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Progress in Surface Science 78 (2005) 1–39 www.elsevier.com/locate/progsurf

Review

Time- and angle-resolved two-photon photoemission studies of electron localization and solvation at interfaces P. Szymanski 1, S. Garrett-Roe, C.B. Harris

*

Department of Chemistry, University of California, Berkeley, CA 94720, United States Chemical Sciences Division, E.O. Lawrence Berkeley National Laboratory, Berkeley, CA 94720, United States

Abstract We review recent work in the study of interfacial electronic states and electron–adsorbate interactions with time- and angle-resolved two-photon photoemission (2PPE) spectroscopy. Results for interfaces between noble-metal surfaces and organic as well as inorganic dielectric overlayers are presented. Layer structure and thickness have pronounced effects on the spatial extents, binding energies, and dynamics of image-potential states (IPS) and molecular orbitals. The transition from delocalized to localized states in the plane of the interface can also occur dynamically through electron-induced nuclear motion in the overlayer. An important example of this class of phenomenon is the formation of polaronic states from initially delocalized IPS, which occurs on sub-picosecond timescales. Dynamic energy relaxation through electron solvation by molecular dipoles, the analogue of the dynamic Stokes shift in bulk solvents, may also accompany localization on ultrafast timescales, and has become the focus of much recent experimental and theoretical interest. The interplay of a static layer structure and an evolving potential from the adsorbate creates a rich environment for interfacial electron dynamics, as evidenced by the alcohol/Ag(1 1 1), nitrile/Ag(1 1 1), and D2O/Cu(1 1 1) systems. We conclude with a discussion of recent attempts to determine the spatial extent of localization parallel

*

Corresponding author. Tel.: +1 510 642 2814; fax: +1 510 642 6724. E-mail address: [email protected] (C.B. Harris). 1 Present address: Department of Chemistry, Brookhaven National Laboratory, Upton, NY 11973, United States. 0079-6816/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.progsurf.2004.08.001

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P. Szymanski et al. / Progress in Surface Science 78 (2005) 1–39

to the interface for electrons following localization and solvation using experimental measurements of the photoelectron distribution in momentum space. Published by Elsevier Ltd. Keywords: Two-photon photoemission; Image-potential states; Angle-resolved photoemission; Ultrafast dynamics; Dielectric/metal interface; Adsorbate molecular orbitals; Localization; Small polaron; Electron solvation; Spatial extent in two dimensions

Contents 1. 2. 3.

4.

5.

6.

7.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Static electron localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Benzene/Ag(1 1 1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Self-assembled monolayers: methylthiolate/Ag(1 1 1) . . . . . . . . . . . . . . . . . . 3.4. Monolayer films of C60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dynamic localization: small polaron formation . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Qualitative scaling arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Quantitative analysis of small polaron formation . . . . . . . . . . . . . . . . . . . . . Solvation and localization at polar interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Introductory remarks and background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Dynamic response of polar organic adsorbates. . . . . . . . . . . . . . . . . . . . . . . 5.3. Models for the dynamic polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Dynamics of electrons at ice/metal interfaces . . . . . . . . . . . . . . . . . . . . . . . . Spatial extent of localized interfacial states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Theoretical basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Experimental examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 4 7 7 8 9 11 12 12 14 17 17 19 25 28 30 31 34 35 35 36

1. Introduction The study of the electronic properties of interfaces between dissimilar materials constitutes a major research area of fundamental interest and technological significance. Chemical and physical processes occurring at interfaces may be understood on a microscopic level in terms of the associated energy levels and dynamics of the interfacial electrons. Hot electrons, for example, can induce surface chemical reactions or desorption of adsorbates [1]. Molecular anion formation via electron transfer from the metal substrate has been implicated as the initial step in these processes [2,3]. Electron trapping and scattering at the interface can drastically affect carrier transport properties and the performance of devices [4,5].


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The sensitivity of interfacial electrons to the composition of the interface may also be exploited to probe the dynamics of adsorbed molecules. A strong electron–adsorbate interaction can cause an electron-induced adsorbate reorganization [6–8] similar to electron solvation in liquids [9,10]. Studies of solvation at an intrinsically asymmetric environment such as a two-dimensional interface is particularly interesting because the reduced dimensionality and hindered solvent motion can result in electron dynamics distinct from those in the isotropic material [11–14]. Characterizing the energy levels of interfacial electrons as a function of the adsorbate reorganization time can elucidate the time scales and mechanisms of both the electronsÕ response as well as the molecular motions of the adsorbate overlayer. To address these issues, an investigation of the properties associated with films of molecular thickness in a well-controlled fashion is necessary. Much of the research on electrons at interfaces has involved the study of imagepotential states (IPS). The IPS are bound by the interaction between an electron outside of a surface and the polarization it induces at that surface (Fig. 1). The polarization can be treated formally by replacing it with the oppositely-charged image of the electron reflected across the surface plane, a configuration that reproduces the boundary conditions of the original problem [15,16]. The resultant one-dimensional Coulombic potential, the image potential (IP), supports an infinite series of hydrogenic states. For metal surfaces, the energies of IPS in electron volts are given by En ¼

0:85eV ðn þ aÞ

2

þ V 0;

ð1Þ

E Surface Polarization

Conduction Band

n=2

z E vac n=3

n=1 ++

+

+

+ ++ +++ + ++ + + ++ +

+ +

Fermi Level Valence Band

Fig. 1. An electron near a surface polarizes the material. This induced polarization binds the electron by forming a potential well that consists of the image potential. Solving the analogous one-dimensional hydrogen atom problem gives rise to Rydberg-like or image-potential states (IPS) that converge toward the vacuum energy level Evac. The relative positions of the IPS with respect to the bulk bands apply to both Ag(1 1 1) and Cu(1 1 1) [17].

4


where n represents the principal quantum number and a is the quantum defect parameter [17–19]. The series converges to V0, which is equal to the vacuum energy for a uniform surface. Image-potential state electrons reside only a few angstroms outside of the interface. The hydrogenic model [20] gives an expectation value of ˚ and 12 A ˚ hzi = 6a0n2, where a0 is the Bohr radius [21]. This distance is roughly 3 A for n = 1 and n = 2 IPS, respectively, making them sensitive to changes in the interfacial electrostatic potential. It has been shown that the surface electronic structure modified by the overlayer also changes the energy and lifetime of the IPS [22]. For a more detailed description of the properties of IPS and calculations of their energies, the reader is referred to review articles by Memmel [19], Fauster and Steinmann [17], Harris et al. [22], and Osgood and Wang [23]. It is the purpose of the present review to focus on recent work using two-photon photoemission (2PPE) to study electron localization, both static and dynamic, and the related process of electron solvation at dielectric/metal interfaces. Both IPS and the molecular orbitals (MO) of adsorbed molecules will be discussed. The angle- and time-resolved 2PPE technique will be discussed in Section 2, followed by a review of structurally-induced localization at interfaces (Section 3). Dynamic localization of electrons by nonpolar (Section 4) and polar (Section 5) adsorbates are covered separately, where the distinction is due to the significant dynamic energy relaxation caused by the latter. Section 5 also compares the localization and solvation that occur at interfaces to the analogous phenomena experienced by excess electrons in bulk liquids. Finally, a discussion of attempts to determine the spatial extent of localization parallel to the interface is presented in Section 6.

2. Experimental methods Two-photon photoemission (2PPE) is a pump–probe spectroscopic technique for exploring interfacial electronic states. Unlike conventional photoemission, which uses one-photon processes, 2PPE is capable of examining initially unoccupied as well as initially occupied states. Initially unoccupied states, such as IPS, as studied by 2PPE are illustrated in Fig. 2a. Electrons from below the Fermi level (EF) of a metal substrate (or from an initially occupied surface [17] or adsorbate [24] state) are excited into an intermediate state with a pump pulse, hm1. The probe pulse hm2 photoemits the excited-state electron by giving it energy greater than the vacuum level, Evac. The binding energy of the unoccupied electronic states can be calculated by measuring the kinetic energy, Ekin, of the photoemitted electrons and then subtracting the energy of the probe pulse photon. This experiment can easily be performed in a time-resolved fashion by delaying the probe pulse with respect to the pump. The excited state lifetimes can then be determined by measuring the number of electrons detected as a function of the time delay. The case of an initially occupied interfacial state is shown in Fig. 2b. Without resonant excitation into a real intermediate state, 2PPE occurs via a virtual state in a coherent two-photon process. The coherences between the initial, intermediate,

P. Szymanski et al. / Progress in Surface Science 78 (2005) 1–39 hν2 e-

E vac En

hν2 e-

} Ekin

Evac

5

} Ekin

hν1 hν1

EF

EF

(a)

Ei

(b) 2hν hν

Dichroic Mirror

MicroTranslation channel Plate Stage

Frequency Doubling

fs laser Flight Tube

eED LE g rin te p ut tu Sp Se

(c)

Sample Mass Spect

UHV Chamber

Fig. 2. (a) Schematic energy diagram for two-photon photoemission (2PPE) of an initially unoccupied state at an interface. (b) The 2PPE process for an initially occupied state at an interface. (c) Schematic of a two-color 2PPE experimental apparatus with a tunable femtosecond laser. Dielectric/metal interfaces may be formed by vapor-phase deposition of materials onto a substrate cooled by liquid nitrogen or liquid helium.

