Three-dimensional Electron Gas Research Articles

The electrostatic coupling of longitudinal optical phonon and plasmon in wurtzite InN thin films

We utilize coherent longitudinal optical phonon as an optical nanoprobe to investigate the plasmonic behavior of wurtzite c-plane InN thin films. The transition from the three-dimensional electron gas in InN bulk toward the two-dimensional electron gas in InN thin film is revealed via measuring the coupling strength of coherent A1(LO) phonon and plasmon coupling mode. The coupling strength diminishes as the film thickness reduces and finally vanishes at 3±1 nm. This phenomenon is ascribed to the detuning of the intersubband plasmon frequency above the A1(LO) frequency, which is originated from the electronic quantum confinement in InN thin films.

Interaction of fast charged projectiles with two-dimensional electron gas: Interaction and collisional-damping effects

The results of a theoretical investigation on the stopping power of ions moving in a two-dimensional degenerate electron gas are presented. The stopping power for an ion is calculated employing linear-response theory using the dielectric function approach. The collisions, which lead to a damping of plasmons and quasiparticles in the electron gas, is taken into account through a relaxation-time approximation in the linear-response function. The stopping power for an ion is calculated in both the low- and high-velocity limits. In order to highlight the effects of damping, we present a comparison of our analytical and numerical results, in the case of pointlike ions, obtained for a nonzero damping with those for a vanishing damping. It is shown that the equipartition sum rule first formulated by Lindhard and Winther for three-dimensional degenerate electron gas does not necessarily hold in two dimensions. We have generalized this rule introducing an effective dielectric function. In addition, some results for two-dimensional interacting electron gas have been obtained. In this case, the exchange-correlation interactions of electrons are considered via local-field corrected dielectric function.

Critically shielded potential in a three-dimensional electron gas: The induced charge density at the origin

The induced electron density at the position of a critically shielded single point charge embedded in a three-dimensional degenerate electron gas is studied at low densities, in a comparative manner. The partial-wave expansion method for scattering states and averaging over the occupied Fermi sphere are used for an attractive potential energy of Hulthen form. The third-order differential equation of March and Murray [N.H. March, A.M. Murray, Phys. Rev. 120 (1960) 830] for the diagonal of the one-particle density matrix is also investigated, for the same continuous set of energy eigenvalues. The comparative study, performed for the s-type component of the total electron density, explicitly demonstrates the equivalence of the two methods.

Spin-resolved correlations and ground state of a three-dimensional electron gas: Spin-polarization effects

We have studied the spin-resolved correlations in a three-dimensional electron gas having arbitrary spin polarization $\ensuremath{\zeta}$ by using the static and dynamical versions of the self-consistent mean-field approximation of Singwi, Tosi, Land, and Sj\olander, the so-called STLS and qSTLS approaches, respectively. The spin-resolved pair-correlation functions and corresponding correlation energies, static density and spin susceptibilities, and ground-state energy are calculated over a wide range of electron number density and selected $\ensuremath{\zeta}$. Wherever available, our results are compared directly with the recent quantum Monte Carlo studies of Ortiz et al. and Zong et al. The qSTLS approach is found to be in better agreement with the simulation data. As an interesting result, it is found that both the qSTLS and STLS methods underestimate the parallel spin-correlation energy while the antiparallel spin contribution is overestimated to the extent that the total correlation energy is in excellent agreement with the simulation data. Furthermore, a direct comparison among the results of ground-state energy at different $\ensuremath{\zeta}$ reveals, in qualitative agreement with the simulation studies, the existence of a continuous spin-polarization transition on decreasing electron density.

Correlation energy of finite two-dimensional systems: Toward nonempirical and universal modeling

The capability of density-functional theory to deal with the ground state of strongly correlated low-dimensional systems, such as semiconductor quantum dots, depends on the accuracy of functionals developed for the exchange and correlation energies. Here we extend a successful approximation for the correlation energy of the three-dimensional inhomogeneous electron gas, originally introduced by Becke [J. Chem. Phys. 88, 1053 (1988)], to the two-dimensional case. The approach is based on nonempirical modeling of the correlation-hole functions satisfying a set of exact properties. Furthermore, the electron current and spin are explicitly taken into account. As a result, good performance is obtained in comparison with numerically exact data for quantum dots with varying external magnetic field, and for the homogeneous two-dimensional electron gas, respectively.

Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field

We derive a closed analytical expression for the exchange energy of the three-dimensional interacting electron gas in strong magnetic fields, which goes beyond the quantum limit $(L=0)$ by explicitly including the effect of the second, $L=1$, Landau level and arbitrary spin polarization. The inclusion of the $L=1$ level brings the fields to which the formula applies closer to the laboratory range, as compared to previous expressions, valid only for $L=0$ and complete spin polarization. We identify and explain two distinct regimes separated by a critical density ${n}_{c}$. Below ${n}_{c}$, the per particle exchange energy is lowered by the contribution of $L=1$, whereas above ${n}_{c}$ it is increased. As special cases of our general equation we recover various known more limited results for higher fields, and we identify and correct a few inconsistencies in some of these earlier expressions.

