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10332

J. Phys. Chem. B 2000, 104, 10332-10338

Electronic Structure at Organic/Metal Interfaces: Naphthalene/Cu(111) Hanfu Wang, Gregory Dutton, and X.-Y. Zhu* Department of Chemistry, UniVersity of Minnesota, Minneapolis, Minnesota 55455 ReceiVed: June 21, 2000; In Final Form: September 8, 2000

Electron transfer at organic/metal interfaces is a fundamental issue of interest to a large number of problems in chemistry. We use two-photon photoemission (2PPE) spectroscopy to investigate heterogeneous electron transport in a model system: naphthalene adsorbed on Cu(111). The dependence of 2PPE spectra on photon energy establishes the occurance of photoinduced electron transfer to an unoccupied state at 3.1 eV above the Fermi level (or 1.1 eV below the vacuum level) at one monolayer coverage. Polarization and dispersion measurements reveal the image-like property of this electron-transfer state. The binding energy of this state is dependent on the thickness of the adsorbate layer. This observation is in agreement with simulation based on the dielectric continuum model. The simulation also shows that, while partially distributed in the adsorbate layer at one monolayer coverage, the excited electron is confined within the adsorbate layer at high coverages, an effect which can be attributed to the electron affinity of naphthalene.

1. Introduction Electron transport at metal/organic interfaces is important in a number of scientific disciplines. In molecule-based electronic and optoelectronic devices, such as organic light-emitting devices (LED) and organic field-effect transistors (FET), charge injection from metallic electrodes into the molecular layer is a critical step in the overall mechanism.1,2 The barrier for electron injection in organic devices is often described as ∆E ) Φ - A, where Φ is the work function of the metal electrode and A is the electron affinity of the organic layer.3 However, ∆E is a thermodynamic quantity, while electron injection at the interface is a dynamic process which depends intimately on the interfacial electronic structure.4 Interfacial electron-transfer dynamics and electronic structure are determined by the electronic interaction between the organic molecule and the metal surface, by the band structure of the metal, and by other surface states such as image states. Interfacial electron transport is important in the emerging field of molecular electronics, which often involves the assembly of organic molecules as functional devices on the surfaces of metal electrodes. In this case, the electronic interaction, i.e., the extent of wave function mixing, between the molecule and surface determines not only contact resistance but also the nature of the molecular device.5 The physical questions of concern to organic LEDs, FETs, and molecular electronics are also being addressed in many other active research fields, such as solar energy conversion6,7 and surface photochemistry.8 We use naphthalene/Cu(111) as a model interface and employ laser two-photon photoemission (2PPE) to study electron transfer at organic/metal interfaces. This system is chosen for the following reasons: (a) Most organic devices use conjugated molecules as active components.1-3 For example, pentacene has been demonstrated in the most successful organic FETs to date.9,10 The naphthalene/Cu(111) system is a simple model for aromatic/metal interfaces. The absence of chemical reaction on this surface provides additional simplicity. (b) 2PPE spectroscopy has been demonstrated in previous studies on image states * Corresponding author. Email: [email protected]. Fax: (612) 6267541.

to be an ideal technique for probing interfacial electron transfer.11-14 Unlike one-photon photoemission spectroscopy, which is limited to occupied states, 2PPE is particularly useful in probing the electron transfer to unoccupied electronic states. When femtosecond laser pulses are used, 2PPE can be carried out in a time-resolved manner to directly probe the ultrafast electron-transfer dynamics. Previous applications of 2PPE have been most successful in the probing image states on metal surfaces.11-14 Image states arise from the Coulomb attraction between an electron outside a metal surface and the polarization charge at the surface. This Coulomb potential results in a series of Rydberg-like bound states for an excited electron. The energetics and dynamics of image states are strongly perturbed by the presence of an adsorbate layer on the metal surface, as determined by the dielectric constant, electron affinity (EA), and thickness of the adsorbate layer. These effects can be successfully accounted for by a dielectric continuum model (DCM), as demonstrated by Harris and co-workers for alkanes and inert gas atoms adsorbed on Ag(111).15,16 In the alkane/Ag(111) system, the repulsive electron affinity forms a tunneling barrier between the vacuum and the surface, leading to an exponential increase in the image state lifetime with increasing layer thickness.15 For Xe adsorbed on Ag(111), the attractive electron affinity of the adsorbate layer is responsible for the coupling of some of the image states to the adsorbate conduction band, resulting in the formation of quantum wells.16 The dielectric continuum model generally predicts that adsorbed molecules with attractive electron affinity tend to trap the image electron wave function within the adsorbate layer.17,18 A key question is whether an adsorbate with sufficiently attractive EA can lead, beyond the simple modification of the image state, to the formation of a transient anionic molecular state from photoinduced electron transfer in the 2PPE process? In strong chemisorption systems, 2PPE studies have shown electron transfer to occur in adsorption-induced unoccupied surface states, including the π* state in the CO/Cu(111) system19,20 and the σ* state in the Cs/Cu(111) system.21-24 Zhu and co-workers studied a weak chemisorption system, C6F6/