and final states do not dephase instantaneously but rather evolve due to scattering events on finite timescales [25,26]. A well-studied example is the Shockley-type surface state of Cu(1 1 1), whose narrow line width reflects the finite lifetime of the hole [25,26]. In general, however, the relevant dephasing times are below 20 fs [26]. This fact is often used to estimate the instrument function relevant to lifetime measurements of longer-lived states. In a two-color experiment probing IPS, for example, photoemission from an occupied state is used to estimate the cross correlation of the two pulses, neglecting the finite response time of the material [17,26]. A comparison of the diagrams in Fig. 2a and b reveals a method for determining the occupancy of interfacial states by means of a wavelength survey. As the pump and probe energies are scanned by hDm1 and hDm2, respectively, the kinetic energies of electrons photoemitted from initially unoccupied states will only vary by hDm2. On the other hand, a shift in energy equal to h(Dm1 + Dm2) must occur if the photoemission is from an initially occupied state. The dependence on the pump and probe frequencies assumes photoemission into a continuum; photoemission into a finalstate resonance produces a feature in the spectrum whose energy is independent of

6


frequency [27]. Care must be taken when assigning occupancies that the states are actually of the interface, as the above rules also do not hold when the photons induce a bulk interband transition [28,29]. To fully explore the dynamics of electrons at interfaces, the experimental technique should probe the interfacial band structure and the electron dynamics on the femtosecond time scale. A typical layout for a two-color 2PPE experiment is shown in Fig. 2c. Many recent experiments have employed mode-locked Ti:sapphire laser systems, which operate in the visible (>700 nm) and near-IR, with tunability throughout the visible and ultraviolet regions provided by standard nonlinear optics. The pump is often the second or higher harmonic of the fundamental laser frequency. In a two-color experiment, the pump and probe beams may be easily separated and recombined by means of dichroic mirrors. A translational stage introduces the variable delay between pump and probe pulses (Fig. 2c). A common variation on this method is monochromatic 2PPE without a variable pump–probe delay [24,30], which is appropriate mainly for determining electronic structure. Petek and Ogawa have performed time-resolved, monochromatic 2PPE by means of a Mach–Zehnder interferometer [26]. Time-of-flight electron detectors (as shown) and hemispherical energy analyzers have both been used successfully, the relative merits of each discussed in an earlier review [26]. To date, 2PPE has been applied to a diverse range of systems and problems: the clean surfaces of magnetic and nonmagnetic metals [17,31–33], semiconductors [34– 37], high-Tc superconductors [38], hot electron and hole dynamics [25,26,39,40], quantum wells [17,22,41,42], small polaron formation [6,7,43,44], the band structures of aromatic/metal interfaces [45–50], chemisorbed atoms and molecules [24,51–55], interfacial electron solvation by polar adsorbates [7,8,44,56–58], the identification of different modes of adsorbate layer growth [17,56], and scattering of electrons by defects and terrace sites [59–61]. The band structure at the interface can be determined by measuring the angledependence of the photoelectron kinetic energy (Fig. 3). Photoemission at well-ordered interfaces preserves the electron momentum parallel to the surface (hk k ) which can be determined experimentally by measuring the angle of emission, as

Delocalized state

θ

e-

E vac

detector axis sample

EF

p = h k|| sin θ ||

(a)

Evac

hν

0

Localized state

kll

EF

hν

0

kll

(b)

Fig. 3. (a) Schematic diagram for the photoemission process of angle-resolved 2PPE. (b) The dependence of photoelectron kinetic energy on parallel momentum hk k is illustrated for delocalized and localized states.


pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2me Ekin sin h; kk ¼ h

7

ð2Þ

with me being the free-electron mass and h the emission angle [19,62]. The quantity kk is referred to as the parallel component of the wavevector of the photoelectron, and the dependence of energy on kk is termed the stateÕs dispersion. For delocalized electrons behaving like free particles parallel to the interface, the angle-resolved 2PPE data will exhibit a parabolically dispersive band characterized by an effective mass (m*) close to the free-electron value (me) Ekin ¼ En þ

2 k 2k h 2m

;

ð3Þ

where En is the energy of the interfacial band at kk = 0. The IPS are typically delocalized in their parallel degrees of freedom, as the potential that gives rise to the states acts only along the surface normal. On the other hand, spatially localized electrons produce nondispersive flat bands. Using the same free-particle basis set as for the photoemitted electrons, a localized state is a superposition of many plane waves. Regardless of the parallel momentum measured, the electron is photoemitted from the same state, so the kinetic energy no longer depends on kk. The signal intensity as a function of h is a reflection of the weight of the given kk state mixed into the localized state. The electronic properties and dynamics of interfaces are critically influenced by the structures of the surface and overlayer. Any systematic study aimed at understanding interfacial properties must therefore control layer structure as much as possible, for which ultrahigh vacuum technology is well-suited. To characterize the various processes that may cause electrons to localize, it is necessary to collect photoemission spectra as a function of angle, surface coverage, and, optionally, delay time. These points are central to the discussion in the remainder of the paper.

3. Static electron localization 3.1. Introduction Electron localization has been observed in many 2PPE experiments, but we are just beginning to understand in detail the mechanisms that cause the electron to localize. The localization can be either static or dynamic. The concept of static vs. dynamic localization refers to whether or not the localized state may be populated directly. If favorable conditions for localization at the interface are not present initially, the electron may localize through self-trapping and the involvement of nuclear coordinates. Examples of static localization that we discuss here are cases where layer structure plays an important role (e.g. methylthiolate/Ag(1 1 1) [24] and C60/

8


Cu(1 1 1) [63]), or where structural disorder induces electron localization (benzene/ Ag(1 1 1) [45]). We save discussions of dynamic self-trapping to Section 4 and localization coupled to solvation to Section 5. There is a wide variety of models to describe electron and exciton localization. Though diverse in their origin and application, the physical pictures behind them are all related. Any model Hamiltonian used to describe a system in which localization may occur contains terms that tend toward delocalization—most importantly the kinetic energy of the electron—as well as terms in the Hamiltonian that tend to collapse the electron to one or a few lattice site(s). Kinetic energy tends toward delocalization because the kinetic energy, hT^ i ¼ 12 r2 wð~ rÞ, is minimized when the curvature of the electron wavefunction is as small as possible, that is, when the electron is spatially extended. In a 2PPE experiment, these eigenfunctions of momentum correspond to particular parallel momentum states, and form a band with a parabolic dispersion. In tight binding pictures, the kinetic energy of the particle is present in the Hamiltonian as a transfer integral—energy is gained by transferring the particle of interest from one site to the next. The localization terms vary depending on the physical situation and are the primary distinction between models. Examples of interactions that can induce charges to localize are electron–phonon interactions, where the presence of the electron at a specific site can decrease the site energy (polaron formation), or a disordered set of site energies (disordered energetic landscape in Anderson localization) [64]. 3.2. Benzene/Ag(1 1 1) Benzene adsorption on noble metal surfaces has been studied with a variety of techniques [50,65–67]. The first monolayer (ML) grows with the plane of the molecule parallel to the surface, while the second monolayer adopts a standing up phase akin to the herringbone structure that many aromatic molecules adopt in crystals. Beyond 2 ML, the film is comprised of amorphous multilayers. Fig. 4a shows the TPPE spectra of the n = 1 IPS for 2, 3.5, and 4 ML of benzene [45]. As the coverage increases, a new feature grows in at higher kinetic energy. This featureÕs energy is independent of parallel momentum (Fig. 4), which suggests that it is a localized state. This localization, however, is due to the structural disorder of the system. The assignment is supported by the observation that this feature disappears with annealing of the benzene film at temperatures too low for desorption. In Fig. 4, the localized state appears at a higher energy than the bottom of the delocalized state band. This reflects the additional energy of confining the electrons to the small structural defects of the layer. This is consistent with experiments of Ag on Pd(1 1 1) surfaces which resolved quantum confinement and increased energy of the IPS electrons on Ag islands [17]. Unannealed films of benzene offer an example of disorder causing localization of the interfacial electrons. The 2PPE spectra also give us some picture of what is happening to cause the localization in this case. Namely, because the energy of the localized state is higher than the delocalized state, it seems reasonable that the disorder causes barriers to the electronÕs propagation along the surface rather than defect


9

(a) III.

Normalized Electron Counts (A.U.)

II. I.

3.05 3.10 3.15 3.20 3.25 3.30

(b)

0o

III.

4.4o 8.4o 12.4o 16.4o 3.05 3.10 3.15 3.20 3.25 3.30

E - E F (eV) Fig. 4. (a) The development of the localized n = 1 IPS of benzene/Ag(1 1 1) as a function of coverage at 0°. I, II, and III correspond to 2 ML, 3.5 ML, and 4 ML, respectively. The two peaks in III, from right to left, correspond to the localized state and the delocalized n = 1 IPS. (b) Dispersion of III. The delay time between the excitation and probe pulses is 70 fs for the 0° spectra and 170 fs for all other angles, which serves to highlight the longer-lived localized state.

or trap sites which attract the electron. That is, the positive energy of confinement is not offset by a negative trapping energy for localizing the charge, something like a particle-in-a-box. Another possibility is that accumulated phase shifts due to scattering events cause the electron to localize [41]. In either case, as the layer anneals the disorder disappears and the delocalized band dominates the spectrum. 3.3. Self-assembled monolayers: methylthiolate/Ag(1 1 1) In the case of methylthiolate/Ag(1 1 1), a different mechanism of localizing the interfacial electrons is active. Thiols and disulfides on noble metal surfaces have received a great deal of attention because of the structural reorganization that they spontaneously undergo, wherein the films spontaneously adopt highly ordered structures at a critical surface density. The reader is referred to recent reviews of the literature [68,69]. Because the organization is due to the molecular interactions