Hartree-Fock Ground State of the Three-Dimensional Electron Gas

In 1962, Overhauser showed that within Hartree-Fock (HF) the electron gas is unstable to a spin-density wave state. Determining the true HF ground state has remained a challenge. Using numerical calculations for finite systems and analytic techniques, we study the unrestricted HF ground state of the three-dimensional electron gas. At high density, we find broken spin symmetry states with a nearly constant charge density. Unlike previously discussed spin wave states, the observed wave vector of the spin-density wave is smaller than 2k(F). The broken-symmetry state originates from pairing instabilities at the Fermi surface, a model for which is proposed.

High-frequency properties of systems with drifting electrons and polar optical phonons

An analysis of interaction between drifting electrons and optical phonons in semiconductors is presented. Three physical systems are studied: three-dimensional electron gas (3DEG) in bulk material; two-dimensional electron gas (2DEG) in a quantum well, and two-dimensional electron gas in a quantum well under a metal electrode. The Euler and Poisson equations are used for studying the electron subsystem. Interaction between electrons and polar optical phonons are taken into consideration using a frequency dependence of the dielectric permittivity. As a result, the dispersion equations that describe self-consistent collective oscillations of plasmons and optical phonons are deduced. We found that interaction between electrons and optical phonons leads to instability of the electron subsystem. The considered physical systems are capable to be used as a generator or amplifier of the electromagnetic radiation in the 10 THz frequency range. The effect of instability is suppressed if damping of optical phonons and plasma oscillations is essentially strong.

Structural and electronic properties of expanding fluid metals

It has been theoretically predicted that interacting electron gas suffers a negativecompressibility when the electron density is sufficiently reduced. Dielectric anomaly isanother expression of compressional instability in which the static dielectric function ofelectron gas changes sign from positive to negative. In a medium with a negativedielectric function, like charges can attract. Expanding fluid alkali metals arethe ideal system in which such instability of electron gas can be probed via thestructural response of ions. We have performed x-ray diffraction and small angle x-rayscattering measurements using synchrotron radiation for expanding fluid rubidiumand cesium. On the basis of the experimental results we discuss the existence ofcompressional instability and dielectric anomaly in three-dimensional electrongas.

Dispersion Relations of Longitudinal Plasmons in One, Two and Three Dimensional Electron Gas of Metals

The longitudinal plasmons are the electrostatic collectiveexcitations of the solid electron gas. In this paper, the dispersionrelations of these plasmons for one-, two- and three-dimensionalelectron gas are compactly derived in two approaches with uniformdisturbed Coulomb potentials. The first approach is adopted usuallyin solid state theory that is the so-called random phaseapproximation (RPA) with the Lindhard dielectric function in thelong-wavelength and high-frequency limits. The second method is atypical plasma fluid description that includes the electron fluidequations with the adiabatic process in the jellium model. Thedisturbed electrostatic (Coulomb) potential produced by theoscillation of electron density is dimensionally dependent andderived from the Poisson equation in Appendix B.

Electronic viscosity in a quantum well: A test for the local-density approximation

In the local density approximation (LDA) for electronic time-dependent current-density functional theory (TDCDFT) many-body effects are described in terms of the visco-elastic constants of the homogeneous three-dimensional electron gas. In this paper we critically examine the applicability of the three-dimensional LDA to the calculation of the viscous damping of 1-dimensional collective oscillations of angular frequency $\omega$ in a quasi 2-dimensional quantum well. We calculate the effective viscosity $\zeta(\omega)$ from perturbation theory in the screened Coulomb interaction and compare it with the commonly used three-dimensional LDA viscosity $Y(\omega)$. Significant differences are found. At low frequency $Y(\omega)$ is dominated by a shear term, which is absent in $\zeta(\omega)$. At high frequency $\zeta(\omega)$ and $Y(\omega)$ exhibit different power law behaviors ($\omega^{-3}$ and $\omega^{-5/2}$ respectively), reflecting different spectral densities of electron-hole excitations in two and three dimensions. These findings demonstrate the need for better approximations for the exchange-correlation stress tensor in specific systems where the use of the three-dimensional functionals may lead to unphysical results.

Analysis of the second-order exchange self-energy of a dense electron gas

We evaluate the six-fold integral representation for the second-order exchange contribution to the self-energy of a dense three-dimensional electron gas on the Fermi surface.

Wigner film ground state in a three-dimensional electron gas

The ground state of a three-dimensional electron gas for an intermediate density is investigated within a framework of the generalized gradient approximation. We found that a fully spin-polarized Wigner film is expected to be the ground state at r s ∼ 24 . This critical density is higher than the results calculated within the framework of the local spin density approximation.

