Plasmon resonances of Ag(001) and Ag(111) studied by power density absorption and photoyield

doi:10.1016/j.susc.2013.02.005

Surface Science

Volume 615, September 2013, Pages 6-20

https://doi.org/10.1016/j.susc.2013.02.005 Get rights and content

Abstract

This paper models the surface and bulk plasmon resonances in photoabsorption and photoelectron spectra (PES) of the Ag(001) and the Ag(111) surfaces in the region of 2.8–10 eV excited with a p or transverse magnetic linearly polarized laser incident at 45°. Using the recently developed vector potential from electron density-coupled integro-differential equations (VPED-CIDE, [1], [2]) model, we calculate the electron escaping probability from the power density absorption, Feibelman's parameter d_⊥, the reflectance and the Fermi PE cross section. In the PES experiment the work function is lowered from 4.5 to 2.8 eV by adsorption of sodium. In our model, this lowering is introduced by adding a phenomenological term to the DFT-LDA model potential of Chulkov et al. [3]. For both Ag(001) and Ag(111), the calculated observables display two plasmon resonances, the multipole surface at 3.70 eV and the bulk at 3.90 eV, in fair agreement with the experimental PES of Barman et al. [4], [5] and the reflectance. Except for the Fermi PE cross section of Ag(001) which does not display the multipole surface plasmon resonance at 3.70 eV. This poor result is probably due to a poor calculation of the conduction band wave functions obtained from the Schrödinger equation using the modified DFT-LDA model potential of Chulkov et al.

Highlights

► Ampère–Maxwell equation modeling of plasmon resonances in Ag(001) and Ag(111) ► Good agreement between calculated observables and experimental photoelectron spectra. ► PES experimental–theoretical disagreement in Ag(001), poor quality final state wf ► Vacuum maximum and zero surface induced by the laser electron density as in TDDFT

Introduction

The plasmon resonances appear on the Ag(001) and Ag(111) surfaces in the 3–4 eV region. These resonances are used in a wide class of applications ranging from physics to medicine (see e.g. Sarid and Challener [6]).

Experimentally the photoelectron spectra (PES) of low index silver surfaces have been obtained by several authors [4], [5], [7], [8], [9], [10], [11], [12]. To lower the work function of the clean silver surfaces from 4.5 to 2.8 eV and observe the surface plasmon resonances, Barman et al. [4], [5], [12] adsorbed 1–180 ML of Na. Then these authors measured the 2.8–10 eV PES and found a multipole surface plasmon resonance $ω$ _m at about 3.70 eV. One can avoid the use of sodium by performing two photon photoemission experiments (see e.g. Ueba and Gumhalter [13] and Winkelmann et al. [11]). However to our knowledge no measurements of the two photon PES have been performed in the region of interest.

The electron energy loss spectra (EELS) [14], [15], [16], [17], [18], [19] also revealed a resonance in the 3–4 eV region first identified as a monopole $ω$ _s then as a multipole $ω$ _m surface plasmon resonance. Using the inverse photoemission technique Himpsel and Ortega [20] found the multipole $ω$ _m surface plasmon resonance at about 4 eV. Using the material constants taken from Palik's tables [21], [22] Marini et al. [23] and other authors calculated at 3.90 eV a dip in the reflectance corresponding to the bulk plasmon resonance.

To study surface plasmon resonances of metallic surfaces Liebsch et al. [24], [25], [26], [27], [28], [29] have developed a “s–d” model. This model is based on the dynamical response function, Poisson equation and the time dependent density functional theory (TDDFT) in its local density approximation form (TDLDA). In the valence region of silver two bands “5s” and “4d” participate in the interaction. The “5s” electron band, modeled as a semi-infinite jellium system, is characterized by a nonlocal response function χ(z,z′,q_∥, $ω$ ). The “4d” electron band is modeled as a polarizable medium using the dielectric function of the bulk. When calculating the EELS, the “s–d” model predicts: bulk plasmon $ω_{p}^{*} \approx ω_{p} / \sqrt{ε_{d}} \approx 3.8$ eV, monopole surface plasmon resonance $ω_{s}^{*} \approx ω_{p} / \sqrt{1 + ε_{d}} \approx 3.7 eV$ and multipole surface plasmon resonance $ω$ _m^∗ ≈ 0.8 $ω$ _p ≈ 6. 7 eV( $ω$ _p = 8. 375 eV) $ω$ _p. The EELS experiments [14], [15], [16], [17], [18], [19] do not cover the region above 6 eV whereas the PES of Barman et al. [4], [5], [12] does but no resonance appears at 6.7 eV. In the region 2.8–10 eV Marini et al. [23] calculated the EELS and the reflectance using a GW method. Their spectrum presents a sharp feature at about 4 eV and another large feature above 8 eV. Contrary to a DFT-LDA calculation and in agreement with the experiment, their GW reflectance presents a single bulk plasmon resonance dip at 3.92 eV.

