Equilibrium Electron Density Research Articles

Heater‐induced ionization inferred from spectrometric airglow measurements

AbstractSpectrographic airglow measurements were made during an ionospheric modification experiment at High Frequency Active Auroral Research Program on 12 March 2013. Artificial airglow enhancements at 427.8, 557.7, 630.0, 777.4, and 844.6 nm were observed. On the basis of these emissions and using a methodology based on the method of Backus and Gilbert (1968, 1970), we estimate the suprathermal electron population and the subsequent equilibrium electron density profile, including contributions from electron impact ionization. We find that the airglow is consistent with heater‐induced ionization in view of the spatial intermittency of the airglow.

Negative differential transmission in graphene

By using the Kubo linear response theory with the Keldysh Green function approach, we investigate the mechanism leading to the negative differential transmission in system with the equilibrium electron density much smaller than the photon-excited one. It is shown that the negative differential transmission can appear at low probe-photon energy (in the order of the scattering rate) or at high energy (much larger than the scattering rate). For the low probe-photon energy case, the negative differential transmission is found to come from the increase of the intra-band conductivity due to the large variation of electron distribution after the pumping. As for the high probe-photon energy case, the negative differential transmission is shown to tend to appear with the hot-electron temperature being closer to the equilibrium one and the chemical potential higher than the equilibrium one but considerably smaller than half of the probe-photon energy. We also show that this negative differential transmission can come from both the inter- and the intra-band components of the conductivity. Especially, for the inter-band component, its contribution to the negative differential transmission is shown to come from both the Hartree-Fock self-energy and the scattering. Furthermore, the influence of the Coulomb-hole self-energy is also addressed.

Carrier Generation in Multicomponent Wide-Bandgap Oxides: InGaZnO4

To exploit the full potential of multicomponent wide-bandgap oxides, an in-depth understanding of the complex defect chemistry and of the role played by the constituent oxides is required. In this work, thorough theoretical and experimental investigations are combined in order to explain the carrier generation and transport in crystalline InGaZnO4. Using first-principles density functional approach, we calculate the formation energies and transition levels of possible acceptor and donor point defects as well as the implied defect complexes in InGaZnO4 and determine the equilibrium defect and electron densities as a function of growth temperature and oxygen partial pressure. An excellent agreement of the theoretical results with our Brouwer analysis of the bulk electrical measurements for InGaZnO4 establishes the Ga antisite defect, GaZn, as the major electron donor in InGaZnO4. Moreover, we show that the oxygen vacancies, long believed to be the carrier source in this oxide, are scarce. The proposed carrier generation mechanism also explains the observed intriguing behavior of the conductivity in In-rich vs Ga-rich InGaZnO4.

Enhanced thermal self-focusing of a Gaussian laser beam in a collisionless plasma

Theory given by Wang-Zhou [Phys. Plasmas 18, 043101 (2011)] for the thermal self-focusing of a Gaussian laser beam in a collisionless plasma is revisited by including the effect of a localized upward plasma-density ramp. As the equilibrium electron density is an increasing function of the distance of propagation of the laser beam, the diffraction length decreases rapidly as the beam penetrates deeper into the plasma and the diffraction effect becomes reduced; thus, the laser becomes more focused. A significant enhancement in laser thermal self-focusing in a collisionless plasma is consequently observed if a localized plasma density ramp is introduced.

Dust-acoustic solitary waves in a strongly coupled inhomogeneous dusty plasma in the presence of polarization force and effective dust-temperature

The nonlinear propagation of the dust-acoustic waves is studied in a strongly coupled inhomogeneous dusty plasma which consists of the strongly correlated negatively charged dust grains and weakly correlated electrons and ions. The Korteweg-de Vries equation with variable coefficients and an additional term due to the density gradient is deduced, and its solution is found by appropriate transformations. The propagation of two possible modes (fast and slow) and their evolution are investigated. Only the fast rarefactive solitary waves are found to propagate in such plasma with parameter ranges corresponding to the experimental conditions. It is shown that the special patterns of nonlinear DA waves (e.g., amplitude and width) are significantly modified in a way that depends upon the effects of polarization force (which arises due to the interaction between thermal ions and highly negatively charged dust grains), effective dust-temperature (which arises from the electrostatic interactions among highly negatively charged dust and from the dust thermal pressure), equilibrium electron density, and ion temperature. The amplitude of solitary waves also decreases as the wave propagates in the direction of increasing dust concentration.