10


between the thiolates and the substrate and between each other rather than any external patterning (e.g. lithography), this is known as self-assembly. The possibility to use a ‘‘bottom-up’’ approach to assemble molecules for molecular electronic devices has sparked a wealth of research on these systems. The details of the electronic structure of these films, however, will determine their ability to fulfill the promise for molecular electronic devices [70,71], so 2PPE is an important tool to probe both the occupied and unoccupied structure of these self-assembled monolayers. Dimethyldisulfide dissociatively chemisorbs on Ag(1 1 1), causing the S–S bond to break and two Ag–S chemical bonds to form [69]. Monochromatic 2PPE is able to access the highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO) of this chemical bond and probe their properties as a function of the surface density [24]. The assignment of the occupied and unoccupied electronic states follows directly from the wavelength dependence of the statesÕ kinetic energies (Fig. 2a and b). Two-photon photoemission shows that the Ag–S LUMO is very sensitive to the structure of the thiolate film. This sensitivity shows not in the energetic positions of the states, but, rather, their dispersions. At low coverages, approximately 1 L exposure, the Ag–S LUMO has a very large effective mass, indicating that the state is localized (Fig. 5, circles). At intermediate coverages, (2.5 L exposure), the localized electrons are accompanied by delocalized electrons which have an effective mass m* = 0.5me (Fig. 5, triangles). Finally, at a saturated monolayer (4 L), there are only delocalized electrons (Fig. 5, squares). This can be understood using the phase diagram and self-assembly phase transition of the thiolate covered surfaces [72]. At low surface densities, the methylthiolates lie mostly flat to the surface where they are a mobile ‘‘lattice gas’’ (Fig. 6). Here, each S–Ag bond is isolated from the others, and the states are highly localized.

2.1 1 langmuir 2.5 langmuirs 4 langmuirs

E - EF (eV)

2.0 1.9 1.8 1.7 1.6 0

4

8

12

16

20

Angle (degrees)

Fig. 5. Dispersions of the LUMO of methylthiolate/Ag(1 1 1) at three different exposures. The 1 L coverage shows only a delocalized state. 4 L give only a delocalized state. 2.5 L show a superposition of localized and delocalized features. These are interpreted in terms of the self-assembling phase transition of methylthiolate which brings the neighboring S–Ag bonds nearer together, allowing the electronic state to delocalize.


11

Phase1

Transition

Phase2 Fig. 6. Adsorbed methylthiolate laying flat against the surface in a lattice gas phase (‘‘Phase 1’’). As the coverage is increased, a transition occurs to the denser phase of upright molecules (‘‘Phase 2’’).

As the surface density increases, the nearest-neighbor distance between molecules decreases. When this distance becomes approximately the size of a molecule (the surface is saturated) then the molecules self-assemble into a compressed ‘‘standing up’’ phase which reduces the distance between the neighboring S–Ag bonds. When the overlap between neighboring sulfur atoms increases sufficiently, the LUMO is able to form a delocalized band. 3.4. Monolayer films of C60 C60 is unusual among molecular adsorbates on noble metal crystals because it induces strong electron transfer from the metal substrate to the first monolayer of the molecular film without forming a specific chemical bond. This charge transfer is quite large in magnitude, ranging from 1.5 to 2 electrons per C60 on Cu, 0.7 on Ag, and 0.8 on Au for the (1 1 1) surfaces [73]. This leaves the first C60 monolayer with a partially filled band of states, which becomes metallic with a workfunction of 4.9 eV, regardless of substrate [74]. This strong metal-to-layer charge transfer has a strong effect on the IPS electrons. Zhu et al. [63] have found that the bandwidth of the n = 1 IPS electron in one monolayer is less than 0.04 eV, while the second monolayer disperses much more, 0.17 eV. They explained this dramatic shift in the effective mass as the interaction of the IPS electron with both the transient charge located on each C60 and that chargeÕs image. Thus the charge transfer from the metal to the first monolayer of the C60 forms a lattice of dipoles which strongly corrugates the potential energy surface that the IPS electron samples. For one monolayer, the electron resides near this dipole lattice, and, therefore, the effective mass is renormalized to a larger value (especially noticeable near the Brillouin zone boundary). When the electron is pushed away towards the vacuum in the two-monolayer film, the electron samples a much smoother potential and behaves like a free electron.

12


Strictly speaking, because the localizing potential in the C60 films has all the translational periodicity of the overlayer, the electron is not localized to one or even a few unit cells. Rather, the electron is delocalized over the crystal and is still an eigenfunction of momentum. This is manifest in the observed dispersions, which display clear band-like behavior. The IPS for 1 ML C60 is just a very narrow band. The wavefunction within each unit cell, however, should be very structured. This may offer a testbed for the spatial extent estimates developed in Section 6. The electronic structure due to molecular states (HOMO, LUMO, LUMO+1, . . ., LUMO + n), rather than the IPS, of C60 films have also been investigated [27,75]. These states are nondispersive on Cu(1 1 1) [27], but, due to the large peak widths ( 0.5 eV), it is very difficult to analyze the dispersions of the states and definitively assign whether these are localized molecular states or narrow bands. 4. Dynamic localization: small polaron formation 4.1. Qualitative scaling arguments Benzene, methylthiolate, and C60 each represent a case where the static structure of the layer dictates the spatial extent of the interfacial electrons. Nevertheless, electrons may localize in a dynamic process, where the mutual interaction of the electron and the layer changes the spatial extent of the electron over time. Fig. 7 shows the dispersion of the n = 1 state of 2 ML of n-heptane/Ag(1 1 1). At 0 fs, the n = 1 IPS is delocalized in the plane of the surface, with an effective mass of

Intensity (A.U.)

(a) 20˚ 18˚ 16˚ 14˚ 12˚ 10˚ 8˚ 6˚ 4˚ 2˚ 0˚

(b)

3.5

3.6

3.7

3.8

3.9

20˚ 18˚ 16˚ 14˚ 12˚ 10˚ 8˚ 6˚ 4˚ 2˚ 0˚

E - EF (eV)

Fig. 7. Dispersion of the n = 1 IPS in 2 ML n-heptane/Ag(1 1 1): (a) at 0 fs the electrons are delocalized. The smaller feature present at roughly 0.2 eV lower energy is the n = 1 IPS present on patches of 1 ML thickness and (b) at 1 ps most of the electrons are localized. The 1 ML signal, being shorter-lived, has decayed completely.


13

m* = 1.2. At a pump–probe delay of 1 ps, however, the effective mass of the electron is dramatically larger—m* is greater than 100me. This can be qualitatively understood in the framework of electron–phonon coupling. The attraction of the heptane molecules to the electron weakly perturbs the layerÕs configuration. As the molecules distort to accommodate the new charge distribution, they break the translational symmetry of the surface and start to create a potential energy well for the electron. The excess electron then contracts to spend more time near the distortion, which magnifies the polarization of the distorted molecules which further localizes the electron. In this way the electron may collapse from a delocalized state to a localized one. Emin and Holstein analyzed the effect of dimensionality on the energetic minimum as a function of the electronÕs characteristic radius, R [76,77] using a continuum picture. If the interactions between the charge and the deformable medium are purely short-range, the electronÕs energy will be EðRÞ ¼ T ðRÞ þ V ðRÞ:

ð4Þ

The potential of interaction scales like V ðRÞ ¼ V Sint =Rd

ð5Þ

and the kinetic energy of the electron always scales like T ðRÞ ¼ T e =R2 ;

ð6Þ

where R is the radius of the electron and d is the number of dimensions. Te and Vint are physical constants that define the magnitude of the kinetic and potential energies, respectively. As a function of dimensionality, therefore, d¼1:

EðRÞ ¼ T e =R2 V int =R;

ð7aÞ

d¼2:

EðRÞ ¼ T e =R2 V int =R2

ð7bÞ

d¼3:

EðRÞ ¼ T e =R2 V int =R3 :

ð7cÞ

In one dimension, because T and V scale differently with R, and V is longer ranged, the total energy is always minimized at a finite polaron radius, R. The three-dimensional case is qualitatively different, as there is no longer a finite radius minimum but rather minima at R ! 1 and R ! 0. These two solutions correspond to free electronic band states and a polaron localized to a single lattice site, a small polaron. Between the two regimes will be a barrier which will require some thermal energy to cross, or else the nuclei must tunnel through it. Adding a long-range interaction V ¼ V Lint =R4d one can recover the finite radius minimum, which corresponds to the classical large polaron. Finally, in two dimensions, both T and V scale with R2, so if there is a localized state, it should collapse to a single lattice site with no barrier crossing. On these very short length scales, any continuum treatment is no longer accurate and should be supplemented with more discrete models to obtain the details [78]. Following this simple scaling argument, it seems reasonable that the electron should be localized to a single unit cell in the quasi-two dimensional films investi-

