Temperature dependent energy relaxation time in AlGaN/AlN/GaN heterostructures

The two-dimensional (2D) electron energy relaxation in Al_0.25Ga_0.75N/AlN/GaN heterostructures was investigated experimentally by using two experimental techniques; Shubnikov-de Haas (SdH) effect and classical Hall Effect. The electron temperature (T_e) of hot electrons was obtained from the lattice temperature (T_L) and the applied electric field dependencies of the amplitude of SdH oscillations and Hall mobility. The experimental results for the electron temperature dependence of power loss are also compared with the current theoretical models for power loss in 2D semiconductors. The power loss that was determined from the SdH measurements indicates that the energy relaxation of electrons is due to acoustic phonon emission via unscreened piezoelectric interaction. In addition, the power loss from the electrons obtained from Hall mobility for electron temperatures in the range T_e > 100 K is associated with optical phonon emission. The temperature dependent energy relaxation time in Al_0.25Ga_0.75N/AlN/GaN heterostructures that was determined from the power loss data indicates that hot electrons relax spontaneously with MHz to THz emission with increasing temperatures.     

Polar optical phonon limited energy and momentum relaxation of hot electrons in a GaAs-quantum well (QW)

The average energy loss rate, the energy- as well as the momentum relaxation time of hot electrons confined in a GaAs-square quantum well are calculated as a function of the external controllable parametersn _s (electron density),T (lattice temperature) andT _e (electron temperature) for the interaction of the charge carriers with bulk- and surface polar optical phonons. Analytical expressions are derived in the limit of vanishing quantum well width at non-degeneracy and degeneracy of the electron system. Both energy-and momentum relaxation time are found to be complicated functions of the ratiosT _D /T _e andT _D /T withT _D being the Debye-temperature of the polar optical phonon involved in the scattering. In a thick (very thin) QW the energy loss rate to bulk PO-phonons is found to be larger (smaller) than the corresponding loss rate to surface modes. The energy- (momentum-) relaxation times are found to be constant (increasing) functions ofn _s at non-degeneracy (degeneracy) of the electron system. Dedicated to Professor Karlheinz Seeger on the occasion of his 60th birthday     

Relaxation of the electron temperature in an inert-gas afterglow plasma at elevated pressures

The relaxation of the electron temperature T _e in helium and neon afterglow at elevated pressures is studied theoretically and experimentally. It is shown that the processes in which fast electrons are produced are accompanied by the heating of thermal electrons. The high-energy part of the electron energy distribution function is studied in the intermediate regime (between the local and nonlocal regimes) of its formation. It is shown that, in this case, the calculated effective energy transferred from the fast electrons to the thermal electrons depends substantially on the wall potential of the discharge tube. Comparison of these calculations with experiments testifies to the reliability of the probe technique for measuring T _e in an afterglow at elevated pressures.     

Investigation of the Beam Plasma Discharge in Electronegative Gases Using the Second Derivative of Langmuir Probe Characteristics

The distribution of the charge carriers is measured and the influence of the attachment processes on the electron energy distribution function is demonstrated for beam plasma discharges in SF₆, CF₄ and O₂ with the aid of the second derivative of Langmuir probe characteristics. The structuration of the plasma into regions of predominating negative ions and regions of predominating electrons is determined by the the established radial T_e-profile. The dimension of the quasi electronfree plasma changes significantly as well at transition from the turbulent heating mechanism into the electron impact plasma generation as by occuring low-frequency instabilities. With increasing n_?/n_e a deficit of low energetic electrons appears in the electron energy distribution parallel to the formation of the negative ion peak. The saturation currents at n_e/n_?=0 yield the mass ratios between negative and positive ions.     

Non-equilibrium effects and self-heating in single-electron Coulomb blockade devices

We present a comprehensive investigation of non-equilibrium effects and self-heating in single electron transfer devices based primarily on the Coulomb blockade effect. During an electron trapping process, a hot electron maybe deposited in a quantum dot or metal island, with an extra energy usually of the order of the Coulomb charging energy, which is much higher than the temperature in typical experiments. The hot electron may relax through three channels: tunneling back and forth to the feeding lead (or island), emitting phonons, and exciting background electrons. Depending on the magnitudes of the rates in the latter two channels relative to the device operation frequency and to each other, the system may be in one of three different regimes: equilibrium, non-equilibrium, and self-heating (partial equilibrium). In the equilibrium regime, a hot electron fully gives up its energy to phonons within a pump cycle. In the non-equilibrium regime, the relaxation is via tunneling with a distribution of characteristic rates; the approach to equilibrium goes like a power law of time (frequency) instead of an exponential. This channel is plagued completely in the continuum limit of the single-electron levels. In the self-heating regime, the hot electron thermalizes quickly with background electrons, whose temperature T_e is elevated above the lattice temperature T_ol. We have calculated the coefficient in the well-known T⁵ law of energy dissipation rate, and compared the results to experimental values for aluminum and copper islands and for a two-dimensional semiconductor quantum dot. Moreover, we have obtained different scaling relations between the electron temperature, the operation frequency and device size for various types of devices.     