Enhanced response of current-driven coupled quantum wells

We have investigated the conditions necessary to achieve stronger Cherenkov-like instability of plasma waves leading to emission in the terahertz regime for semiconductor quantum wells. The surface response function is calculated for a bilayer two-dimensional electron gas (2DEG) system in the presence of a periodic spatial modulation of the equilibrium electron density. The 2DEG layers are coupled to surface plasmons arising from excitations of free carriers in the bulk region between the layers. A current is passed through one of the layers and is characterized by a drift velocity vD for the driven electric charge. By means of a surface response function formalism, the plasmon dispersion equation is obtained as a function of frequency ω, in-plane wave vector q∥=(qx,qy), and reciprocal lattice vector nG, where n=0,±1,±2,… and G=2π/d, with d denoting the period of the density modulation. The dispersion equation, which yields the resonant frequencies, is solved numerically in the complex ω-plane for the real wave vector q∥. It is ascertained that the imaginary part of ω is enhanced with decreasing d and with increasing doping density of the free carriers in the bulk medium for a fixed period of the spatial modulation.

Electron dynamics at a positive ion

The dynamics of electrons in the presence of a positive ion is considered for conditions of weak electron-electron coupling but strong electron-ion coupling. The equilibrium electron density and the electric field time correlation functions are evaluated for semiclassical conditions using a classical statistical mechanics with a regularized electron-ion interaction for molecular dynamics simulation (MD). Results are reported for the autocorrelation function of the electron electric field at the ion for 0< or =Z< or =40 , including conditions of strong electron-ion coupling. The electron stopping power and self-diffusion coefficient are determined from these results. Interpretation is provided by a theoretical analysis using the nonlinear Vlasov equation for the equilibrium structure, and a corresponding linear Vlasov equation for time correlation functions. The agreement of a simple mean field model with the semiclassical MD simulation is found to be quite good except for one state condition.

Local plasma processes and enhanced electron densities in the lower ionosphere in magnetic cusp regions on Mars

Both the MARSIS ionospheric sounder and the charged particle instrument package ASPERA-3 are experiments on board the Mars Express spacecraft. Joint observations have shown that events of intense ionospheric electron density enhancements occur in the lower ionosphere of magnetic cusp regions, and that these enhancements are not associated with precipitation of charged particles above a few hundred electron volts (<300 eV). To account for the enhancement by particle precipitation, electron fluxes are required with mean energy between 1 and 10 keV. No ionizing radiation, neither energetic particles nor X-rays, could be identified, which could produce the observed density enhancement only in the spatially limited cusp regions. Actually, no increase in ionizing radiation, localized or not, was observed during these events. It is argued that the process causing the increase in density is controlled mainly by convection of ionosphere plasma driven by the interaction between the solar wind and crustal magnetic field lines leading to excitation of two-stream plasma waves in the cusp ionosphere. The result is to heat the plasma, reduce the electron–ion recombination coefficient and thereby increase the equilibrium electron density.

Nonlinear electromagnetic plasma eigenmodes and their stability to stimulated Raman scattering

Transverse mode structure of nonlinear laser eigenmodes in underdense and overdense plasmas has been obtained by numerically solving the wave equation under relativistic and ponderomotive nonlinearities. The mode structure closely resembles a Lorentzian with half width scaling inversely as the axial intensity of the laser. The threshold condition for laser penetration in an overdense plasma turns out to be γ0≡(1+a02∕2)1∕2⩾2n0∕ncr−1, where n0 is the equilibrium electron density, ncr is the critical density at laser frequency, and γ0 is the electron Lorentz factor due to the laser of normalized axial intensity a02. The nonlinear laser eigenmode, in a low density plasma, is unstable to stimulated Raman backscattering off a copropagating space charge reactive quasimode. The growth rate increases with laser intensity as a0 rises up to a0∼1. Beyond this value, growth rate decreases with a0, due to the enhancement of electron mass and depletion of electrons from the axial region. Geometrical effects also reduce the growth rate.

On the linear dynamic response of average atom in plasma

The theory of linear response of an average atom (AA) in plasma is considered. It is assumed that the model of the AA is of the density functional theory (DFT) type, i.e., can be characterized by an equilibrium electron density in terms of a complete set of bound and free one-electron wave functions of a screened self-consistent-field (SCF) potential. The starting point in the linear response theory is the cluster expansion of the energy extinction coefficient. This coefficient expresses the rate of extinction of the energy due to an external potential irradiating a plasma composed if ions and electrons. As shown in previous publications the first-order term in the cluster expansion correctly gives the linear response of the AA. The first-order formula for the extinction coefficient is directly related to the AA photo-absorption cross-section. The cluster expansion technique shows how the homogeneous plasma contribution shall be correctly subtracted from the response of the AA and its surrounding plasma. The linear response is considered in the dipole approximation and in the framework of the random phase approximation which can be viewed as a version of a time-dependent DFT with local density approximation to the exchange–correlation potential. In the paper, we discuss a possible practical scheme for calculation of the dipole linear response and obtain some theoretical results that allow one to reduce the theoretical and numerical difficulties of the approach. We show formally how in the dipole approximation the homogeneous plasma contribution to the induced potential results in the appearance of the cold-plasma dielectric function. We also derive a new sum rule which allows one to calculate the induced dipole using the localized density and potential gradients of the AA in equilibrium. We further propose a change of variables that allows us to eliminate the leading dipole divergence in the first-order Schrödinger equations. We next discuss some aspects of a simplified case in which the induced potential is neglected. Finally, we present and comment on the radial equations for the SCF frequency-dependent induced density and potential.

