Femtosecond electron dynamics of image-potential states on clean and oxygen-covered Pt „ 111 ...

We have investigated the lifetimes of image-potential states on the Pt ~111! surface with time-resolved two-photon photoemission and first-principles calculations. Electrons populating the first two image-potential states decay into bulk states after 26 67 and 6267 fs, respectively. This is in agreement with results of theoretical calculations. Oxygen adsorption reduces the image-potential state lifetimes by a factor of 2. This is caused by a strong change of the electronic structure near the Fermi level.


I. INTRODUCTION
The reduced dimensionality at a solid surface can introduce additional electronic states localized at the solidvacuum interface.These surface states are of interest in epitaxy since they were found to modify energy barriers for adatom diffusion. 1A special class of surface states are the so called image-potential states ͑IPSs͒.They occur if an electron is trapped in front of a metal surface by its own image charge.If a gap in the bulk electronic density of states ͑DOS͒ in the solid prevents the electron from decaying into the crystal a Rydberg series of bound IPSs can form.Theoretical analysis showed 2 that these states occur at binding energies E B ϭe v 0 Ϫ0.85/(nϩa) 2 eV converging towards the vacuum level e 0 v .Here, n is the IPS quantum number and a is a quantum defect with values 0Ͻaр0.5 related to the phase change upon electron reflection at the crystal surface. 3Electrons in the normally unoccupied IPSs are localized in front of the crystal and experience the full translational symmetry for motion parallel to the surface.Thus, IPSs can provide model systems to study excitations of a two-dimensional electron gas.
Experimental detection of IPSs involves populating these states with electrons.This has been done either by adding an additional electron to the solid as in inverse photoemission spectroscopy ͑IPE͒ 4 or by photoexciting electrons from occupied states followed by a second photoemission step.This two-photon photoemission spectroscopy ͑2PPE͒ has become increasingly popular with the development of suitable highpower laser light sources. 5Electron lifetimes of IPSs have initially been determined from the intrinsic linewidths of these states probed with both IPE and 2PPE.A more recent development is the utilization of spin polarization in IPE ͑Ref.6͒ and variable light polarization in 2PPE. 7Such measurements allowed the determination of magnetic exchange splitting of IPSs ͑Refs.6,7͒ and the observation of different relaxation times of spin-up and -down electrons 6,8 at the surfaces of ferromagnets.
A breakthrough in the accurate measurement of IPS life-times has been time-resolved 2PPE ͑TR2PPE͒ utilizing advances in the generation of femtosecond laser pulses. 9In TR2PPE a pump pulse is used to populate the IPEs.The evolution of the IPS population is then probed in real time with a time-delayed second laser pulse.Measurements on noble metal surfaces have resulted in a wealth of data on the decay of IPSs ͑Refs.10,11͒ that can be understood quantitatively within a many-particle framework of energy relaxation processes at surfaces. 12,13The lifetime of IPSs is determined by different factors.On noble metal ͑100͒ surfaces the IPSs are located near the center of a gap in the electronic DOS.They decay mainly through electron-hole pair creation and a lifetime increase proportional to n 3 is expected in good agreement with experiments. 10The situation is more complex at the close-packed noble metal ͑111͒ surfaces.In this case the IPSs are located near the upper edge of a gap in the bulk electronic DOS.With increasing quantum number, n, the IPSs become energetically degenerate with bulk states and can decay into them.As a consequence the lifetime is observed to be reduced with increasing n. 11 The lifetime of the nϭ1 IPS was found to be strongly influenced by other surface states closer to the Fermi level. 14n contrast to noble metals the decay of IPSs on transition metal surfaces is more poorly understood.Early linewidth measurements on Ni͑111͒ indicated a very short lifetime of the nϭ1 IPS of less than 10 fs. 15 This is most likely a consequence of the large 3d DOS bisecting the Fermi level which provides a very effective decay channel due to electron-hole pair creation. 15,8A significant lifetime increase for the nϭ1 IPS has been observed on Pd͑111͒ ͑Ref.16͒ where the 4d band occupation is higher compared to that of the Ni 3d states.The experimental value of 24 fs is in good agreement with theory. 16Unfortunately, no lifetimes for higher n IPS could be measured with TR2PPE on Ni͑111͒ and Pd͑111͒ due to technical restrictions of the available photon energy.In this paper we used TR2PPE and firstprinciples calculations to investigate the lifetimes of the n ϭ1 and nϭ2 IPSs on Pt͑111͒.We find a similar lifetime of the nϭ1 IPS compared to Pd͑111͒ in excellent agreement with theory.In contrast to noble metal ͑111͒ surfaces we find a longer lifetime for the nϭ2 IPS.Upon oxygen adsorption we find a significant decrease of both IPSs lifetimes.This can be accounted for by the changing electronic DOS near the Fermi level on the Pt͑111͒-(2ϫ2)O surface.
The paper is organized as follows.In the next two sections we describe the experimental setup and theoretical approach, respectively.In Sec.IV the results obtained for the Pt͑111͒ and Pt͑111͒-(2ϫ2)O surfaces will be presented.This is followed by the discussion of the results in Sec.V. A summary section concludes the paper.

