Plasmon Dispersion Curve Research Articles

Thickness dependence of the surface plasmon dispersion in ultrathin aluminum films on silicon

The collective excitation in Al films deposited on Si(1 1 1)-7 × 7 surface was investigated by high-resolution electron-energy-loss spectroscopy (HREELS), X-ray photoelectron spectroscopy (XPS) and scanning tunneling microscopy (STM). At the Al film thickness d < 10 ML, the surface plasmon of Al film has only a small contribution to the observed energy-loss peaks in the long wavelength limit ( q ∥ ≈ 0 ) , while its contribution becomes significant for q ∥ > d - 1 . More interestingly, for thin Al films, the initial slope of the surface plasmon dispersion curve is positive at q ∥ ∼ 0 , in a sharp contrast to bulk Al surface where the energy dispersion is negative. These observations may be explained based on the screening interaction of the space charge region at the Al–Si interface.

Plasmon of Shockley surface states inCu(111): A high-resolution electron energy loss spectroscopy study

High-resolution electron energy loss spectroscopy was used to investigate the low-energy collective excitations of the $\mathrm{Cu}(111)$ surface. Measurements showed a collective mode with an energy of $1.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The measured dispersion of the plasmon mode was negative. We suggest that this mode arises from the oscillation of electrons confined to the $\mathrm{Cu}(111)$ surface within quasi-two-dimensional Shockley surface states. Moreover, we show that the acousticlike mode theoretically proposed for the (111) surface of noble metals is not observed in copper. The behavior of the plasmon dispersion curve and the lack of the acoustic mode call for specific theoretical interpretations of the present experimental results.

Nonsteady-state surface plasmons in periodically patterned structures

The properties of nonsteady-state surface plasmon modes are analyzed for general grating structures and in particular for short pitch, high aspect ratio gratings and lamellar gratings. Numerical simulations of grating structures are described including a transformed coordinate, coupled plane wave approach known as the Chandezon method. A model of radiating light-surface plasmon coupling is then developed that allows for the extension of steady-state calculations involving time independent incident and reflected intensities to nonsteady-state situations involving no incident light but exponentially time dependent decaying emission intensity. Properties such as surface plasmon dispersion curves, electromagnetic field profiles, incident light-surface plasmon coupling efficiency, surface plasmon-radiating light coupling efficiency, overall radiation efficiency, and lifetime or decay constant are analyzed. It is seen that the surface plasmon modes of several structures couple strongly to incident and radiating light producing high surface plasmon-radiating light conversion and short lifetimes.

Substrate reconstruction and electronic surface states: Ag(0 0 1)

We present the result of a combined ab initio theoretical study and ultraviolet photoemission spectroscopy experiment of the electronic surface states of the clean and of the oxygen covered, unreconstructed and missing-row reconstructed, Ag(0 0 1) surface. For the clean and for the unreconstructed oxygen covered surface, theory and experiment find an electronic surface state at about 0.4 eV below the Fermi energy ( E F) at the X ̄ point of the surface Brillouin zone. At the same point, theory predicts the existence of an empty state at +3 eV. Upon reconstruction, the photoemission signal of the filled state is strongly reduced and, according to calculations, the state shifts in energy above E F. The surface interband transition (SIT) between the two states exists thus only for the unreconstructed surfaces and nearly matches the surface plasmon energy. Our investigation confirms therefore the correlation between the presence of this SIT and the anomaly of the surface plasmon dispersion curve of unreconstructed Ag(0 0 1).

Effect of finite temperature correlations on plasmon and coulomb drag in coupled quantum wells

We calculate the temperature dependence of correlations in coupled quantum wells using an STLS formalism generalized to finite temperatures. We investigate the effects of the temperature dependence of the correlations on the acoustic and optical plasmon dispersion curves and on Coulomb drag. Correlations are known to depress the energies of the two plasmons, while finite temperatures tend to increase the energies. We find this can result in considerable cancellation between the two effects at finite temperatures. We find that at temperatures k B T< E F, the local fields do not change appreciably with temperature so that in calculating the temperature dependence of the Coulomb drag using the zero temperature local fields suffices. The pair correlation function within the layers is also found to be insensitive to temperatures for k B T< E F. For higher temperatures than this the pair correlation function for small separations starts to increase as the exchange-correlation hole shrinks.