14


gated by these 2PPE measurements. This particular point will be taken up in Sections 5 and 6. Polaron theory has been extended in recent years in both semiclassical approaches as well as fully quantum–mechanical calculations that are extending the physical picture of the localization process in two dimensions beyond this simple scaling argument. Several analyses have actually determined that there may be a barrier to localization in two dimensions [78–81], though perhaps for the experimentally relevant parameters it is not present [81]. One analysis even suggests that the quasi-two dimensional nature of the problem may allow the size of the trapped particle to vary from large to small as a function of the dimensionless coupling constant [81]. The potential of these theories to compare calculated results to experimental measurements of electron localization dynamics as well as energetics (electron solvation) is a very important recent development [78,81]. 4.2. Quantitative analysis of small polaron formation The data for IPS localization in films of 2 ML n-heptane/Ag(1 1 1) were interpreted quantitatively as small polaron formation using a formalism based on electron-transfer theory [6]. The lifetime of the delocalized n = 1 state is highly dependent on the stateÕs parallel momentum, whereas the lifetime of the localized n = 1 state is independent of the parallel momentum (Fig. 8). In an analogy to Marcus electron-transfer theory, one can plot the potential energy of the system as a function of the distortion of the lattice (Fig. 9a). The stack of curves labeled Vf(kk,Q) represents the band of delocalized states, while the curve VS(Q) represents the energy of the localized state; Q is the relevant lattice distortion. At zero distortion the localized state is defined at the mid-point of the delocalized band (point C) because the localized state can be expanded on the basis of delocalized momentum states, and should contain an equal component of each parallel momentum to be localized to a single unit cell. From Fig. 9b, one can see that the height of the barrier to transfer from the delocalized state to the localized state should depend on the parallel momentum of the delocalized electron. So the rate of transfer from the delocalized state to the localized state should increase from the bottom of the band up to the band midpoint. At the mid-point of the band (point C) the transfer should be barrierless and the rate maximal. Above this point, however, the rate should decrease because there is a barrier again. This corresponds to the Marcus inverted region. The classical, nonadiabatic result of electron-transfer theory is ! rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 p ðD þ E Þ rel k st ¼ H 2fs exp : ð8Þ 4Erel k b T h2 Erel k b T Here kst is the rate of self-trapping, Erel is the relaxation energy (analogous to the reorganization energy in the electron-transfer literature), and D is the exoergicity of the trapping event. The best fit to the data is given as the dashed line in Fig. 10. It matches the rise of the localization rate with exoergicity, but predicts a rapid decrease of the rate in the inverted region. In part, this is a failure to incorporate


15

(a)

1600 fs

Intensity (A.U.)

360 fs

0

2000

4000

6000

8000

(b)

6˚

70 fs

0.07 A-1 550 fs

8˚

510 fs 18˚ 20˚ 0.23 A-1 210 fs

0

500

14˚ 16˚

12˚

10˚

1000 1500 Delay time (fs)

2000

2500

Fig. 8. Angle-resolved dynamics of the n = 1 IPS in 2 ML n-heptane/Ag(1 1 1): (a) the localized state population is independent of angle (parallel momentum), while (b) the delocalized stateÕs population decay time decreases from 550 fs at 0° to 210 fs at the highest angles.

(a)

(b)

Energy

E

E

Vf (k||, Q) Vs (Q)

C

2B B

F

Est

Ea

Erel S

0

T

2Hfs

−∆ε

Q 0 Self-Trapping Coordinate

Q

Fig. 9. The picture for the transfer of an electron from a delocalized band to a localized state.

quantum–mechanical tunneling in the inverted region, which can substantially affect the rate there. Several approaches to including quantum–mechanical effects as well as interpolating between adiabatic and nonadiabatic regimes have been developed

16

P. Szymanski et al. / Progress in Surface Science 78 (2005) 1–39 1013

kst (s-1)

(a)

1012

Hfs = 91 cm-1 Erc = 0.057 eV Erq = 0.18 eV hω q = 750 cm-1 1011

0

0.05

0.1

0.15

0.2

0.25

−∆ε (eV) 1013

kst (s-1)

(b)

1012

8

10

12

14

16

18

20

1000 /T (K-1)

Fig. 10. The self-trapping rate as a function of exoergicity for electron localization in 2 ML n-heptane/ Ag(1 1 1). The dashed line represents the best fit to the data using (8). The parameters given are the best fit to the data using the formalism of Stuchebrukhov and Song, which accounts for both classical and quantum mechanical reorganizational energy (Erc and Erq, respectively) with one quantum–mechanical mode of frequency hx, and a coupling strength of Hfs between the localized and delocalized states.

[82,83]. Using the results of Stuchebrukhov and Song to account for all orders of the coupling between the delocalized state and the localized state as well as both classical and quantum mechanical vibrations, one can fit the decay rate of the delocalized state vs. the exoergicity (Fig. 10a). Reasonable agreement between the theory and experiment is achieved using a single quantum–mechanical mode at 750 cm1 in the model. This mode corresponds well to the in-phase methylene rocking motion of a heptane molecule. This discussion is predicated on several assumptions. Most importantly, this treatment assumes that the decay of the delocalized state as a function of parallel momentum is entirely due to the transfer of the electron from the delocalized band to the localized state. Recent experiments on other systems have shown that intraband relaxation—that is relaxation of the electron from one parallel momentum state to another, while remaining delocalized—can significantly alter the lifetimes of IPS as a function of parallel momentum [21,84,85]. There have been several attempts to develop theory for intraband scattering at an interface. Echenique and coworkers [84] have calculated the momentum dependent inelastic scattering of IPS electrons at a clean Cu(1 1 1) surface using the GW approximation. They showed that due to the coupling of the electron to the substrate, the probability of the intraband scattering from one parallel momentum state to another (and creating an electron–hole pair in the substrate to conserve energy and momentum) can be significant. Wolf and


17

coworkers [85] devised an experiment to examine the effects of electron–phonon coupling when there is no localization. They built a compound interface of N2/Xe/ Cu(1 1 1), and interpreted the change in lifetime of the n = 1 state from the bottom of the band to higher momenta as primarily due to scattering from N2 librations. Again, in this case, they argue that the electron–phonon coupling is substantial enough to scatter the electron but not enough to localize it. For heptane, the electron– phonon coupling should be higher and the intraband scattering should be enhanced, which would provide a significant competing channel for electron relaxation. This leaves a variety of mechanisms to be incorporated into a full understanding of the dynamic localization of electrons. Indeed, one open question in the localization literature is which materials will localize electrons and which will not. For example, the linear alkanes heptane and pentane localize electrons, while the branched neopentane does not. Cyclohexane, however, also localizes electrons [22]. Perhaps the best speculation is that because of the particular arrangement of attractive and repulsive interactions between the electron and different parts of the molecule either it is favorable to trap on a molecule or the interactions balance in such a way that the electron remains free. This point of view was used to explain the mobility of electrons in a great variety of liquids [86]. Indeed, the mobility of electrons in neopentane is more than 300 times that of electrons in linear alkanes. The addition of a substantial permanent molecular dipole moment to the material enhances the electron-molecule interaction greatly compared to the coupling in nonpolar materials. The stronger potential is also the source of greater complexity in the dynamics of the system.

5. Solvation and localization at polar interfaces 5.1. Introductory remarks and background The observation of dynamic localization at polar interfaces shows that the coupling of the electron to the molecular modes of an adsorbate can influence critically the dynamics of the electron. The coupling to these modes can, however, do more than simply alter the electronÕs spatial extent. Polar adsorbates interact more strongly over longer ranges, and their motion causes dynamic changes in the energy of the electron through the process of solvation. The topic of solvation dynamics is easy to define in general terms: following a change in the properties, such as the charge density, of a species (the solute) in solution, the surrounding medium (the solvent) may find itself in an orientation such that its interaction with the solute is no longer optimal. Reorganization of the solvent then occurs to re-establish an energetic minimum. Despite having such a simple definition, the details behind the phenomenon, as well as the vast number of other phenomena to which solvation is related, have made for a long history of study and provide a seemingly inexhaustible source for future work. Solvation dynamics are well-known to influence, for example, the rates of chemical reactions [87–91], ion transport [92], and processes in biological systems [93,94].

18


In many systems, the solute is an excess electron. Extending the understanding of solvated electron dynamics developed from bulk systems to those of reduced dimensionality is of clear interest given the many processes that occur in quasi-two-dimensional environments relevant to electrochemistry [95] and molecular electronic devices. For instance, conduction across a molecular wire is dependent on the reorganization energy of the surrounding medium in a charge-transfer process [96]. The physical properties of heterogeneous systems, distinct from those of bulk materials, exhibit hindered motion due to the presence of the interface and thus significant differences in the solvation dynamics [12,13]. Such differences are present even for the case of a weakly-wetting liquid at an interface [13]. For interfacial and isotropic systems alike, the time-dependent interaction of an electron with a surrounding medium provides an ideal system for the study of solvation phenomena. The electron has no internal degrees of freedom, so the dynamic changes in electronic properties result solely from the response of the material to the charge of the electron. Two-photon photoemission has recently been applied to studies of electron solvation at dielectric/metal interfaces [7,8,44,56–58]. As demonstrated earlier by work with nonpolar alkane overlayers, a negative electron affinity forces electron density out of the overlayer and into the vacuum above the dielectric [22]. Consider now the influence of the IP giving rise to bound electronic states in this spatial region. The presence of the IPS provides a way to introduce an excess charge and confine it near the layer/vacuum interface. In a time-resolved experiment, one can then probe the dynamic response of the adsorbate to the electric field caused by the IPS electron by monitoring the properties of the IPS as a function of pump–probe delay. As will be seen, these concepts can be applied to non-IPS as well [8,57,58]. The 2PPE approach is similar to the transient absorption method used to study electron solvation in condensed phases [97,98] in that both are pump–probe measurements of a soluteÕs energy. In measurements in bulk solvents, photodetachment of electrons from the neat liquid [97,99,100], or, alternatively, from a readily photoionized solute [98,101,102] is used to generate excess electrons. The photodetachment process itself is of interest, as it influences the initial stages of solution photochemistry [103]. To examine the effects of solvation alone, it is possible to allow the electron to relax into its equilibrated ground s state before exciting it [100,102]. Recently, studies of aqueous reverse micelles have extended the techniques to interfacial systems [104]. Of particular fundamental importance is the spatial extent of the excess electrons. The currently accepted model for water [105], which is the result of much experimental and theoretical effort, is that the electron is excited into the nonequilibrated ground state or excited p states, which are localized, or into the delocalized conduction band of the liquid which lies at higher energies. From the conduction band, the electron localizes within 300 fs into a solvent cavity. Similar cavity models have been used successfully to describe solvation in alcohols [106]. Other polar liquids, such as acetonitrile, are more controversial with evidence suggesting that excess electrons may form molecular anions in addition to localizing to solvent cavities [107]. With 2PPE, an electron from the metal substrate interacts with the pump pulse and is injected into the solvent environment. This allows studies to be conducted on the neat solventÕs interaction with the electron, the hole being screened in the me-