10.1021/jp002257p CCC: $19.00 © 2000 American Chemical Society Published on Web 10/19/2000

Organic/Metal Interfaces: Naphthalene/Cu(111) Cu(111), in which the molecule possesses a high EA, and observed the formation of a molecular anionic state at 1.8 eV below the vacuum level.25,26 This was interpreted as photoinduced electron transfer to the σ* lowest unoccupied molecular orbital (LUMO). However, beyond C6F6/Cu(111), evidence for molecular anion formation is scarce in 2PPE studies of adsorbate/metal systems. Several groups have carried out 2PPE studies of benzene adsorbed on metal surfaces, but the results are not conclusive.17,27-28 Velic et al. reported the observation of an unoccupied state at 0.6 eV above the vacuum level for bilayer benzene adsorbed on Cu(111) and attributed this to the occupation of the benzene π*e2u LUMO.28 Gaffney et al. studied the benzene/Ag(111) system and reported the absence of an anionic molecular resonance.17 Instead, these authors found that adsorbed benzene modifies the n ) 1 image state due to its attractive EA. In the present study, we investigate the naphthalene/Cu(111) system using 2PPE. Naphthalene has a more attractive electron affinity than that of benzene. In the condensed phase, the electron affinity of naphthalene is 1.42 eV.29 Frank et al. studied a series of aromatic hydrocarbons adsorbed on Ag(111) using inverse photoemission (IPE).30 For 2-3 monolayers (ML) of naphthalene on Ag(111), they assigned an unoccupied state at 1.1 eV below the vacuum level as the π*b2g first-electron affinity level of molecular naphthalene. As shown below in the naphthalene/Cu(111) system, we also observe an unoccupied state at 1.1 eV below the vacuum level in 2PPE at 1 ML coverage. However, dispersion measurement reveals that this electron transfer state has substantial image-like character. The image-like property is confirmed with measurements of coverage dependence and with simulation by the dielectric continuum model. 2. Experimental Section All experiments were carried out in an ultrahigh vacuum (UHV) chamber pumped by a turbo molecular pump with a base pressure of 1 × 10-10 Torr. The system consisted of two levels. The upper level was equipped with a low-energy electron diffraction (LEED) and Auger electron spectrometer (AES) for surface analysis, an ion sputtering gun for surface cleaning, and a quadrupole mass spectrometer (QMS) for residual gas analysis (RGA) and thermal desorption spectroscopy (TDS). The lower level housed a homemade electron time-of-flight (TOF) spectrometer for 2PPE spectroscopy. The total flight distance (fieldfree region) was 30 cm. Electrons were detected by multichannel plates with a φ40 mm active area. The signal from the anode was coupled out via a vacuum compatible capacitor (270 pF) mounted on the back of the anode and, after preamplification, was recorded by a multichannel scaler (MCS) with 5 ns resolution (EG&G). The TOF spectrometer was protected by a magnetic shield. The Cu sample was inserted through a hole at the top of the magnetic shield and positioned 1-2 mm from the opening of the flight tube. Laser light for 2PPE was from a tunable dye laser (Continuum ND6000) pumped by the second harmonic output of a Qswitched Nd:YAG laser (Continuum Powerlite 7010). The frequency-doubled dye laser output (300-350 nm, 5 ns pulse width) was guided through an iris (1 mm ID) and a quartz window and directed at the Cu(111) surface. Except during dispersion measurements, the angle-of-incidence was 60° from surface normal, and the reflected light exited the UHV chamber through an UV window. This corresponds to the detection of photoelectrons along the surface normal, i.e., with zero parallel momentum. In dispersion measurements, the sample was rotated;