One-electron excitations, correlation effects, and the plasmon in cesium metal

We study the dynamical electronic response of Cs at a first-principles level. The spatially localized 5p semicore shell induces a physical interplay between crystal local fields and electron correlations, leading to a novel, and relatively large, many-body shift of the plasmon energy. This effect, combined with that of oneelectron transitions into empty states near the plasmon energy, yields a plasmon dispersion curve which is in excellent agreement with experiment for small wave vectors. In addition, our results feature a flat dispersion for large wave vectors, in qualitative agreement with experiment. @S0163-1829~97!07504-8#

Dipolon-plasmon interaction in high-Tc superconducting materials.

In this article interaction between the dipolon waves and the longitudinal plasma waves has been studied adopting a self-consistent field approach. The combined dispersion relation has been obtained which shows that both the dipolon waves and the plasma waves are modified. We discuss our results in relevance to free-electron plasma peaks observed at \ensuremath{\sim}1.1 eV in inelastic electron scattering and optical spectroscopy measurements in high-temperature superconductors. Our calculations for ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ show that the plasma frequency decreases whereas the slope of the plasmon dispersion curve at long wavelength increases because of interaction with dipolon excitations, consistent with the experimental result due to Romberg et al. Our investigation has made it possible to propose that the experimentally observed peak at \ensuremath{\sim}1.1 eV may be due to plasmons interacting with dipolon excitations in high-temperature superconductors. \textcopyright{} 1996 The American Physical Society.

Monte Carlo simulations of the charged boson fluid at T=0.

The diffusion Monte Carlo (DMC) method is used to analyze various properties of the three-dimensional plasma of charged bosons in the homogeneous fluid regime, over the density range 1\ensuremath{\le}${\mathit{r}}_{\mathit{s}}$\ensuremath{\le}160 extending from the so-called uniform limit (${\mathit{r}}_{\mathit{s}}$1) to the crystalline phase (${\mathit{r}}_{\mathit{s}}$\ensuremath{\gtrsim}160). The data on the static density response function \ensuremath{\chi}(k) extend to intermediate and high wave number k the work of Sugiyama, Bowen, and Alder [Phys. Rev. B 46, 13 042 (1992)] and allow us to extract the static local-field factor G(k) for exchange and correlation. The DMC results for the momentum distribution n(k) show that the condensate fraction decreases with increasing coupling strength from 83% at ${\mathit{r}}_{\mathit{s}}$=1 to less than 1% at ${\mathit{r}}_{\mathit{s}}$=160. We also present results for the ground-state energy ${\mathit{E}}_{\mathit{g}}$(${\mathit{r}}_{\mathit{s}}$) and for the structure factor S(k). The results for ${\mathit{E}}_{\mathit{g}}$(${\mathit{r}}_{\mathit{s}}$), n(k), and \ensuremath{\chi}(k) are summarized in analytic interpolation formulas embodying the known asymptotic behaviors. A rigorous upper bound on the plasmon dispersion curve is obtained from the DMC data through a sum-rule argument. \textcopyright{} 1996 The American Physical Society.

Static and dynamic properties of coupled electron-electron and electron-hole layers.