19

A

Electron Counts (A.U.)


tal. Of course, the presence of the metal provides considerable influence on the electronÕs local environment and the bound electronic states themselves; for investigating the effects of the metal interface on solvation, this is an ideal arrangement. Furthermore, studies may be performed as a function of layer thickness by metered dosing in an ultrahigh-vacuum environment. As mentioned in the previous section, reduceddimensionality effects will cause fundamental changes in the properties and dynamics of interfacial electrons as the molecular coverage approaches the monolayer or submonolayer limit. When comparing 2PPE with condensed-phase measurements, one caveat is that the techniques must employ very different conditions. In the former, the substrate must be cooled well below room temperature to allow physisorption or weak chemisorption of solvent molecules to occur. However, temperature affects the diffusional component of solvation dynamics much more strongly than the higher-frequency modes, such as librations [108–111]. Higher-frequency modes are believed to dominate dynamics in the first several hundred femtoseconds, known as the inertial response [112–115]. The conditions of reduced temperature and pressure may also affect the local order of the molecules in contact with the substrate, which may in turn influence their ability to solvate charge. For example, the tendency of liquids to form surface layers is enhanced at lower temperatures [13,116]. The most unique aspect of the photoemission approach lies in its ability to measure the energies of electrons as a function of both the residence time of the electron at the interface and the momentum parallel to the interface. By monitoring the dispersions of the electronic states as a function of time, the dynamics of the localization process are obtained independently of the solvation dynamics even though the two processes may occur simultaneously.

A

C B

0

fs) y( ela eD Tim

fs) y( ela eD Tim

0

A

C

500

400

B

1000

800 2.5

2.7

2.9

) E - E F (eV

(a)

3.1

1500 2.5

3.1

2.9

2.7

)

E - E F (eV

(b)

Fig. 11. (a) Time-resolved 2PPE of the n = 1 state (A) for 1 ML 1-butanol/Ag(1 1 1) taken at kk = 0. (b) As the coverage is increased to slightly beyond 1 ML, additional series of IPS corresponding to different local surface environments appear. The n = 1 states for series B and C are shown. The dynamic energy relaxation is most pronounced in B.

20


5.2. Dynamic response of polar organic adsorbates Straight-chain alcohols on Ag(1 1 1) were the first systems to show evidence of electron solvation with 2PPE [56]. Representative series of spectra for monolayer and mixed coverages of 1-butanol on Ag(1 1 1) are shown in Fig. 11. As the pump–probe delay time increases, the kinetic energies of the electrons photoemitted from the interfacial states decrease monotonically from their values at t = 0 fs. Addi-

3.4

(a)

3.3

n=2

E - E F (eV)

3.2 3.1 3.0 2.9

n=1

2.8 2.7

0

500

1000

1500

2000

Time Delay (fs)

0.58

(b)

0.56 0.54

∆E (eV)

0.52 0.5 0.48 0.46 0.44 0.42

0

200

400

600

800

1000

1200

1400

Time Delay (fs) Fig. 12. (a) Time-dependent photoelectron energy from 1-butanol/Ag(1 1 1) IPS. The n = 1 and n = 2 states are each present as a triplet corresponding to, from top to bottom, A, B, and C in Fig. 11. (b) Spacing between n = 1 and n = 2 states for each of the three series. The energy relaxation maintains an approximately constant spacing, signifying a dynamic local workfunction effect.


21

tional states with lower binding energies, not shown in Fig. 11, accompany each of the larger features. At all times, the energies of each pair of states follow the hydrogenic progression described by (1); this is illustrated in Fig. 12. The states are therefore assigned to the n = 1 and n = 2 IPS of different local environments on the surface. For IPS, it is the quantum defect parameter, a, that determines the binding energies relative to Evac and, thus, the energetic spacings between the members of the series. In Fig. 12, the difference in the n = 2 and n = 1 photoelectron kinetic energies is independent of time. Thus, the value of a and the binding energies of the states must be constant as well. That the energy relaxation of both states is identical is surprising, given that the n = 2 wavefunction has its maximum further away from the surface and adsorbate than that of n = 1. A simultaneous decrease in the kinetic energies of both IPS can only be explained by a changing surface potential affecting the energy to which the series converges. The nature of this potential is addressed by the concept of the local workfunction [17,117,118]. The workfunction of a homogeneous surface is defined as the difference in energy between an electron at the highest-occupied energy level of the solid, i.e. the Fermi level, and an ionized electron at rest infinitely far from the solid. A major contribution to the workfunction comes from the dipole layer that forms at the surface from electrons spilling out into the vacuum at the termination of the solid. For a finite, inhomogeneous surface, defects and adsorbed species change the charge density at the interface and, consequently, the surface dipole [118]. The resulting effect is a lateral variation of the potential near the interface due to different structural regions. Static local workfunction effects have been observed previously due to heterogeneous surface conditions. Photoemission from adsorbed xenon atoms [117,118], as well as 2PPE of IPS [17,118], have been used in their detection. That electrons can be sensitive to differing local conditions that they themselves induce is not unreasonable in light of the previous work on localization discussed in Section 4 and forms the basis of the dynamic local workfunction described below. While the dynamics of the IPS are determined by changes in the local structure of the overlayer, the 2PPE spectra at zero delay time are a function of the equilibrium adsorption geometries of the molecules. Studies of straight-chain alcohol adsorption on Ag(1 1 0) provided evidence that the molecules adsorb flat on the surface [119,120]. The reported temperatures necessary to achieve a saturated monolayer of methanol through pentanol on Ag(1 1 1) [56] scale with increasing chain length, following the same trend as the monolayer desorption temperatures on Ag(1 1 0) [120]. The 1 ML alcohol/Ag(1 1 1) IPS lifetimes, however, are largely independent of chain length [56], suggesting a similar tunneling barrier for escape into the substrate in each case. It was thus concluded that straight-chain alcohols should initially lie more parallel then perpendicular to the surface on Ag(1 1 1) as well. From a molecular standpoint, the energy relaxation may be viewed as a reorientation of the molecular dipoles solvating the electron. At t = 0 fs, the molecules lie on the surface with a significant component of their dipole moments parallel to the interface. A rotation of the positive end of a dipole toward the electron (away from

22


Evac

(b) equilibrium layer structure

Evac

initial n = 2

_V

0

initial n = 1

dipole reorientation

Energy

Energy

(a)

final n = 2

image potential

final n = 1

z

image potential

z

∆t Fig. 13. Illustration of the dynamic local workfunction for (a) initial and (b) final conditions. After a lowering of the local workfunction from Evac (thick dashed line) to EvacV0 (dotted line), the IP (curved line) is modified to cause the IPS (dashed-dotted lines) to converge to the new energy. The transition from (a) to (b) is a result of the interaction between the adsorbed molecules and the IPS electron.

the surface) will result in a more energetically favorable interaction. This molecular dipole opposes the surface dipole, lowering the workfunction (Fig. 13). As a collection of dipoles reorient themselves, the electron experiences a decreasing surface potential. The series of IPS, which are now pinned to the energy given by the local workfunction rather than the global workfunction, must follow suit. The energies evolve in this fashion because the dynamically decreasing local workfunction only exists after the electron is excited into an IPS, assuming sequential interactions with the laser fields where the pump precedes the probe. The observed kinetic energies are still determined by the global (static) workfunction. As a result, the peaks in the 2PPE spectra shift to lower energies as a function of the amount of time the electron populates an IPS due to the dynamic electron-molecule interaction. In other words, the binding energies relative to the vacuum level are increasing. By contrast, a decreasing global workfunction, which occurs statically in the experiment due to adsorption of the alcohol molecules onto the Ag(1 1 1) substrate, would cause the experimentally-observed kinetic energies to increase. Another, equivalent, way to describe the local workfunction is to consider the interaction between the electron and a patch of the molecules. A necessary condition for the observed behavior to be a measurement of electron solvation is that the electron is sensitive only to the motions of the adsorbate molecules while the electron is in an IPS and not after photoemission. For electrons photoemitted with kinetic energies on the order of 1 eV, typical values for visible probe wavelengths, this is achieved provided the potential due to the adsorbate tends towards a constant with increasing distance more rapidly than the image potential (/ 1/z). The classical charge–dipole interaction is inversely proportional to distance cubed. An electrostatic model for a collective response, called the ‘‘disk-dipole’’ model, has a potential that rapidly ap-