J. Phys. Chem. B, Vol. 104, No. 44, 2000 10333 thus, both the light incident angle and the electron detection angle varied in this experiment. The polarization of the incident light was controlled by a half-wave plate. For p-polarization, the electric field vector is parallel to the plane-of-incidence (defined by the light propagation direction and the surface normal). For s-polarization, the electric field vector is perpendicular to the plane-of-incidence. The s-polarized light was only used in experiments on polarization dependence; all other measurements were performed with p-polarized light. All 2PPE spectra were recorded with a laser pulse energy density of e5 mJ/cm2 to avoid any possible space charge effect. The sample temperature was maintained at 115 K in these experiments. Except during dispersion measurements, a positive bias was applied to the sample to improve energy resolution. The onset of the secondary electron signal in each 2PPE spectrum was used to determine the work function of the surface. In these experiments, a negative sample bias was used to accelerate the photoemitted electrons. The value of the onset is plotted as a function of the bias voltage, and the value at zero bias voltage is extrapolated from the plot to obtain an accurate value of the work function. The Cu(111) sample (φ10 mm, polished to within 1° of the 〈111〉 direction) was mounted at the center of the chamber on a sample manipulator. It was cooled with liquid nitrogen and heated resistively through two W wires mounted on the edge of the sample. The temperature was measured by a type-K thermocouple inserted into a small hole on the edge of the Cu crystal. Cleaning was achieved with repeated cycles of Ar+ sputtering (1.1 keV) and annealing (750 K) to yield a sharp (1 × 1) LEED pattern. The clean surface was further confirmed by AES. Naphthalene (Aldrich, 99%) was degassed at 350 K on a vacuum line to remove impurities, particularly water, and the purity of naphthalene was verified by RGA. Naphthalene vapor was introduced into the chamber by a pinhole doser, with the end of the doser tube terminated at ∼1 mm from the surface. The entire gas-handling assembly was kept at a constant temperature of 350 K during dosing. The substrate temperature was 165K for the dosing of multilayers and 205 K for one monolayer. Thermal desorption spectra (TDS) were recorded with the QMS set to the parent ion signal at a sample temperature ramp of 1.5 K/s. All coverages were presented using a relative scale, with 1 ML corresponding to the saturation of the high temperature (>200 K) desorption peak in TDS. 3. Results and Discussions This part is organized into four sections. In section 3.1, we discuss the adsorption of naphthalene on Cu(111) from TDS and work function measurements. The energetic position of an unoccupied surface state is determined in section 3.2 on the basis of the dependence of 2PPE spectra on photon energy; optical transitions involved in this 2PPE process show σ symmetry, as revealed by the dependence of 2PPE signal on light polarization. In section 3.3, dispersion measurements are used to establish the image-like property of the unoccupied state. Section 3.4 presents experiments on coverage dependence and simulation based on the dielectric continuum model. 3.1. Adsorption of Naphthalene on Cu(111). Naphthalene adsorbs molecularly on Cu(111), and there is no dissociation upon heating. Molecular naphthalene is the only species observed in the QMS during the temperature ramp, and the clean Cu(111) surface is recovered each time after TDS measurement. This observation agrees with previous measurements of the adsorption of aromatic molecules on Cu(111)31 and similar surfaces.32-33

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Figure 2. Work function of Cu(111) as a function of naphthalene coverage.

Figure 1. Temperature programmed desorption spectra of naphthalene from Cu(111) surface at the indicated coverages (0.6-4.8 ML). The inset shows an expanded view of spectra at 0.6, 1.0, and 1.2 ML coverages. The QMS signal of C10H8+ was followed in the measurement. The linear heating rate was 1.5 K/s.