Spatial correlations in the electron gas: Path integral Monte Carlo simulation

Thermally excited states of the three-dimensional electron gas in a neutralizing background are computed by path integral Monte Carlo simulation for values of the Wigner-Seitz radius within the interval 5 < r s < 15. Coulomb and exchange interactions, permutation symmetry, and spin state are treated explicitly. Variation of electron correlation functions with density and temperature is analyzed. Quantum effects suppress and enhance spatial correlation at low and high densities, respectively. Transition between the electron-gas states characterized by these opposite trends corresponds to a density of approximately 2.5 × 1021 cm−3. A transition line between liquid-like and gaslike phases is determined in the temperature-density diagram. Weak anisotropy of many-body correlations in the liquid-like state stimulates excitation of spherically symmetric collective rotational modes. The effective short-range pseudopotential exhibits strong temperature dependence due to exchange effects. For strongly correlated systems, the characteristic screening length deviates from that predicted by the Thomas-Fermi screening model ( $$ \sim \sqrt {r_s } $$ ), approaching a linear function of r s. The effective short-range interaction substantially differs from the Yukawa potential in mean field theory. Coulomb interaction shifts the Fermi level up by an order of magnitude or higher, and this effect becomes stronger with decreasing density.

Erratum: Applicability of the ladder theory to the three-dimensional homogeneous electron gas [Phys. Rev. B71, 125105 (2005)

Erratum: Applicability of the ladder theory to the three-dimensional homogeneous electron gas [Phys. Rev. B<b>71</b>, 125105 (2005)

Decoherence of localized spins interacting via RKKY interaction

We theoretically study decoherence of two localized spins interacting via the RKKY interaction in one-, two-, and three-dimensional electron gas. We derive the kinetic equation for the reduced density matrix of the localized spins and show that energy relaxation caused by singlet-triplet transition is suppressed when the RKKY interaction is ferromagnetic. We also estimate the decoherence time of the system consisting of two quantum dots embedded in a two dimensional electron gas.

Changes in nonlinear potential scattering theory in electron gases brought about by reducing dimensionality

Recent work has shown the essential equivalence of stopping power, force-force correlation function, and phase-shift analysis for nonlinear potential scattering in a three-dimensional electron gas. In the present study, we first demonstrate that the above situation is markedly different when the scattering occurs from a localized potential in a two-dimensional (2D) electron gas. Only to second order in the potential do the three methods referred to above precisely agree. However, all these methods can still be applied in 2D, some fully nonlinear evaluation proving possible. The one-dimensional case is also discussed, albeit more briefly. Scattering from a two-center modeling of the localized potential is also calculated, but now only in the Born approximation, due to the added complication of a noncentral potential.

Physics-based model of quantum-mechanical wave function penetration into thin dielectric films for evaluating modern MOS capacitors

We propose an analytical expression of the local carrier density inside silicon and SiO 2 films assuming surface-accumulation and inversion conditions to simulate the capacitance of the modern MOS system. We assume a three-dimensional electron gas system and discuss the penetration of the electron wave function into SiO 2 or high- k material films. It is demonstrated that this penetration slightly influences the capacitance–voltage characteristics. We show how the wave function penetration influences MOS capacitance under accumulation and inversion conditions by proposing advanced local carrier density models for electrons and holes. We also address the influence of the interlayer between the high- k material and the silicon substrate.

The three-dimensional electron gas at the weak-correlation limit: how peculiarities of the momentum distribution and the static structure factor give rise to logarithmic non-analyticities in the kinetic and potential correlation energies

Partial summations of the ring diagrams for the momentum distribution n ( k ) and the static structure factor S ( q ) of the uniform three-dimensional electron gas at the weak-correlation limit are revisited. New light is shed on the thus-far overlooked properties of n ( k ) and S ( q ) . In particular, it is elucidated how the peculiar behavior of n ( k ) near the Fermi surface and of S ( q ) near its q-space origin give rise to the logarithmic divergences in the kinetic and potential energies, respectively. Moreover, the trajectory of the inflexion point of S ( q ) and the jump discontinuity of S ″ ( q ) at q = 2 are analyzed.

Applicability of the ladder theory to the three-dimensional homogeneous electron gas

Emphasizing a proper description of short-range interactions, the ladder theory (LT) is incapable of reliably reproducing any property of the three-dimensional electron gas except for the correlation function at the electron coalescence limit (the on-top density) $g(0)$ and the related large-$k$ tail of the momentum distribution $n(k)$. Because of the violation of the cusp condition, poor accuracy of the predicted $g(r)$ is expected for any nonvanishing $r$. Although the LT yields components of the correlation energy that satisfy the virial theorem for homogeneous interaction potentials, in the case of the Coulomb potential these components turn out to be infinite. A straightforward analysis shows that any effort at alleviating this problem by introducing a long-range screening is bound to violate the virial condition. A commonly employed approximate version of the LT, which avoids Coulomb singularities, yields incorrect energy components and an unphysical momentum distribution despite producing reasonable values of $g(0)$. Since lessening of the approximation worsens the accuracy of the high-density limit of $g(0)$, this result appears to be due to a fortuitous cancellation of errors.