23

proaches an asymptotic value at distances larger than the length scale of the region of reorienting molecules [56]. This is an intermediate-range potential which can be time-dependent and uniformly changes the kinetic energy of the n = 1 and n = 2 states relative to the static, global workfunction. Further comments on this model are presented in Section 5.3. Electron solvation at the 1-butanol/Ag(1 1 1) interface may therefore be viewed as a dynamically decreasing workfunction local to the electron induced by its interaction with the adsorbate layer [56]. Similar behavior has been seen for 1–2 ML films of methanol, methanol-d4 (CD3OD), 1-propanol, 1-butanol-d (C4H9OD) and 1-pentanol, as well as monolayers of acetonitrile [7], all on Ag(1 1 1). It is not expected, however, that the dynamic local workfunction effect should be a universal interpretation of electron solvation by polar interfacial molecules. The examples given above are all small linear molecules, with few atomic sites for physisorption or chemisorption and relatively low steric effects to hinder rotation off of the surface. Furthermore, IPS higher than n = 1 may give only weak signals in some systems, which limits the ability to test the model. Work is currently ongoing in this area studying these and other families of polar molecules to look for exceptions and gain a better understanding of electron–adsorbate interactions. One difficulty with the organic/metal systems studied is that layer-by-layer growth of adsorbate overlayers does not usually occur. Desorption studies, either through temperature-programmed desorption (TPD) mass spectrometry [120–124] or temperature-dependent 2PPE [56], reveal monolayer and multilayer regimes characteristic of either Stranski–Krastanov or monolayer-with-simultaneous-multilayers growth modes [125]. The multilayers of alcohols [120,124] and acetonitrile [126,127] on silver substrates, in particular, are largely amorphous. Overlayers with heterogeneous thicknesses result, which may give rise to multiple series of states [56]. Such complications can potentially make it difficult to measure the dispersions of interfacial states, to examine the dependence of solvation and energy rates on the size of the molecule and the thickness of the layer, and to uncover the dynamics of any simultaneous localization processes. In addition, monolayers may possess defects or different domains which further add to the multiplicity of the peaks and the complexity of the dynamics. Based on the above list of concerns, the ideal system for studying simultaneous solvation and localization and independently measuring the dynamics of energy relaxation and population of nondispersive states should possess an adsorbate layer with a reasonably uniform thickness. One such system is found in a 2 ML coverage of butyronitrile (also known as propyl cyanide and hereby written as PrCN) on Ag(1 1 1) [7,44]. As this molecule is reasonably expected to follow the same monolayer-and-multilayer trend, the coverage should be interpreted as an exposure of two monolayer equivalents. Although it is an excellent candidate for solvation studies, the relative simplicity and reproducibility of the spectra have made it ideal for localization experiments. The general features are summarized in Fig. 14. The t = 0 fs spectra are dominated by dispersive IPS, with photoelectron kinetic energies decreasing as a function of time. A nondispersive state is detected to the lowerenergy side of n = 1 with a rise time longer than that of the delocalized IPS, similar

24

P. Szymanski et al. / Progress in Surface Science 78 (2005) 1–39 localized

Solvation

16.4° 12.4° 8.4° 4.4°

24.4° 22.4° 20.4°



24.4° 22.4° 20.4°

delocalized

16.4° 12.4° 8.4° 4.4° 0°

0° 2.6

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2.6

(c)

2.7

2.8 2.9

3.0

3.1

3.2

E - EF (eV)

Fig. 14. Angle-resolved 2PPE dynamics for 2 ML PrCN/Ag(1 1 1), normalized to unit maximum amplitude and offset vertically by the value of kk. The light gray and dark gray dashed curves are guides to the eye providing the positions of the delocalized (dispersive) and localized (nondispersive) states, respectively. (a) Only the delocalized state is visible at 0 fs delay. The thin dashed vertical lines mark the peak positions at 0 fs and 600 fs; the latter is at lower energy, the effect of solvation. (b) Both the delocalized and the localized states are equally intense at 267 fs. A representative Voight fit of the spectrum at 0° to overlapping delocalized and localized states is shown. (c) Only the localized state survives past 600 fs.

to the case of n-heptane/Ag(1 1 1) [6]. Both states exhibit a smooth energy relaxation until only the nondispersive state remains. Modest relaxation occurs beyond this point, during which the remaining population decays. The conclusion supported by the above observations is that the presence of the excess electron at the interface perturbs at least the topmost of the two molecular layers, inducing reorientation. The resulting distortion in the layer structure can cause the initially delocalized electron to collapse into a localized state. Upon localization, the surrounding molecules continue the solvation process until an energetic minimum is reached or the electron tunnels back into the metal substrate. The longer rise time for the localized state vs. the delocalized state signifies that this process is not entirely due to the static structure at the interface but requires the participation of other factors, namely the motion of adsorbed molecules occurring on the same time scale.


25

It is interesting to compare the nature of excess electrons at a layer of interfacial nitriles with electrons in bulk nitriles. Evidence exists that electrons in liquid acetonitrile, as well as the a phase of solid acetonitrile, take the form of dimeric anions with the two molecules in an antiparallel configuration [107,128]. In the b phase of the solid, this arrangement is prevented and a monomeric CH3CN forms [128]. There is also a temperature-dependent equilibrium in the liquid between the dimeric anion and a more diffuse multimeric state, which may be analogous to the solvated electron in other polar liquids such as alcohols and water [107]. These anionic species, formed by attachment of the electron to the solvent molecules, photodissociate under visible or near-IR light. Other nitriles, including PrCN, show similar behavior [107,129]. The 2PPE experiments show little or no change in the spectra and dynamics over the course of the measurements, where only an extremely limited supply of nitrile molecules are present. Both this observation and the detection of hydrogenic progressions of states demonstrate that the nature of the electrons studied are unique to the interfacial environment, retaining much of their IPS character even after interaction with the solvating molecules. 5.3. Models for the dynamic polarization The majority of the dynamics due to solvation and localization processes in 2 ML PrCN/Ag(1 1 1) both occur on similar time scales: approximately 500 fs. Although the rate of localization can be measured independently, the 2PPE experiment cannot distinguish the energetics of the two processes. In a model of small polaron formation isomorphic with the theory of electron transfer, i.e. the Holstein model [6,43] described by (8), there is a reorganization energy for the localization process. However, both solvation and localization are due to the induced polarization in the adsorbate layer, so a separation of the two effects requires them to have distinct polarization modes in the material. If the same modes are involved, a situation suggested by the similar time scales, then localization should be thought of not as a separate phenomenon but rather as a consequence of the same induced polarization that leads to solvation. Sebastian et al. [81] have modeled electron solvation by polar adsorbate layers with a continuum approach, which is expected to be valid during the early stages of the molecular response. In this model, the electron induces a polarization in the molecular layer in the direction normal to the surface. This polarization is treated as a collection of hindered rotational modes, as suggested by Harris and coworkers [7,56], each with a characteristic frequency. Alternatively, vibrational modes can be used, yielding analogous results [81]. Treating the adsorbate layer and its polarization modes in the continuum limit, where the discrete molecular nature of the layer is neglected, the interaction energy between the electron and the induced polarization ~ P ð~ s; tÞ is then given by the expression Z Eint ¼ d~ s~ Eð~ r;~ sÞ~ P ð~ s; tÞ; ð9Þ

26


where ~ Eð~ r;~ sÞ is the electric field,~ s is a point on the surface, and~ r is the position of the electron. A trial wavefunction is constructed for the electron with a Gaussian shape in the parallel degrees of freedom and an exponential decay with increasing perpendicular distance z. A hard-wall condition restricts the electron to the vacuum region, an approximation for the case of an IPS electron above a dielectric of negative electron affinity. The polarization is assumed to occur in the topmost layer of molecules and is described by a Gaussian potential well. Values for the spatial extent of the electron that minimize the total energy are then determined for a range of potential well magnitudes and spatial widths. The minimum energy as a function of the parameters describing the potential defines a potential energy surface, upon which the existence of stable solutions can be investigated. The above approach can be successfully applied to the 2 ML PrCN/Ag(1 1 1) system using a single rotational mode [81]. Approximating the adsorbates as two close˚ and total thickness 3.1 A ˚ , two extrema are packed layers of lattice constant 7.2 A found in the potential energy surface. The solution for zero polarization is a saddle point and corresponds to a delocalized electronic state. The energetic minimum occurs at a nonzero polarization strength and predicts an electronic wavefunction ˚ full width at half maximum (FWHM) parallel to the surface. localized to 29.58 A A lower bound on the effective mass of the localized state was estimated to be approximately 250me, so it would indeed appear nondispersive if it were correct to assign it an effective mass. Models that attempt to measure the spatial extent are discussed in the next section. As discussed in Section 4, the existence of stable self-trapped states in two dimensions and whether or not the trapping is activated depends critically on the coupling strength [79]. There is no barrier between the delocalized and localized states in the continuum treatment of the above system [81]. The localization is therefore spontaneous once an appropriate potential well is created. The initial response of the layer, however, is slow and weak, due to the delocalized charge density, but as the polarization becomes more intense and more localized the electron enters the trapped state. It is worthwhile to describe the aforementioned ‘‘disk-dipole’’ model in greater detail at this point in the discussion [56]. The model treats a circular region of surface molecules as a pair of oppositely-charged, uniform disks, with the product of the charge q and the distance between the disks ‘ giving the projection of the molecular dipole moment onto the axis perpendicular to the surface. A net rotation of the dipole moment towards the electron corresponds to an increase in the length ‘. The situation is illustrated in Fig. 15 and quantified by (10a) and (11) V ðzÞ ¼ V 0 V0 ¼

q‘r ; 20

1 2 1=2 2 1=2 ½ðR þ z2 Þ ðR2 þ ðz þ ‘Þ Þ þ 1 ‘

ð10aÞ

ð10bÞ


27

Fig. 15. Illustration of the ‘‘disk-dipole’’ model. Orientation of the molecular dipoles with respect to the surface normal modifies the surface dipole. Two parallel charged disks represent the charge distribution of a patch of molecular dipoles, and collective rotation of the dipoles is equivalent to a change in the disk separation ‘.

where z is the distance perpendicular to the surface, R is the radius of the disks, and r is the magnitude of the charge density on each disk. Eq. (10a) may be expanded to give " V ðzÞ ¼ V 0

4

z þ ‘=2 ðz þ ‘Þ þO 1 R ‘R3

!# :

ð11Þ

For z R, the potential may be approximated by the constant V0. In this region, the effect of the dipole layer is an offset to the IP which causes the series of IPS to converge to a different energy lower than the vacuum level. The change in the IPS energies is the local workfunction effect described previously. To a first approximation, one can make the ‘‘disk-dipole’’ model a dynamic one by allowing ‘ to change as a function of time. This is a crude treatment of the polarization component perpendicular to the surface. The energy relaxation observed is then given by V0(t), which should affect equally n = 1 and n = 2 states for a sufficiently large radius R. For 1-butanol/Ag(1 1 1), this approach was used with an esti˚ [56]. A major limitation of this approach is that it assumes mated radius of R = 50 A no dynamic localization. In reality, the lattice distortion induced by the electron need not remain uniform and is probably an oversimplification to assume so. The structural reorientation in the molecular layer will therefore become most pronounced for a relatively small number of molecules, analogous to the first solvation shell in liquids, with smaller effects in subsequent ‘‘shells’’. In other words, the initially delocalized IPS electron becomes localized through self-trapping in the lattice distortion that it induces while the surrounding environment further stabilizes the resulting polaron. The model as used with constant R should thus be regarded as an illustration

28

P. Szymanski et al. / Progress in Surface Science 78 (2005) 1–39 16

1.0

8 4

Bulk Interface

0.6 0.0

0.4

0

500

1000

0.2

0

0.0 0.0

(a)

1.0

0.8

Response

Nmol

12

H O CH3

Probability (A.U.)