Figure 1 shows a set of thermal desorption spectra of naphthalene at various coverages. At low coverages, there is only one broad desorption peak (R) centered at ∼285K. As coverage increases, a sharp peak (β) at 202 K appears. This desorption peak saturates at coverages above 2 ML. At higher coverages, a third desorption peak (γ) at 194 K appears and grows. Above 4 ML, the two lower-temperature peaks merge into a single peak which does not saturate with further dosing. The thermal desorption of naphthalene from Cu(111) is very similar to that of other aromatic molecules on noble metal surfaces,31-33 including C6H6 on Cu(111).31 A common observation in these systems is the substantial broadening of the thermal desorption peak with increasing coverage in the monolayer region, an effect which can be attributed to the repulsive interaction between adsorbed molecules. Thermal desorption spectra in these systems often show a second-layer desorption peak at a temperature slightly higher than that from multilayer desorption. For example, for C6H6 on Cu(111), the monolayer desorption peak starts at 240 K and broadens to ∼150 K at near-saturation.31 TDS of benzene from Cu(111) features a sharp second-layer peak at 157 K, which is only 5 K higher than the multilayer desorption temperature. The assignment of a second molecular layer of benzene on Cu(111) was supported by high-resolution electron energy loss spectroscopy (HREELS) and near-edge X-ray absorption fine structure (NEXAFS).31 These techniques also show that benzene adsorbs on Cu(111) with the π ring parallel to the surface in the first molecular layer and perpendicular to the surface in the second layer. In view of previous studies on benzene/Cu(111)31 and other aromatic/metal systems,32,33 we assign the high-temperature desorption peak (R) to monolayer desorption and the two lowertemperature desorption peaks (β and γ) to desorption from the second layer and multilayers, respectively. Previous studies on Ag, Ru, and Pt single-crystal surfaces have shown that, like benzene, naphthalene adsorbs with the π ring parallel to the surface in the monolayer region.34-41 A recent STM study in aqueous solution also shows that naphthalene forms a highly ordered adlayer on Cu(111) in a flat-lying geometry.42 In the present UHV study, we expect that the first

Figure 3. Two-photon photoemission spectra of the clean Cu(111) surface obtained at hν ) (a) 4.00 and (b) 4.20 eV. (c) Two-photon photoemission spectra for 1 ML naphthalene/Cu(111). SS, surface state; IS, image state; X,adsorbate-induced state.

layer of naphthalene also adsorbs with the molecular plane parallel to the surface, with the second layer in a perpendicular geometry. We have determined the change in surface work function as a function of naphthalene coverage on Cu(111). Each data point in Figure 2 is obtained from the onset of secondary electron signal in the 2PPE spectrum at a particular coverage. Adsorption of 1 ML naphthalene reduces the work function considerably from 4.9 eV for clean Cu(111) to 4.2 eV. Further increase in surface coverage only reduces the work function slightly. When the coverage is above 3ML, the surface work function becomes stable around 4.0 eV. This observation is typical for the adsorption of aromatic molecules on metal surfaces.28,34 The decrease in surface work function can be attributed to the polarizability of π electrons in the aromatic molecule. 3.2. Unoccupied State in Naphthalene/Cu(111). Figure 3 compares the 2PPE spectra of clean Cu(111) (hν ) 4.0 and 4.2 eV) with that of 1 ML naphthalene-covered surface. Note that the kinetic energy is scaled to the Fermi level. For clean Cu(111) at hν ) 4.0 eV, the spectrum features a single peak at 7.6 eV, which results from the two-photon ionization of an occupied surface state (SS) at 0.4 eV below the Fermi level.28 At this

Organic/Metal Interfaces: Naphthalene/Cu(111)

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Figure 5. Comparison of two-photon photoemission spectra obtained under the irradiation of p-(solid) and s-(dashed) polarized light for 1 ML naphthalene/Cu(111) at a photon energy of 3.76 eV.

Figure 4. (a) Two-photon photoemission spectra for 1 ML naphthalene/ Cu(111) at the indicated photon energies (3.70-4.07 eV). (b) Position of peak X in panel a as a function of photon energy. The solid line is least-squares linear fit, which yields a slope of n ) 1.00 ( 0.04.