Spin-polarized current amplification and spin injection in magnetic bipolar transistors

The magnetic bipolar transistor (MBT) is a bipolar junction transistor with an equilibrium and nonequilibrium spin (magnetization) in the emitter, base, or collector. The low-injection theory of spin-polarized transport through MBTs and of a more general case of an array of magnetic {\it p-n} junctions is developed and illustrated on several important cases. Two main physical phenomena are discussed: electrical spin injection and spin control of current amplification (magnetoamplification). It is shown that a source spin can be injected from the emitter to the collector. If the base of an MBT has an equilibrium magnetization, the spin can be injected from the base to the collector by intrinsic spin injection. The resulting spin accumulation in the collector is proportional to $\exp(qV_{be}/k_BT)$, where $q$ is the proton charge, $V_{be}$ is the bias in the emitter-base junction, and $k_B T$ is the thermal energy. To control the electrical current through MBTs both the equilibrium and the nonequilibrium spin can be employed. The equilibrium spin controls the magnitude of the equilibrium electron and hole densities, thereby controlling the currents. Increasing the equilibrium spin polarization of the base (emitter) increases (decreases) the current amplification. If there is a nonequilibrium spin in the emitter, and the base or the emitter has an equilibrium spin, a spin-valve effect can lead to a giant magnetoamplification effect, where the current amplifications for the parallel and antiparallel orientations of the the equilibrium and nonequilibrium spins differ significantly. The theory is elucidated using qualitative analyses and is illustrated on an MBT example with generic materials parameters.

Dynamics of dissipative quantum Hall edges

We examine the influence of the edge electronic density profile and of dissipation on edge magnetoplasmons in the quantum Hall regime, in a semiclassical calculation. The equilibrium electron density on the edge, obtained using a Thomas-Fermi approach, has incompressible stripes produced by energy gaps responsible for the quantum Hall effect. We find that these stripes have an unobservably small effect on the edge magnetoplasmons. But dissipation, included phenomenologically in the local conductivity, proves to produce significant oscillations in the strength and speed of edge magnetoplasmons in the quantum Hall regime.

First results from the multichannel interferometer system on HSX

Measuring the equilibrium electron density distribution and its response to perturbations provides important information to magnetically confined plasma research. A multichannel interferometer system is now routinely operating on the new quasihelically symmetric stellator (HSX) to measure the equilibrium profile and electron density dynamics. The interferometer system has nine viewing chords with 1.5 cm spacing. The source is a bias-tuned Gunn diode at 96 GHz with passive solid-state tripler providing output at 288 GHz (8 mW). The HSX plasma is produced by 28 GHz electron cyclotron resonance heating and first results of the interferometer measurement are reported. The density spatial distribution is reconstructed from the measured line-integrated density. At high density [n̄e&amp;gt;2×1012 cm−3], an m=1 density oscillation with frequency of 1–2 kHz is observed. Plans to determine the radial particle flux and transport coefficients will be discussed.

Surface modes in metal clusters and cavities

Solving the hydrodynamical equations by means of a variational principle, we obtain a simultaneous description of the surface and volume modes of the valence electrons in a metal. This variational scheme, which has been previously used in the context of nuclear fluid dynamics, is applied to describe the dynamics of the valence electrons in a spherical metal cluster and of the valence electrons in the metal surrounding a spherical cavity (void). The eigenmodes fulfil the linear energy-weighted sum rule , the inverse energy-weighted sum rule and orthogonality relations. The surface modes predicted by Mie (in clusters) and by Natta (in cavities) appear in this model as natural solutions of the equations of motion and boundary conditions. We have considered a stabilized spherical jellium model. The parameters of the effective interaction are obtained by means of a variational method taking into account the experimental values of the density, compressibility and bulk energy. In the present model we have ignored the diffuseness of the equilibrium electron density, taking into account, however, the surface degrees of freedom of the valence electrons and thus allowing them to penetrate into the vacuum (outside of the jellium) when undergoing collective oscillations. The spectra of the excitation energies, and the electronic transition currents and transition densities are obtained for spherical clusters and voids.