Pt Pt Pt

0.5

1.0

Distance (nm)

1.5

0

(b)

250

500

750

1000

1250

Time (fs)

Fig. 16. Simulation of MeOH on Pt(1 0 0). (a) The radial distribution function that shows the localized solvated electron between the second and third methanol monolayers. (b) The simulated solvation response function of the electron solvated by a quasi-two-dimensional bath. The 22 fs Gaussian component is attributed to inertial motion of the methanol while the longer time scale is due to diffusive rearrangement. Comparison to bulk solvation results (inset) shows that the response at the interface differs significantly in the first 300 fs.

of the initial stages of interfacial electron solvation immediately following the introduction of the excess electron and not as a quantitative description of the process. An alternative to continuum models is provided by calculations of the electronic wavefunction that rely on a molecular description of the solvent. One approach that has proved successful in treating solvation dynamics in isotropic systems is mixed quantum–classical molecular dynamics. Such work has increased greatly the understanding of electron solvation in polar liquids such as water [115,130,131] and methanol [106,132–134]. An extension of this method to polar organic/metal interfaces is the recent simulation of an electron at the methanol/Pt(1 0 0) interface [135], as shown in Fig. 16. Unlike the 2PPE experiments, a prelocalized electron is injected into the interfacial environment and allowed to equilibrate. The solvation response is therefore determined by the decay of spontaneous fluctuations from equilibrium, which may be compared to nonequilibrium experiments through the linear response formalism. The time evolution of solvent molecules is calculated via NewtonÕs equations of motion. The propagation of the electron, however, must use methods based firmly in quantum mechanics. This is accomplished by using a pseudopotential to couple the solvent to the excess electron and a pseudospectral (fast Fourier transform) method to solve the Schro¨dinger wave equation for each given solvent configuration [133,134]. The solvation response, plotted as the normalized functions in Fig. 16b, is modified on ultrafast timescales relative to the bulk. The binding energy of the interfacial electron, however, is approximately half that of the bulk excess electron. Although the preliminary results are encouraging, the present implementation of this split-operator method cannot treat dynamic localization and other nonequilibrium behavior.


29

Fig. 17. Time- and angle-resolved 2PPE of 3 BL D2O/Cu(1 1 1) at delay times of (a) 0 fs, (b) 200 fs, and (c) 300 fs [58]. The angle of photoemission is a, equivalent to h in the notation of this paper. (d) Dispersion of the first moment of the electron intensity. The time evolution shows the rapid localization of the electrons. Reprinted with permission from Bovensiepen et al. [58]. Copyright 2003, American Chemical Society.

Fig. 18. Coverage-dependent electron solvation for D2O/Cu(1 1 1) [57]. The solvation is independent of both layer thickness and layer crystallinity above 2.0 BL. Reprinted from Gahl et al. [57]. Copyright 2003, with permission from Elsevier.

30


5.4. Dynamics of electrons at ice/metal interfaces The work by Wolf and coworkers [8,57,58] on the D2O/Cu(1 1 1) system provides a number of interesting contrasts with the organic/metal systems. Over a large range of coverages, a transition between a broad, delocalized state to a localized state is observed, which is complete within the first 100 fs (Fig. 17). As in the case of 2 ML PrCN/Ag(1 1 1), a continuous shift to lower kinetic energies accompanies the localization and continues after the delocalized population is depleted. The energy relaxation of the localized state as a function of D2O coverage is shown in Fig. 18. The units of coverage require some explanation. In the growth of water and D2O layers on Cu(1 1 1), the adsorbate forms bilayers (BL) two molecules thick. The second bilayer appears, and continues to grow with increasing exposure, before the first is completed [57]. Similar behavior is observed for Ag(1 1 1) substrates [136]. The layers lack long-range order [8,137], although crystallization of the film occurs upon heating [8,138]. By contrast, a well-ordered D2O bilayer of homogeneous thickness forms on Ru(0 0 0 1) [137,138]. The amount of D2O required for one bilayer on Ru(0 0 0 1), measured by TPD, is used as the unit of coverage on the Cu(1 1 1) substrate as well [8]. The rate of solvation is largely independent of layer thickness for coverages greater than 2.0 BL for both amorphous and crystalline layers. This has been interpreted as the electron becoming trapped and being solvated inside a cavity within the D2O layer rather than the layer/vacuum interface. Based on this hypothesis and the lack of structure in the dispersive feature in the spectrum, the delocalized precursor is assigned to the conduction band of the layer [8]. Below 2.0 BL, the rate increases with decreasing coverage. As the average layer thickness decreases, the likelihood of the electron density residing at the D2O/vacuum interfaces increases. The response of dangling O–H bonds at the surface is expected to be more rapid because of the lower degree of hydrogen bonding [57]. A curious aspect of the angle-resolved spectra in Fig. 17 is the time-dependent evolution of the solvated electronÕs dispersion. The localized state, which dominates the spectra at delays greater than 100 fs, appears as if it develops a negative effective mass. Bovensiepen et al. [58] have performed a thorough analysis of this ‘‘apparently negative dispersion’’. Due to the large inhomogeneously-broadened width of the state, the 2PPE spectra contain contributions from electrons in different local surface environments. The distributions of electrons may arise from differing rates of solvation and localization, potential-well depths due to electron self-trapping, and spatial extents after localization; the latter two points are further discussed in Section 6. There is also the influence of the measurement itself on the shape of the spectrum. As shown in (2), the range of kk sampled over the entire range of a kinetic energy spectrum depends on the angle of emission. For the localized states with a finite width in kk, assumed most intense at kk = 0, the decrease in signal intensity with angle should be sharper as the kinetic energy increases. In all likelihood, both the energy-dependent measurements and an inhomogeneous distribution of solvated electrons play roles. The ‘‘apparently negative dispersion’’ is therefore not inconsistent with photoemission from a localized state and should become a larger factor as


31

the linewidth of the state increases. The distribution can be characterized further by relating the angle-dependent intensity of the photoemission spectra to the degree of localization.

6. Spatial extent of localized interfacial states In the study of localization at interfaces, the question of the spatial extent of localization arises. While estimates for higher-energy, delocalized electrons in bulk liquids have been made through modeling the reactions of the electrons with other solutes [139] and measurements of electron–hole recombination rates [140], localized states have been limited to quantum–mechanical calculations of the radius of gyration [130–132]. At interfaces, the nature of the electronic states are modified compared to the bulk and would be modified further by coadsorption of other species. In 2PPE, recombination rates only give information about the rate of tunneling back into the metal. Furthermore, detailed calculations are scarce because of the complexity in treating an anisotropic environment [135]. Recent work has focused on estimating the spatial extent of localization through the photoelectron angular distributions obtained in 2PPE experiments [7,44,58]. The results for systems studied to date are consistent with localization on molecular length scales and provide interesting contrasts with the relevant length scales in bulk systems. Angle-resolved photoemission has been used traditionally as a probe of band structure in two and three dimensions [22,141]. Measuring the dispersions, or lack thereof, of electronic states at interfaces has proved a powerful tool, especially when combined with time-resolved spectroscopy. Although it is known a priori that parallel momentum ( hk k ) is not a good quantum number for a localized state, its wavefunction can be described in the free-particle basis of the photoelectrons. The rate for photoemission into a final state with a given momentum depends on the weight of the momentum state in the initial localized state. The photoelectron angular distribution is therefore a function of the original state of the electron, with the intensity as a function of momentum dependent on the superposition of momentum states that describes the localized electron. How much of this information is preserved in the experimental observables, and how should it be interpreted? 6.1. Theoretical basis As detailed in Section 2, the IPS electron is (assuming a lack of significant structural disorder) initially localized in a single dimension, the direction perpendicular to the interface, and delocalized in the parallel degrees of freedom. When the electron is localized in all three dimensions by interacting with the polarization of the molecular layer, it can no longer be described in terms of a single kk state but, rather, as a superposition of states with differing parallel momenta, hk k . With a known distribution in kk, the spatial extent of the electron parallel to the interface is obtained from the Uncertainty Principle