photon energy, image states (IS) are not accessible. At a higher photon energy, hν ) 4.2 eV, both the surface state and the first image state, located at 0.8 eV below the vacuum level, are observed in the 2PPE spectrum. These results are in agreement with those from previous studies of the Cu(111) surface.28,44 When Cu(111) is covered with 1 ML naphthalene, the 2PPE signal from the surface state is significantly diminished, as expected from chemisorption. A new peak (X), at the lower kinetic energy side of SS, now dominates the spectrum. To establish the nature of this new peak, we record 2PPE spectra as a function of photon energy. In 2PPE measurement, if an electron is excited directly from a filled state below the Fermi level by the absorption of two photons, the shift in electron kinetic energy ∆Ekin is scaled with 2∆hν. If 2PPE involves onephoton photoexcitation of an electron into an empty state between the Fermi level and the vacuum level followed by the photoionization of this transient state, ∆Ekin should be scaled with ∆hν. Figure 4a shows a set of 2PPE spectra for 1 ML naphthalene/ Cu(111) at the indicated photon energies between 3.70 and 4.07 eV. The positions of both peaks increase with increasing photon energy but at different rates. For the surface state, ∆Ekin scales with 2∆hν, as expected for the two-photon ionization of the occupied surface state. The position of peak X increases with hν at a slower rate. This is shown more clearly in Figure 4b, which plots Ekin versus hν for peak X. The data can be well described by a straight line with a slope of n ) 1.00 ( 0.04. Thus, peak X in the 2PPE spectra from 1 ML naphthalene/ Cu(111) results from electron-transfer to an empty level between the Fermi and vacuum levels. In the following section, we will refer to this state as an “unoccupied state” or an “electrontransfer state”. The energetic position of this state can be calculated from the kinetic energy of the photoelectron and from the photon energy. It is located at 3.10 ( 0.05 eV above the Fermi level or 1.10 ( 0.05 eV below the vacuum level. This result is in excellent agreement with a study of naphthalene/Ag(111) using

inverse photoemission (IPE) spectroscopy, which revealed an unoccupied state at 1.1 eV below the vacuum level.30 The IPE study assigned the unoccupied state as the π*b2g first-electron affinity level of molecular naphthalene. Supporting this assignment, the authors found that, for a series of aromatic molecules (benzene, naphthalene, anthracene, and tetracene), the unoccupied level in the adsorbate state decreases with increasing molecular size, in agreement with the trend for the first-electron affinity level in the gas phase. However, as we show below, the unoccupied state observed for naphthalene/Cu(111) is not a simple molecular anionic state. It is strongly coupled to the n ) 1 image state on the Cu surface. The optical transitions involving the unoccupied state on 1 ML naphthalene/Cu(111) have predominantly σ symmetry. This is shown in the dependence of the 2PPE signal on light polarization. Figure 5 compares the 2PPE spectra for 1 ML naphthalene/Cu(111), obtained using p- and s-polarized light, respectively; the 2PPE signal from the unoccupied state drops almost to zero when the light is switched from p- to spolarization. Similar observation is well-established for the image states on metal surfaces.11-17,28, 44 3.3. Dispersion Measurement and Free-Electron-Like Behavior. To understand the nature of the unoccupied state observed for naphthalene/Cu(111), we carry out dispersion measurements to establish the extent of declocalization parallel to the surface using angle-resolved two-photon photoemission. In this experiment, the angle of electron detection is varied by rotating the sample. The sample is not biased, and the kinetic energy of the photoelectron, Ekin, is referenced to the vacuum level of the sample. The electron momentum vector parallel to the surface is given by12

k| )

x

2meEkin p2

sin θ

(1)

where me is the free-electron mass and k| is the parallel momentum vector; θ is the angle with respect to the surface normal. Figure 6 shows the measured dependence of Ekin on k| for 1 and 4 ML of naphthalene, respectively, at a photon energy of 3.67 eV. Each dispersion curve can be represented by an effective electron mass derived by fitting to the following parabolic function:12

pk|2 Ekin ) Eo + 2meff

(2)

where meff is the effective electron mass. The fits give the

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Figure 6. Dispersion of peak X for 1 and 4 ML of naphthalene/Cu(111) at a photon energy of 3.76 eV.