We have investigated coupled layers of electron and hole liquids in semiconductor heterostructures in zero magnetic field for densities ${\mathit{r}}_{\mathit{s}}$\ensuremath{\lesssim}20 using the Singwi-Tosi-Land-Sj\"olander self-consistent formalism generalized for layers of unequal density. We calculate susceptibilities, local fields, pair correlation functions, and the dispersion of the collective modes for a range of layer spacings. We include cases where the densities in the two layers are not equal. We find generally that static correlations acting between layers do not have a large effect on the correlations within the layers. For coupled electron-hole layers we find that as the spacing between the layers decreases there is a divergence in the static susceptibility of the liquid that signals an instability towards a charge-density-wave ground state. When the layer spacing approaches the effective Bohr radius the electron-hole correlation function starts to diverge at small interparticle separations. This effect is a precursor to the onset of excitonic bound states but this is preempted by the charge-density-wave instability. The acoustic plasmon exhibits a crossover in behavior from a coupled mode to a mode that is confined to a single layer. Correlations sometimes push the acoustic plasmon dispersion curve completely into the single-particle excitation spectrum. For layers with different densities the Landau damping within the single-particle excitation region is sometimes so weak that the acoustic plasmon can exist inside the region as a sharp resonance. We find for the electron-hole case that proximity to the charge-density-wave instability has an unusual effect on the dispersion of the optical plasmon mode. \textcopyright{} 1996 The American Physical Society.

Collective excitations in semiconductor superlattices

Collective excitations in semiconductor superlattices are studied beyond tbe random-phase approximation (RPA). The Singwi, Tosi, Land and Sjölander (STLS) theory, which accounts for exchange and short-range correlations effects through an effective potential depending on the structurc factor, is generalized to the layered electron system described by the model of Visscher and Falicov. The exact numerical solution of the STLS self-consistent equations provides information about intraplane and interplane correlations. The plasmon dispersion curves are evaluated for some typical values of the coupling constant r s of the electron system and the distance between the planes for GaAs/AlGaAs semiconductor superlattices. For comparison, the RPA and the Hubbard approximation are also considered.

Collective modes in the two-dimensional electron liquid near the Wigner phase transition

We have investigated the properties of the collective modes of the two dimensional electron liquid in regions of phase space near the Wigner phase transition. We used a new method which we have recently developed for dealing with the strongly correlated electron liquid. We find that the dynamical correlations cause the dispersion curve of the 2D plasmon to pass through a maximum, leading to negative dispersion for largerq values and a much reduced value for the plasmon cut-offqc. It was of interest to discover, on comparing the plasmon dispersion curve with the corresponding curve for the phonon in the Wigner crystal, that the negative dispersion of the plasmon duplicated the turnover of the phonon dispersion curve at the edge of the Brillouin zone,q=1.2G, and that the two curves were in close agreement for allq less than the plasmon cut-off. A new collective mode in the liquid phase on the highq side of the single-particle excitation spectrum was also found to match up with the phonon dispersion curve nearq∼G.

Silicon plasmon resonances in the local-density approximation.

As a continuation of earlier work, we present the results of a local-density-approximation-based calculation of some dielectric properties of silicon. In particular, we have calculated the plasmon-resonance line shape for k\ensuremath{\rightarrow}0 and the plasmon dispersion curves including local-field effects and exchange-correlation corrections. The results are compared with both our earlier empirical-pseudopotential results and experimental data.

Layer-coupled plasmons in a sawtooth-type potassium double-layer model on Si(001)-2 x 1 surfaces.

Using a sawtooth-type potassium double-layer model, we have calculated the layer-coupled interband and intraband plasmon modes of alkali-metal adatoms on Si(001)-2\ifmmode\times\else\texttimes\fi{}1 surfaces. For K adlayer on Si(001)-2\ifmmode\times\else\texttimes\fi{}1 surfaces, our calculated plasmon dispersion curves successfully reproduce the diplike shape in the [100] direction of the overlayer-plasmon dispersion curves observed in an experiment by using angle-resolved electron-energy-loss spectroscopy. The agreement between our calculated results and the experimental results is found to be good.

Study of the platinum/electrolyte interface using surface plasmon excitation at stratified electrodes Part I. Preparation and characterization of the electrodes: Part I. Preparation and characterization of the electrodes

In order to study the platinum/electrolyte interface by surface plasmon excitation we have built up a stratified electrode made of a plasma underlayer covered by a continuous Pt layer. We present the preparation of the samples in UHV, their characterization by SIMS, TEM and surface Auger analysis and their optical and electrochemical behavior. The evidence of the formation of Pt x Al 1− x alloy and its effect on the surface plasmon dispersion curve are discussed.