Electron heating in a submicron-size n GaAs wire

We have studied electron heating in a submicron-size GaAs wire from 4.2 K to 50 K. We find that the energy relaxation rate for the electrons is of the form τ_E⁻¹ = α + βT_eⁿ where α, β are constants and T_e is the electron temperature. We associate the temperature-independent term with a quasi-elastic surface scattering process in which an electron losses 1% of its energy at each collision. The temperature dependent term may be due to electron-phonon scattering. It is possible to fit the data to 2 < n < 3.     

Non-Maxwellian Electron Velocity Distribution Resulting from Electron-SF6 Attachment Collisions

A model reaction system is considered consisting of a heat bath of argon atoms (c) and small concentrations of SF₆-molecules (m) and electrons (e) (number densities: n_e ? n_m ? n_c). Within the model the time behaviour of the electron velocity distribution function is studied under the influence of elastic electron-argon collisions and electron SF₆ attachment collisions. On the basis of the distribution function time-dependent macroscopic quantities (kinetic electron temperature. nonequilibrium rate constant of the attachment reaction) are calculated.     

Transient response of photoexcited electrons with a partially inverted distribution

A nonstationary electron magnetotransport is studied for electrons with a partially inverted distribution formed in the passive region after an ultrashort interband photoexcitation and the emission of a cascade of optical phonons. In the case of a peaked distribution in the passive region, the conductivity is positive because of the greater contribution from the decreasing part of the distribution, while the inverted part of the distribution may give rise to a negative magnetoresistance in classical fields. If the energy of photoexcited electrons in the c zone is a multiple of the optical phonon energy, a pair of half-peaks occurs at the boundaries of the passive region. In this case, the contribution from the inverted part of the distribution (with an energy close to the phonon energy) leads to a total negative conductance and a considerable change in the magnetotransport.     

Nonequilibrium energy of Rayleigh waves in half-limited crystals with hot electrons close to the defect surface

Nonequilibrium energies of surface (Rayleigh) lattice oscillations in half-limited crystals with static defects and a two-dimensional layer of hot Fermi and Boltzmann electrons close to the stress free surface were calculated. Substances with electrons heated by an external field retaining their intrinsic temperature for a certain time, T _e ? T, where T is the temperature of the lattice, were considered. As shown earlier, the thermodynamic characteristics of thin films can then be determined by nonequilibrium energy of Rayleigh waves (R-phonons) caused by their interaction with hot electrons. This energy decreases as the widths of the energy spectrum of R-phonons increase. In this work, the earlier calculated spectrum widths are used. These widths are caused by the scattering of R-phonons by electrons and static defects close to the surface (point and extended surface defects, edge dislocations perpendicular to the surface and emerging to it, and random lattice grooves in the lattice plane). In all the calculations, the Keldysh diagram technique transformed for half-limited media was used.     

Velocity distribution of plasma electrons in the negative H2- and He-glow with superimposed longitudinal magnetic field

The negative glow plasma has been found nearly field free in axial direction. Therefore plasma electrons in the stationary glow can thermalize down to the temperature of the neutral gas, whenever their diffusion—and recombination—lifetime is high enough. Applying Boltzmann's equation to this problem, the conditions of thermalization of plasma electrons are derived as a function of the outer parameters of the plasma: vessel diameter 2R, neutral gas pressurep and longitudinal magnetic fieldB. — If plasma electrons have a too short diffusion—and recombination—lifetime to be in thermal equilibrium with the neutral gas, the electron energy increases. For this case the distribution function of plasma electrons is derived using Boltzmann's equation. Approximating the calculated energy distribution by a Maxwellian distribution function, the electron temperature in the glow is obtained as a function of the parameters:R, p, B. OurT _e -measurements carried out in the H₂- and He-glows of different tube diameters, neutral gas pressures and magnetic fields agree closely with the theoretical results. TheT _e -measurements have been performed with Langmuir probes and by the method of reversal of the radial ambipolar electric field in a longitudinal magnetic field.     

