the resistivity resulting from impurity scattering, are expressed in terms of the first and second derivatives of ${\ensuremath{\tau}}_{0}$ at the Fermi energy ${\ensuremath{\epsilon}}_{F}$. The anomalous electron-phonon resistivity will cause sharp peaks to appear in the atomic-resistivity temperature curves of very dilute magnetic-impurity systems (e.g., $\mathrm{Cu}\mathrm{Fe}$, $\mathrm{Au}\mathrm{Fe}$, $\mathrm{Au}\mathrm{Mn}$). Experimentally, measurements of deviations from Matthiessen's rule should furnish useful information on the energy dependence of the electron-impurity scattering.