Surface plasmons on corrugated metal films

The dispersion relation for a surface plasmon, propagating across a corrugated metal film on a dielectric substrate, is obtained by the method of reduced Rayleigh equations. It is found that the surface plasmon dispersion curve has an infinite number of branches. Numerical solutions of the dispersion relation are obtained for a film, characterized by a free-electron metal dielectric function and a sinusoidal profile function.

The dynamic structure function for electron gas

The dynamic structure function S(q, omega ) of the homogeneous electron gas is calculated in a formalism where both the collective and particle-hole excitations of the electron system are described in terms of interacting bosons. The author presents numerical results only for the electron density corresponding to aluminium. The curve S(q, omega ) as a function of omega for a fixed momentum transfer q does not quite agree with the experimentally observed curve, although a definite shift is found in the peak value towards lower energies plus a tail. Also the plasmon dispersion curve is discussed.

Systematic inclusion of the effect of an arbitrary surface profile on the dispersion of surface plasmons

The classical Boltzmann equation approach is developed to systematically include the effect of surface diffuseness in the random phase approximation (RPA) surface plasmon dispersion relation. This is achieved by the introduction of an arbitrary surface potential energy barrier into the distribution function. The resulting Fourier-transformed, linearized equation is solved by a perturbative-iterative scheme based on an expansion of the response function beyond the usual step-function form. The surface plasmon dispersion curves obtained lend support to the more recent experimental results which indicate an almost flat to slightly increasing small wavenumber behaviour. Noticeable dipping of the curves only occurs for broad surface regions, suggestive of surface contamination.

Surface plasmon dispersion for surfaces covered by thin layers supporting longitudinal plasma waves

We analyse the effect of a superficial plasma layer on the substrate surface plasmon dispersion taking into account non local effects related to plasma oscillations in the surface layer. Surface plasmon dispersion and ATR reflectivity curves for an Aluminium surface covered by a potassium film 20 Å thick are computed. We show that new branches exist when longitudinal polarization waves are considered in the surface layer.

Hybrid bulk-surface polaritons for solid plasma slabs in the ω S to ω P frequency range

The existence of a particular surface mode in the ω S-to-ω P frequency range is established, for thick plasma slabs, independently of the dielectric function damping term. The studied mode presents an hybrid behaviour characterized by a standing surface charge oscillation and the propagation in the bulk of partially longitudinal radiations normal to the slab surface. A new interpretation of the plasmon dispersion curve back-bending is deduced. Experimental procedures for putting the hybrid mode in evidence are proposed and applications in photoemission, wave guiding etc. anticipated.

Plasmon structure in the x-ray absorption spectra of metals

The effect of plasmon production on the x-ray photoabsorption spectra of metals has been studied in the framework of the many-body perturbation theory. The plasmon starts to contribute very weakly at the frequency ${E}_{F}+{\ensuremath{\omega}}_{p}^{o}$ (${E}_{F}$ is the absorption-edge frequency and ${\ensuremath{\omega}}_{p}^{o}$ is the frequency of a zero-momentum plasmon). The plasmon absorption edge at this frequency is, in fact, so weak that it does not have any significant effect on the calculated spectrum and possibly cannot be detected. However, a new structure appears at a higher frequency. This structure occurs as a dip of 5%-7% at the frequency ${E}_{F}+{\ensuremath{\omega}}_{p}^{c}$ where ${\ensuremath{\omega}}_{p}^{c}$ is the highest frequency of the plasmon dispersion curve beyond which plasmon production is precluded. The physical significance of ${E}_{F}+{\ensuremath{\omega}}_{p}^{c}$ is that it is the lowest x-ray frequency at which the plasmon excitation can become a real process during x-ray photoabsorption in metals. The existence of the plasmon structure at this frequency allows an estimation of the extent of plasmon dispersion in metals.