Effect of Discharge Plasma Potential on Diffusion Plasma Parameters Controlled by a Mesh Grid in a Double Plasma Device

The plasma region under investigation is separated from the discharge region by a mesh grid. Plasma potential and electron number densities and electron temperatures under bi‐Maxwellian approximation for electron distribution function of the multi‐dipole argon plasma are measured. The cold electrons in the diffusion region are produced by local ionization. The hot electrons are the ionizing electrons behaving as Maxwellian. The electron trapping process in the discharge region is produced by potential well due to positive plasma potential with respect to the anode and by a repulsive grid. The dependence of ratios of the density of the hot to the cold electrons N_E (=N_eh/N_ec) and hot to cold electron temperature T(=T_eh/T_ec) in the diffusion region on the depth of the potential well has been investigated. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ultrahigh charging of dust particles in a nonequilibrium plasma

Charging of dust particles in a plasma with the two-temperature energy distribution of electrons has been studied. It has been shown that the dust-particle potential divided by the electron temperature decreases with increasing electron temperature in the plasma with cold ions. Owing to this behavior, the potential of the dustparticle surface increases with the electron temperature more slowly than the linear function and is lower than the electron temperature (divided by the elementary charge) for T _e > 5.5 eV in hydrogen and for T _e > 240 eV in argon. The fraction of fast electrons at which these electrons begin to contribute to the charge of dust particles has been determined. It has been shown that the charge of micron particles can reach 10⁶ elementary charges. The effect of the cold and thermal field emission on the charge of dust particles has been analyzed. The possibility of obtaining ultrahigh charges (to 10⁷ elementary charges on dust particles with a radius of 50–100 μm irradiated by a 25-keV 1-mA electron beam has been demonstrated.     

Kinetic Current-Convective Instability in Hot Electron Plasma

The kinetic current-convective instability excited in a hot electron plasma, i.e. for T_e ? T_i, is investigated in the linear stage. Density and temperature of plasma components have gradients along the x-direction. In the absence of longitudinal current (u = 0) and homogeneous temperature the instability is also excited with maximum growth rate much exceeding that obtained in the case of u ≠ 0. Gradual increasing of the ion temperature over that of the electrons and a large density gradient leads to reduce the instability in the linear stage.     

Elimination of the mott interband s-d enhancement of the electrical resistance of nickel and platinum owing to the excitation of electrons by femtosecond laser pulses

The dependence of electrical, σ, and thermal, κ, conductivities of metals on the electron temperature T _e at high (～1 eV) T _e values has been calculated. The two-temperature states for which the temperature T _e of heated electrons exceeds the temperature T _i of ions in the crystal lattice result from the excitation of electrons by femtosecond laser pulses. It is well known that the existence of empty d levels with a high density of states near the Fermi surface (as, e.g., in nickel, platinum, and iron) leads to a pronounced enhancement of the electrical resistance (Mott, 1936). This is due to an increase in the statistical factor related to the electron transitions to the empty states induced by collisions with phonons. It is found that the excitation of the electron subsystem significantly reduces the electron-phonon scattering to unoccupied d states since the chemical potential μ(T _e ) rises above the upper edge of the d band. The decrease in the scattering probability leads to the anomalous behavior of the conductivity σ_el-ph, which increases with the temperature T _e . Such a behavior turns out to be inverse with respect to the usual situation in condensed matter.     

On the inelastic-loss approximation for keV-energy ion collisions in solids

Inelastic energy-loss in a single collisionT _e and related stopping cross-sectionT _e based on the Firsov model are evaluated for different screening functions in the elastic interaction potentials. Various approximations ofT _e andS _e for keV-ions in solids are discussed.     

Direct measurements of energy relaxation times on an AlGaAs/GaAs heterointerface in the range 4.2–50 K

The temperature dependence of the energy relaxation time τ_e (T) of a two-dimensional electron gas at an AlGaAs/GaAs heterointerface is measured under quasiequilibrium conditions in the region of the transition from scattering by acoustic phonons to scattering with the participation of optical phonons. The temperature interval of constant τ_e, where scattering by the deformation potential predominates, is determined. In the preceding, low-temperature region, where piezoacoustic and deformation-potential-induced scattering processes coexist, τ _e decreases slowly with increasing temperature. Optical phonons start to participate in the scattering processes at T∼25 K (the characteristic phonon lifetime was equal to τ_LOτ4.5 ps). The energy losses calculated from the τ_e data in a model with an effective nonequilibrium electron temperature agree with the published data obtained under strong heating conditions. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 5, 371–375 (10 September 1996)     