following effective masses: meff ) (1.43 ( 0.12)me and (1.70 ( 0.19)me for 1 and 4 ML coverages, respectively. These results show that the observed electron-transfer state is free-electron-like. For comparison, the effective electron mass of anionic states in organic crystals is typically in the range of (102-104)me at a temperature range between 0 and 100 K.45 In solid naphthalene, meff for the c′ direction is about 3 × 104me at 100 K.45 Thus, we conclude that the observed electron-transfer state for monolayer or multilayer naphthalene adsorbed on Cu(111) is not due to a pure molecular anionic resonance, as assigned previously as the π*b2g first-electron affinity level in the inverse photoemission study.30 The free-electron-like behavior must involve a significant, if not dominant, contribution from delocalized metal states. Because the energetic position of the observed molecular resonance is close to that of the n ) 1 image state on Cu(111), the molecular anionic resonance can couple strongly to the image state. Indeed, the experimental results are in good agreement with results from the simulation based on the dielectric continuum model, as detailed below. Gaffney et al. recently reported a time- and angle-resolved 2PPE study of the benzene/Ag(111) system.17 The effective mass of the first image state was (0.9 ( 0.1)me, (1.0 ( 0.1)me, and (1.2 ( 0.2)me for 1, 2, and 3 ML of adsorbate, respectively. The electron masses for naphthalene/Cu(111) in the present study are higher than those in the benzene/Ag(111) system. Such a difference may indicate more contribution to the electron wave function from naphthalene than from benzene. This is understandable because the electron affinity of naphthalene is higher than that of benzene. 3.4. Coverage Dependence and the Dielectric Continuum Model. Figure 7 shows a set of 2PPE spectra taken at a photon energy of 4.00 eV for naphthalene/Cu(111) at various surface coverages. Only the surface state (SS) is observed on clean Cu(111); image states are not accessible at this photon energy. With the adsorption of 0.6 ML naphthalene, the image-like state (X) appears at Ekin - EFermi ) 7.2 eV, a result of the significant decrease of the surface work function (φ). Based on φ and hν, we obtain a binding energy, EB ) 1.03 ( 0.05 eV (below the vacuum level). When the surface coverage is increased to 1 ML, the kinetic energy of the image-like state further decreases due to a decrease in work function. At the same time, the binding energy of this state also reaches a minimum. As the coverage further increases beyond 1 ML, the kinetic energy of the imagelike state increases, indicating a decrease in binding energy. No further shifts are observed for coverages above 3 ML. On the bases of photon energy and the calibrated work functions, we have converted the peak positions of the image-like state in

Figure 7. Two-photon photoemission spectra obtained at hν ) 4.00 eV from clean and naphthalene-covered Cu(111) at the indicated coverages (0.6 -4.8 ML).

Figure 8. Binding energies (solid squares) of state X as a function of coverage. The open circles are from the simulation in Figure 9.

Figure 7 to binding energies, shown in Figure 8. The binding energy of the unoccupied state decreases from the monolayer value of 1.13 to 0.86 eV at high coverages. The image-like properties of the unoccupied state warrants simulation based on the dielectric continuum model (DCM). This model has been successfully applied to simulate the imagepotential states at various dielectric/metal interfaces.13,15-17 Instead of considering the detailed band structure of adsorbates, the DCM model uses the electron affinity and the dielectric constant as parameters to modify the Coulomb potential outside the surface.15-17,28 In this simulation, solutions of the nearly free electron (NFE) model15-17,46 are used to represent the evanescent wave for the image state wave function within the Cu(111) substrate. The amplitude and slope of the evanescent wave at the metal dielectric boundary are used as initial values to propagate the wave function numerically through the modified image potential region outside the metal surface via a Runge-Kutta algorithm. Trial solutions of different energies are screened to identify the valid solution for the n ) 1 image state according to the following criteria: (a) the wave function has no nodes along the surface normal direction, and (b) the wave function vanishes at large distance from the metal surface.

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In the NFE model, the crystal potential of the ion core can be expanded by a Fourier series in the reciprocal lattice vectors g. The eigenvalues () are obtained from the secular equation

|

|

(p2/2m*)k2 -  Vg )0 Vg (p2/2m*)(k - g)2 - 

(3)

where Vg is the half-width of the gap; m* is the effective electron mass along the surface normal. The wave function inside the metal crystal is

ΨB ) eqz cos(pz + δ)

(4)

where p and q are the real and imaginary part of the complex wave vector k and δ is the phase shift. These parameters are all obtained from solution to eq 3. ΨB is used as the starting point in the Runge-Kutta algorithm to propagate the wave function outside the metal. The potential outside the metal consists of two regions: a modified image potential within the molecular layer, VM, and an electrostatic potential on the vacuum side, VV. They are given by