A “s–d” model, calculating the ‘5s’ band using DFT-GW approximation and the ‘4d’ one as a polarizabile background, has been successfully used by Garcia-Lekue et al. [30] to calculate the widths of the surface and image states of Ag(001) and Ag(111). This demonstrates that a model studying silver surfaces should take into account these two bands.

In this paper we use the recently developed vector potential from electron density-coupled integro-differential equations (VPED-CIDE, Raseev [1], [2]) model to study the laser excitation of the low index silver surfaces in the 2.8–10 eV region. Section 2 summarizes our model and presents the observables. Section 3 discusses the Chulkov et al. [3] DFT-LDA potential modified to include the adsorbed sodium, the resulting projected band structure and the choice of the material functions. Section 4 presents our results and Section 5 discusses and concludes the paper.

Section snippets

Summary of the VPED-CIDE model

Consider the Ampère–Maxwell equation in the classical approximation written in SI or in the atomic system of units, i.e. ε₀μ₀ = 1/c² with ε₀ and μ₀ the vacuum permittivity and permeability and c the speed of light $\vec{\nabla} \times \vec{H} - \frac{\partial \vec{D}}{\partial t} = \vec{J},$ where $\vec{H}$ , $\vec{D}$ and $\vec{J}$ are the magnetic field, the displacement and the current density. Assuming linear interactions, the matter appears in the Ampère–Maxwell equations through the constitutive tensor relations for the displacement $\vec{D}$ , the polarization $\vec{P}$ and the current

Preliminary calculations

The technical details of the VPED-CIDE model are given in our preceding papers, refs. [1], [2]. Briefly, in the numerical calculations of the vector potential function of the coordinate z, one uses a large slab with the laser incident on the left surface. The wave functions entering in the calculation of the unperturbed electron density ρ(z), Eq. (4), and of the transition moment, Eqs. (16), (17), (18), are obtained by solving the Schrödinger equation with the model potential of Chulkov et al.

Plasmon resonances in Ag(001) and Ag(111)

Before discussing the spectra of the observables of Ag(001) and Ag(111) surfaces calculated using VPED-CIDE model let us recall the retained parameters of our model: i) for the V₅(z) potential (Eq. (20)) we use ζ = 0.2 and V_δϕ = 1.63 eV; ii) for the separation of the bound and conduction electron polarizabilities $K$ the parameters r_s = 3.0135 a.u., m^∗ = 0.96 and τ = 3.1 · 10^− 14 s^− 1 taken from the work of Johnson and Christy [44]; iii) for the bound electron polarizability ${\tilde{K}}^{b} (ω)$ the Palik's experimental material

Discussion and conclusions

This paper presents a theoretical study of the plasmon resonances in the PES spectrum of Ag(001) + Na and Ag(111) + Na low indexed surfaces using the recently developed VPED-CIDE model [1], [2]. We have calculated the EEPY-PDA (Y, Eq. (11)), Feibelman's parameter (d_⊥, Eq. (12)), the non local reflectance (R, Eq. (14)) and the Fermi photoelectron cross section (σ_F, Eq. (15)). To analyze the surface plasmon resonances we have also calculated the induced electron density (δρ Eq. (13) from the

Acknowledgments

We are indebted to Andrew Mayne for the critical reading of the manuscript. We acknowledge the use of the computing facility cluster GMPCS of the LUMAT federation (FR LUMAT 2764).

References (52)

E.V. Chulkov et al.
Surf. Sci.
(1999)
S.R. Barman et al.
Surf. Sci.
(2004)
T. Miller et al.
Surf. Sci.
(1997)
H. Ueba et al.
Prog. Surf. Sci.
(2007)
K. Kempa et al.
Surf. Sci.
(1983)
P.J. Feibelman
Prog. Surf. Sci.
(1982)
J.V. Lill et al.
Chem. Phys. Lett.
(1982)
F. Hao et al.
Chem. Phys. Lett.
(2007)
G. Raşeev
Eur. Phys. J.
(2012)
G. Raşeev
Eur. Phys. J.
(2012)

E.D. Palik

Handbook of Optical Constants of Solids II

(1991)

Cited by (9)