Electronic structure of light metal hydrides

The equilibrium lattice constant, cohesive energy, and electron density of states of light metal hydrides (LiBeH{sub 3}, LiMgH{sub 3}, LiCaH{sub 3}, NaMgH{sub 3}, and LiBH{sub 3}) are calculated using the linear combination of muffin-tin orbitals method on a perovskite lattice structure. Large gaps in the density of states appear at the Fermi energy of LiBeH{sub 3}, LiMgH{sub 3}, LiCaH{sub 3}, and NaMgH{sub 3} indicating that these classes of hydrides are insulators. LiBH{sub 3}, on the other hand, is metallic and could have interesting electronic properties. {copyright} {ital 1997} {ital The American Physical Society}

Electron Densities of Several Small Molecules As Calculated from Density Functional Theory

The electron densities of CH3F, CO, CO2, H2CO, H2O, HCN, HF, and NH3 have been calculated by density functional theory (DFT) methods with various exchange and correlation functionals and are compared with QCISD (quadratic configuration interaction method including single and double substitutions) results. The DFT methods yield electron densities and Laplacians of the densities in good agreement with the QCISD results. As expected, the gradient-corrected functionals including B3LYP, B3P86, BP86, and BLYP improve the densities calculated by the local spin density approximation relative to the corresponding QCISD densities. Relative to his 1988 functional, Becke's three-parameter exchange functional clearly improves the results for equilibrium geometries, vibrational frequencies, dipole moments, and electron densities. For all gradient-corrected functionals, the results are generally insensitive to the numerical accuracy of the grid. The basis set, however, has a significant effect on the electron density, which also shows a large dependence on the particular choice of functionals used in the DFT calculation.

Temperature dependence of equilibrium electron density in AlGaAs governed by Sn-related DX centers

Capacitance and conductance of AlxGa1−xAs/GaAs heterostructures with an Sn-doped Al0.35Ga0.65As layer and with a p-n junction was measured as a function of frequency and temperature. The temperature dependence of the free-electron density n was determined from the measurement. A theoretical relation for n governed by two independent DX centers was derived. The experimental results were explained by the presence of two types of Sn-related DX centers. The binding energies of the two DX centers were determined and found to be in good accord with values, both experimental and theoretical, reported previously by other authors.

Gold on silver(110): an embedded-atom-method study

Calculations for trends in the energy of various configurations of small quantities of gold deposited on a silver(110) surface have been carried out using a simple nearest-neighbor embedded-atom-method model. The primary result is that it is energetically preferable for the outermost plane of atoms to be silver rather than gold. Isolated gold atoms on top of a (110)) surface can readily exchange with silver atoms, but pairs of gold atoms are tightly bound and impede interchange. Gold atoms have little interaction with ledges parallel to tight-packed rows on the (110) surface but bind strongly to ledges parallel to (001) and to kinks. Kinetic effects should play a major role in determining the actual configurations found in experiments, with little initial barrier to the interchange of single adatoms with surface atoms on the (110) surface, but with limited interchange with increasing coverage. Clustering of gold on this surface occurs for the same reason that the gold (110) surface reconstructs: the small ratio of the gold (111)-to-(110) surface energies. The primary unique property of gold that lends to all of these effects is the large positive Cauchy pressure, i.e., the large ratio of the bulk modulus to the average shear modulus. This leads to a large curvature in the embedding function of gold so that the energy penalty is greater in gold than in silver to be a given fraction away from its equilibrium electron density. It is also found that, depending on the range of local volume dependence as given by the range of the electron density function used in the model, there may be a significant repulsion between vacancies and free surfaces one or two atomic layers below the surface.

Coulomb interactions and the integer quantum Hall effect: Screening and transport.

We examine the influence of Coulomb interactions on the integer quantum Hall effect in high-mobility, wide spacer-layer heterostructures. In these devices, the potential due to disorder is expected to be smooth on the scale of the spacer-layer thickness, which can be much larger than the magnetic length. Screening of this potential is accompanied by large fluctuations in electron density and has dramatic consequences. In particular, the screened potential can be pinned to the Fermi energy in regions of the sample, and these regions can percolate over a range of Landau-level filling fractions. We present a theory for transport that includes screening within the Thomas-Fermi approximation. Considering the Hall conductance as a function of filling fraction, we show that risers between quantized Hall plateaus acquire a finite width in the presence of Coulomb interactions. We also show that, under certain circumstances, current flows within the sample only along narrow strips, concentrated around particular contours of the equilibrium electron density.

Short‐wavelength electromagnetic fluctuations and anomalous electron energy transport in collisional tokamak edges

It is shown that free energy stored in the equilibrium electron density and temperature gradients can drive short‐wavelength electromagnetic fluctuations in collisional plasmas embedded in a homogeneous magnetic field. The enhanced electromagnetic fluctuations can cause anomalous cross‐field electron energy transport. The present investigation can have relevance to short scale electric and magnetic field fluctuations, as well as anomalous thermal conduction in tokamak edges.