VM(z) ) -

e2(d - 1)(t + 2z) e2(d - 1) e2 + + 4dz 4d(d + 1)(t - z) 4dt(d + 1)(z + t) δVM(z) - EA

VV(z) ) -

e (d - 1) e + δVV(z) 2(d + 1)z 4d(d + 1)(z - t) 2

2

(5)

where z is the distance from the metal surface, d is the dielectric constant of the adsorbate layer, and t and EA are the thickness and the electron affinity of molecular layer, respectively. δVM(z) and δVV(z) are correction terms, as detailed previously.15-17,47 The parameters for the NFE model describing the Cu(111) substrate are from the literature.18 The bottom of the sp band is -8.6 eV, and the lower and upper edges of the band gap are -0.9 and 4.15 eV from the Fermi level, respectively. The dielectric constant of naphthalene layers was set to be the liquid value of 2.54.48 In the absence of information on the band structure normal to the surface, we use the free-electron mass in simulation. The value of the electron affinity (EA) in the adsorbate layer is not known. EA values for gas-phase and solidphase naphthalene are -0.1949 and 1.42 eV,29 respectively. In our simulation, an EA value of 0.75 eV is chosen to provide the best agreement between the binding energies from 2PPE measurements and eigenvalues from simulation. We assume the thickness of one monolayer naphthalene to be 2.4 Å, which is taken from the value assumed for 1 ML benzene on Ag(111).17 The thickness of each additional layer is assumed to be about 5 Å, obtained from crystalline naphthalene.45 To avoid singularity at the metal/dielectric interface, we cut off the potential was at the Fermi energy near the Cu(111) substrate. At the dielectric/ vacuum interface, the potential is linearly interpolated over a range of 3 Å around the interface. Figure 9 shows the calculated image-like (n ) 1) wave function (solid curve), along with the potential used for each naphthalene coverage. As the coverage increases, the wave function becomes increasingly localized within the molecular layer. This is expected due to the attractive electron affinity of naphthalene. The same trend was also observed in the benzene/ Ag(111) system. The calculated eigenvalues (open circles) are

Figure 9. Calculated image potentials (dotted line) and wave functions (solid curves) for various coverages of naphthalene/Cu(111). Z is the distance from the metal surface. A positive value of Z corresponds to the adsorbate and vacuum side, while a negative value refers to the inside of the metal. The vertical solid line at z ) 0 is the Cu(111)/ adsorbate interface, and the vertical dashed line is the adsorbate/vacuum interface.

compared with experimental measurements in Figure 8. Considering the simplicity of the model, the agreement is satisfactory. Note that the binding energy at 0.6 ML is ∼0.1 eV less than that at 1.0 ML. This difference can be misleading because the average surface work function is used in the calculation. At the submonolayer coverage, adsorbed naphthalene molecules likely form islands with monolayer thickness. The local work function on adsorbate-covered area is the same as that on the 1 ML covered surface. Considering the difference in the average work function between 0.6 and 1 ML coverages (Figure 2), the actual binding energy of the unoccupied state on islands of adsorbatecovered surface at 0.6 ML is likely the same as that at 1 ML coverage since the unoccupied state is pinned to the local vacuum level. It is important to point out that, while the unoccupied state observed for naphthalene/Cu(111) is image-like and can be qualitatively accounted for by the dielectric continuum model, the contribution to this state from the molecular anionic resonance should not be ignored. In fact, the inclusion of electron affinity in the DCM is a simplified representation of the coupling of the molecular resonance with the image state. The observation by Frank et al. in inverse photoemission for a series of aromatic molecules attests to this idea.30 The binding energy of the lowest unoccupied state for aromatic molecules on Ag(111) was found to increase gradually from 0.6 eV for benzene to ∼2.0 eV for tetracene. In the latter case, the unoccupied state is located significantly lower than what is commonly observed for image states. Does it consist predominantly of the anionic molecular resonance? What is the dispersion of this kind of molecular electron-transfer resonance on a metal surface? These questions await experiments using angle- and time-resolved 2PPE in model systems involving molecules with electron affinities higher than those investigated here and in previous studies. These experiments are currently underway in our laboratory.

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