32


1 rxk rkk P ; 2

ð12Þ

where rxk and rk k are the standard deviations in parallel extent and parallel wavevector, respectively. The equality applies for the case of Gaussian distributions in xk and k k. Bezel et al. [7,44] make use of the photoelectron distribution at a fixed energy, assuming a purely nondispersive state. The approach is summarized below. For ease in computation and interpretation, it is assumed that the localizing potential does not break the separability of perpendicular and parallel degrees of freedom that exists while the electron is still delocalized. Wavepacket simulations of photoelectrons emitted from a potential well at the surface show that this approximation is well justified [44]. The simulations also show that, even for self-trapping well depths larger than those encountered in a typical 2PPE experiment, the effects of final state structure on the distribution are minimal. The initial state, assumed localized, and the final photoelectron state are expressed in the plane-wave basis X j Wi ðx; y; zÞi ¼j vðzÞi akk expðik i;x xÞ expðik i;y yÞ expði/kk Þ; ð13Þ kk

j Wf ðx; y; zÞi ¼ expðik f;z zÞ expðik f;x xÞ expðik f;y yÞ; ð14Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where k k ¼ k 2x þ k 2y ; akk aki;x ;ki;y , and the /kk are phase factors. Photoemission is induced by the action of fields acting in the z direction, so it does not affect the x and y components of the states. The rate of photoemission is then 2p 2 jz qf ðEf Þ j hwf ðx; yÞ j wi ðx; yÞij dðEf Ei hxÞ h X 2 ¼ j akk j expði/kk Þ expði/kk Þ

P ðEf Þ ¼

ð15aÞ

kk

Z Z

dxdy expðiðk i;x k f;x ÞxÞ expðiðk i;y k f;y ÞyÞ

2p jz qf ðEf ÞdðEf Ei hxÞ; h

ð15bÞ

where ^ j vðzÞij2 jz ¼j hexpðik f;z zÞ j dH

ð16Þ

^ is the perturbation applied by the elecdescribes the transition in the z direction, dH tric field, and Ei and Ef are the initial and final energies, respectively. The qf(Ef) is the density of final states which depends only on the coordinates in which the transition takes place qf ðEf Þ ¼ qz /

1 : hk f;z

ð17Þ


33

The total momentum is fixed by the angle-independent kinetic energy. Because the final state is dispersive, the component of momentum in the z direction will vary depending on the magnitude of kk in the final state. The dependence on parallel momentum causes the density of states to be a function of the photoemission angle qf ðEf Þ /

1 1 : ¼ hk f;z hk f cos h

ð18Þ

Clearly, the rate of photoemission is zero unless the parallel momenta of the initial and final states are equal. The expression for the photoelectron angular distribution is thus X 2 2p P ðEf Þ ¼ jz qf ðEf ÞdðEf Ei hxÞdki;k ;kf;k j ak k j ð19aÞ h kk X j ak k j 2 ð19bÞ / kk

or, in terms of kk 2

P ðk k Þ /j akk j :

ð19cÞ

Further details are provided in an article by Bezel et al. [44]. Several comments are in order. First and foremost, the rate of photoemission from a localized state is proportional to the squares of the Fourier coefficients for each kk state. It is, however, independent of the relative phases /kk of the various states in the superposition. In other words, the experiment is sensitive not to the amplitudes of the kk states but rather their squared amplitudes, so all phase information is lost. The amplitude of the 2PPE signal as a function of angle should be multiplied by 1=cos4 ðhÞ to account for the angle-dependent electric field components perpendicular to the surface for both pump and probe pulses, which is generally a small correction. The resulting distribution, calculated for a fixed energy, yields the width of the localized state in kk. Results obtained for 2 ML PrCN/Ag(1 1 1) and D2O bilayers on 2 Cu(1 1 1) give Gaussian envelopes for j akk j vs. kk, centered at kk = 0 [7,44,58]. With a known width characterized by a standard deviation rkk , (12) may be rearranged to get a lower bound for the spatial extent, rxk . In the case that the terms in the superposition are exactly in phase with each other, there will be maximum constructive interference giving the most localized particle. Both the distribution of j akk j2 and the actual wavefunction jwi(kk)iare Gaussians when this occurs. The Fourier transform of a Gaussian distribution in kk is a Gaussian distribution in xk, satisfying the conditions that give the minimum uncertainty in (12). It is convenient to express the result in terms of the FWHM for xk and kk Dxk ¼

4 ln 2 : Dk k

ð20Þ

34


In general, the relative phases in the superposition need not be equal. In this case, destructive interference between kk states will lead to a larger spatial extent. If it were possible to actually measure jwi(kk)i and apply the Fourier transform, the effect would be obvious. The width in kk, however, does not change. The Fourier transform of the photoelectron distribution should therefore be taken as a lower bound on the spatial extent of the localized state, exactly as predicted by the Uncertainty Principle in (12). It is difficult to predict exactly how large the electron could get and still be considered nondispersive, and there is no analogous method to determine the spatial extent of a delocalized electron to suggest an upper bound. Both dispersive and nondispersive states can persist even in the absence of long-range order in the adsorbate layer [7], so, strictly speaking, the relevant domain size cannot be obtained through photoemission or diffraction techniques. However, a completely random phase distribution will tend to delocalize the particle. This implies that there should be at least partial coherence in the construction of the localized state. Theoretical predictions of localization in two-dimensional systems state that the electron collapses to the size of a single lattice site [78,79,142]. The continuum model, highlighted in Section 5, agrees with previous predictions but does not rule out the possibility of larger spatial extents as stable bound states [81]. 6.2. Experimental examples In the case of 2 ML PrCN/Ag(1 1 1), the lower bound the above method provides ˚ FWHM, or approximately the size of a single molecule [44]. The PrCN is 15 ± 4 A results are interesting in that they do not show a significant dependence on time. Theoretical calculations of this system predict that, once localization completes, the electron indeed collapses to the size of a single molecule [81]. The photoelectron angular distribution is blind to more subtle evolution of the spatial extent caused by coherence issues, i.e. evolution of the relative phase factors. The probability of finding the electron localized after a given amount of time at the surface is correlated with the degree of solvation. Solvation is still observed at longer times after the local-

Table 1 Spatial extent of localized states for excess electrons in bulk systems and at interfaces ˚) System Standard deviation (A Method Reference Methanol H2O D2O/Cu(1 1 1) PrCN/Ag(1 1 1) PrCN/Ag(1 1 1)

2.5a; 3.5–3.8b 2.05 ± 0.1a; 3b 4–8c 6.4 ± 1.6c 12.56c

Calculated radius of gyration Calculated radius of gyration 2PPE 2PPE Continuum model

Standard deviations are calculated from Gaussian distributions. a s state. b p states. c Parallel to interface.

[132] [130,131] [58] [44] [81]


35

ized state dominates, but at a reduced rate [7]. Therefore, the greatest amount of energy relaxation occurs during the formation of a molecular-scale trap site. The results make use of a kk intensity distribution calculated at a single fixed energy, i.e. the energy of the peak center at h = 0°. In general, a distribution of trap sizes caused by heterogeneity in the environment experienced by different electrons results in inhomogeneous broadening in the 2PPE spectra. The effects of inhomogeneity on angle-resolved measurements of localization have been discussed extensively by Bovensiepen et al. [58] and taken into account in their analysis of the spatial extent of electrons in D2O/Cu(1 1 1). The energy-dependent kk distribution has been fit over the entire solvated electron peak, over 200 meV FWHM. The width of the kk distribution was found to be inversely proportional to kinetic energy and could be well modeled as a linear relationship. The results, a spatial extent varying from ˚ FWHM at the low-kinetic-energy side to 19 A ˚ FWHM at the high-kinetic-energy 9A side, are consistent with electrons in deeper trap sites with higher binding energies being localized more tightly. The spatial extents estimated for several different systems, both interfacial and bulk, by different experimental and theoretical techniques are summarized in Table 1. In general, the excess electrons are found to have a smaller spatial extent in bulk systems. This may be in part due to the full three-dimensional localization potential experienced by an electron in a cavity. For D2O/Cu(1 1 1), where electron density within the molecular layers was suggested, the shorter lifetime of the electron compared to measurements in bulk water can prevent the formation of a fully equilibrated solvent cavity and thus a larger spatial extent [58]. The effects of the metal interface on the static layer structure may also play a role. Further work is needed to elucidate the effects of substrate and layer structure on the dynamics and spatial extent of localization.

7. Conclusions Since the original studies of IPS at vacuum/metal interfaces, 2PPE has established itself as a valuable technique for determining the electronic properties of a variety of interfaces as a function of composition and structure. With recent demonstrations of the ability to measure the dynamics, energetics, and spatial extent accompanying electron localization, the utility of 2PPE as a probe of electron dynamics is greatly extended. Further experimental and theoretical work will likely expand the range of systems studied as questions relevant to electrochemical and molecular–electronic interfaces are explored. Although the application of 2PPE to dielectric/metal systems is still a relatively young field, there is enormous potential to describe quantitatively the fundamental natures and ultimate fates of electrons at interfaces. A physical picture for the mechanism of solvation and localization is coalescing. In the earliest moments, the electron is diffuse, though finite, and the polarization of the layer is weak. As the electron localizes, the filmÕs response to the charge also in-

36


creases. The correspondence of the rise time of the localized state and the fastest time constant of the solvation response suggests that the initial component of the solvation is due to the electron collapsing to a solvent cavity, and the remainder of the solvation, the picosecond components, are due to the structural rearrangement of the solvent around the localized charge. In this picture, the fastest solvation time scale observed (250 fs in the 2 ML PrCN/Ag(1 1 1) system, 6100 fs for D2O/ Cu(1 1 1) interfaces) corresponds to the collapse of the electron wavefunction together with the inertial response of the solvent.

Acknowledgement The authors would like to thank T. Heinz for helpful discussions. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the US Department of Energy, under Contract No. DE–AC03–76SF00098. The authors acknowledge the National Science Foundation support for specialized equipment used in the experiments described herein.

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