Plasmonic decay into hot electrons in silver
2023, Progress in Surface Science
Light at optical frequencies interacting with a metal surface can excite interband quantum transitions, or intraband currents at frequencies approaching the PHz range. Momentum conservation enables the interband excitation to occur in first order as a dipole transition, while intraband excitations involve second-order momentum scattering processes. The free electron response to optical fields can also be collective, causing the optical field to be screened by the multipole plasmon response. We describe the exitation of single crystal silver surfaces in the region where the dielectric response transits from negative to positive passing through the epsilon near zero (ENZ) condition. There, electrons can no longer screen the optical field, so that it penetrates as a collective charge density wave of the free electron plasma, in other words, as a bulk transverse or longitudinal plasmon field. We examine two-photon photoemission (2PP) signals from Ag(1 1 1), (1 0 0) and (1 1 0) surfaces through the ENZ region under conditions where intraband, and interband single particle, and bulk plasmon collective responses dominate. We are specifically interested in the bulk plasmon decay into plasmonic photoemission. Plasmonic decay into excitation of electrons from the Fermi level, which we observe as a nonlinear 2PP process, has been established for the free electron and noble metals, but its significance to transduction of optical-to-electronic energy has not penetrated the plasmonics community. 2PP spectra show evidence for intraband hot electron generation, interband surface and bulk band excitation, and nonlinear bulk plasmon driven plasmonic single particle excitation. Because the intraband and plasmonic decay into hot electron distributions have been extensively considered in the literature, without reference to explicit experimental measurements, we discuss such processes in light of the directional anisotropy of the electronic structure of single crystalline silver. We note that projected band gaps in silver exclude large regions of the unoccupied state density from hot electron generation, such that it predominantly occurs in the (1 1 0) direction. Moreover, the excited hot electron distributions do not follow expectations from the joint density of the occupied and unoccupied states of a free electron metal, as assumed in majority of research on hot electron processes. We describe the strongly anisotropic hot electron distributions recorded by 2PP spectroscopy of Ag surfaces, and the plasmonic photoemission process that occurs on all surfaces irrespective of the momentum-dependent single particle band structure of silver. Plasmonic photoemission, or its linear analog that excites hot electrons at energies below the work function of Ag, is an important process for harvesting hot electron energy in photocatalytic and electronic device applications because the plasmon energy is not distributed between an electron and hole. This plasmonic decay channel is robust, but many aspects raise further questions. The accompanying publication by Gumhalter and Novko discusses the plasmonic photoemission from a theoretical point of view and its extension to Floquet engineering, as an exploration of novel plasmonic excitation processes in metals.
Complementary perturbative and nonperturbative pictures of plasmonically induced electron emission from flat metal surfaces
2023, Progress in Surface Science
Recent high resolution multiphoton photoemission studies of low index Ag surfaces have revealed spectral features whose energetics was controlled by multiple quanta of plasmon energy rather than the photon energies appearing in the standard Einstein’s one-electron energy scaling in photoeffect. To elucidate these peculiar features we introduce and elaborate the mechanism of bulk- and surface plasmon-induced electron emission from metal surfaces, conveniently termed plasmoemission. Our point of departure is the cloud of hot plasmons generated in the primary interactions of external electromagnetic (EM) field(s) with the system. Such hot plasmon distributions acquire the form of a coherent state plasmonic bath which may serve as a source of energy and momentum required for electron emission from the system. These plasmoemission channels are complementary to the standard photoemission channels driven directly by the primary EM fields. Adopting this paradigm we analyze the plasmonically induced electron yield by using perturbative and nonperturbative approaches in the length and velocity gauge representations of the electron–plasmon interaction. Pursuing the perturbative approach to one- and two bulk plasmon-induced electron emission from Ag(110) surface we have investigated the effects of underlying band structure on the electron yield and proposed as how to discern them in the measured spectra. This also enables putting the perturbative descriptions of plasmoemission into the general context of pump–probe spectroscopy. The more demanding nonperturbative approach has been implemented by invoking the Volkov ansatz type of electron wavefunction in the velocity gauge and applied to surface plasmon-induced electron emission from quasi-two-dimensional surface bands on Ag(111). In this formulation the electrons emanate from the surface Floquet bands generated from the parent surface state band by the action of prepumped plasmonic coherent state field. A quantitative assessment of the multiplasmoemission yield is presented in terms of the plasmonic coherent state parameters controlled by the external pumping fields. The opposite limit of plasmonically induced electron tunneling regime is recovered in the quasistatic strong field limit. The pump–probe concept can be established also in the nonperturbative picture albeit in a more complex form.
Electron emission from plasmonically induced Floquet bands at metal surfaces
2022, Physical Review B
Electron emission from plasmonically induced Floquet bands at metal surfaces
2022, arXiv
Plasmonic Photoemission from Single-Crystalline Silver
2021, ACS Photonics
Ultrafast Photoemission Electron Microscopy: Imaging Plasmons in Space and Time
2020, Chemical Reviews

View all citing articles on Scopus

View full text

Plasmon resonances of Ag(001) and Ag(111) studied by power density absorption and photoyield

Abstract

Highlights

Introduction

Section snippets

Summary of the VPED-CIDE model

Preliminary calculations

Plasmon resonances in Ag(001) and Ag(111)

Discussion and conclusions

Acknowledgments

Surf. Sci.

Surf. Sci.

Surf. Sci.

Prog. Surf. Sci.

Surf. Sci.

Prog. Surf. Sci.

Chem. Phys. Lett.

Chem. Phys. Lett.

Eur. Phys. J.

Eur. Phys. J.

Phys. Rev. B

Modern introduction to surface plasmons

Phys. Rev. B

Phys. Rev. Lett.

Phys. Rev. B

Phys. Rev. B

Curr. Sci.

Phys. Rev. Lett.

Phys. Rev. Lett.

Phys. Rev. B

Phys. Rev. Lett.

Phys. Rev. B

Phys. Rev. B

Phys. Rev. B

Handbook of Optical Constants of Solids

Handbook of Optical Constants of Solids II