Nanoscale combined reactions: non-equilibrium α-Co formation in nanocrystalline ϶-Co by abnormal grain growth

Electrodeposited nanocrystalline Co offers a relatively unique opportunity to study the interaction of two fundamentally different elementary solid state reactions: grain growth and ε (HCP) to α (FCC) allotropic phase transformation. Samples were isothermally annealed at temperatures above and below the equilibrium transformation temperature (T_εα?=?695?K) and quenched to ambient for subsequent characterization by X-ray diffraction (XRD) and transmission electron microscopy (TEM). Isothermal annealing above 695?K resulted in concurrent grain growth and ε to α transformation. Unexpectedly, however, simultaneous grain growth and ε to α transformation also occurred during isothermal annealing at temperatures as low as 573?K, i.e. 122?K below the expected equilibrium T_εα. It was observed that non-equilibrium α-Co formed within a matrix of nanocrystalline ε-Co via abnormal grain growth, and is therefore fundamentally different from the ε to α transformation typically observed in conventional polycrystalline Co.     

The influences of gas and electron temperatures on electron attachment in gas electrical discharges

Various electron attachment processes are reviewed, emphasising the way in which the rates and products of some selected reactions vary with the attaching gas temperatureT _g, the temperature,T _e, and the energy of the attaching electrons. The examples illustrating the variety of reactions are the efficient dissociative attachment reaction to CCl₄, attachment to SF₆ which involves both dissociative and non-dissociative attachment, attachment to CHCl₃ which requires activation energy, and attachment to CCl₃Br which results in both Cl- and Br- product ions. A model has been presented which is able to quantitatively explain the difference influences ofT _g andT _e on the rates of some of these reactions. Also described are the unusually efficient attachment properties of the fullerene molecules C₆₀ and C₇₀ as revealed by our FALP experiments, noting that these molecules have potential importance as efficient suppressers of electrical breakdown through gases such as those used to insulate high voltage devices. We emphasise throughout this paper the importance of an understanding of the separate influences of gas and electron temperature on attachment reactions for the modelling of practical gas discharge media such as etchant plasmas. We dedicate this paper to Professor Jan Janča on the occasion of his sixtieth birthday in recognition of his major contributions to gas discharge physics.     

Electron Temperature Relaxation in Afterglow Plasmas: Diffusion Cooling

We have carried out a thorough theoretical analysis of the cooling and heating processes of the electron gas in Ne, Ar and Kr afterglow plasmas. Thus the rate of relaxation of the electron temperature, T_e, is seen to be in good agreement with the experimental measurements when spatial gradients of T_e in the early afterglow and heating of the electron gas by superelastic collisions between the electrons and metastable atoms are accounted for. At low pressures of the rare gases, p_g, the phenomenon of diffusion cooling occurs in which T_e relaxes to an equilibrium temperature, T_ee, which is less than the gas temperature, T_g. This reduction in T_ee below T_g is mirrored in a reduction in the ambipolar diffusion coefficient, D_a, for the rare gas atomic ions and electrons. Thus the D_a can be calculated as a function of p_g using the values of T_ee, and when this is done, properly accounting for the heating by metastable atoms, the calculated and experimental values of D_a in all three rare gas afterglows are seen to be in agreement.     

Materials parameters and ion-induced track formation

ABSTRACT

The role of various materials parameters in track formation is discussed. Experimental information is utilized showing a direct quantitative relationship in different solids between the melting points T_m and the ion-induced track radii R_e without involving other materials parameters. It is shown for Θ?=?T_m???T_ir (T_ir – irradiation temperature) that Θ～exp{?R_e²/w²} for S_e/N?=?constant, where S_e and N are the electronic stopping power and the number density of atoms and w?=?4.5?nm. The validity of this universal-type relation is demonstrated for 14 different insulators including LiNbO₃ and BaFe₁₂O₁₉. It is shown that the thermal diffusivity D, the heat of fusion L the band gap energy E_g and the absorption radius α_e of the electron distribution must not affect the track sizes as this would not be coherent with this identical behavior. Original reports on LiNbO₃ and BaFe₁₂O₁₉ with opposite conclusions are critically analyzed. It is shown that an arbitrary value of the ion energy was used in the analysis that modified substantially the results leading to an undue justification of the contribution of L and E_g in apparent agreement with the experimental data.