II. EXPERIMENT
Ultrashort laser pulses are generated by a Ti:sapphire laser system pumped by an Ar-ion laser ͑Coherent Innova 400͒.The tunable ͑780-860 nm͒ output of an oscillator ͑Coherent Mira Seed͒ is first stretched temporally and then coupled into a regenerative amplifier ͑Coherent RegA͒.Subsequent temporal compression results in pulses with a total energy of up to 5 J, a bandwidth of 25 nm and a duration of 60 fs at 250 kHz repetition rate.The pulses are frequency doubled using a ␤-BBO crystal.This second harmonics output is separated from the fundamental by a dichroic mirror and split into two parts.One part is again frequency doubled.This fourth harmonics serves as the pump pulse to populate the IPSs.The other part of the second harmonics is delayed through traversing an optical delay line and is used to probe the population dynamics of IPSs.
TR2PPE experiments were performed in a UHV chamber at a base pressure in the lower 10 Ϫ10 mbar range.The sample was cleaned by cycles of Ar ϩ sputtering and subsequent annealing to 1000 K. Residual carbon contamination was removed by oxygen adsorption and flashing the sample to 670 K.This procedure resulted in a clean and well ordered Pt͑111͒ surface as was judged by 2PPE and low-energy electron diffraction ͑LEED͒.Photoelectrons were detected with a hemispherical energy analyzer ͑Leybold EA200͒ with 100 meV energy resolution.A bias of Ϫ10 V was applied to the sample during the 2PPE measurements in order to improve the transmission of the electron spectrometer.We obtained a sample work function of 5.97Ϯ0.03eV for the clean Pt͑111͒ surface from 2PPE experiments in good agreement with results reported previously. 17,18Oxygen adsorption at room temperature resulted in a well ordered p(2ϫ2) LEED pattern at a saturation coverage of 0.25 monolayers. 19,20The work function for the Pt͑111͒-p(2ϫ2)-O was determined to 6.16Ϯ0.03eV. 19n the 2PPE experiments space charge effects were avoided by using low light fluences and by keeping the photon energies below the work function of the respective surface .The pump and probe photon energies were 5.84 ͑6.06͒ and 2.92 ͑3.03͒ eV, respectively, for the clean ͑oxygen satu-rated͒ Pt surface.The probe-pulse duration at the sample was 60 fs for both photon energies as was determined from autocorrelation measurements 3 eV above E F where the estimated lifetimes are below 5 fs.The pump-pulse duration at 5.84 eV photon energy was 140 fs obtained from the crosscorrelation also measured at an energy of 3 eV above E F .At a photon energy of 6.06 eV the pump-pulse duration was 260 fs.

III. THEORY
For better understanding of the electron dynamics in IPS on the clean Pt͑111͒ surface we have initially calculated the surface electronic structure with the use of the ab initio fullpotential augmented plane wave ͑FLAPW͒ method. 21The generalized gradient approximation 22 of the density functional theory was employed to describe the exchangecorrelation potential.Spin-orbit coupling was included in a pseudopertubative manner. 23The surface was modeled by a 13 layer film embedded in a semi-infinite vacuum.This thickness is necessary to prevent interaction between the two surfaces of the film, although a small splitting of the sp-derived surface state at 0.4 eV above the Fermi level at the Brillouin-zone center ⌫ ¯resulting from this interaction can still be observed.Figure 1 shows the Pt͑111͒ projected bulk bandstructure ͑gray symbols͒ and states localized at the surface ͑black symbols͒.The unoccupied sp-like surface state is visible in early IPE experiments about 0.5 eV above E F . 24An occupied d-derived surface resonance observed below E F in Fig. 1 has been reported in photoemission experiments. 1,17he information obtained from the first-principles calculations was used to construct a one-dimensional model potential along the lines of Ref. 25.To this end we used the width and position of the energy gap at ⌫ ¯, the sp-surface state energy position of 0.4 eV together with the experimen- tally determined binding energy of Ϫ0.65 eV relative to e v 0 for the nϭ1 image state.From this potential one-electron wave functions where L is a normalization length, and one-electron energies were evaluated in order to calculate the damping rate ͑inverse lifetime͒ of the nϭ1,2 IPSs.In Eqs.͑1͒ and ͑2͒ numerates electron bands and k ¯is the two-dimensional electron wave vector.We computed the inverse lifetime within a many-body theory where the decay rate of an excited electron (EϾE F ) in a quantum state (r) with energy E was obtained as the projection of the imaginary part of the selfenergy ⌺(r,r;E) onto the state itself.The self-energy was calculated within the GW approximation 26 when only the first term in the series expansion of ⌺ in terms of the screened Coulomb interaction W is used.We also replaced the full one-electron Green function G by the noninteracting Green function G 0 .The technique of the calculation of the decay rate of image states was described in detail in Refs.12,16,13 where it was used for evaluations of the lifetime of IPSs on Cu͑100͒, Cu͑111͒, and Pd͑111͒ surfaces.We do not give more details of the calculation here and refer readers to Refs.12,16,13.Though our model does not contain d electrons it is reasonably accurate for description of electron dynamics in image states on Cu͑100͒ and Cu͑111͒.In bulk Cu the 3d states are totally occupied and lie in an energy interval of 2-5 eV below E F and transitions involving these states are not expected to play a direct role.On the other hand bulk Pd and Pt possess empty d orbitals which lie in a narrow energy interval of 0.3 just above E F .However, the total number of unoccupied d states is small and they are not expected to give a dominant contribution to the decay rate of IPSs.This is confirmed on Pd͑111͒ where the theoretical model gives results which are in good agreement with TR2PPE measurements. 16Our recent first-principles calculations 27 of the decay rate of the surface (nϭ0) and image (nϭ1) states on Pd͑111͒ confirm this conclusion.For the 50 layer Pt͑111͒ film we obtained lifetimes of 1 ϭ29 fs and 2 ϭ73 fs for the nϭ1 and nϭ2 IPSs, respectively.

A. The clean Pt"111… surface
Energy resolved 2PPE spectra of IPSs on the clean Pt͑111͒ surface are shown in Fig. 2. The spectra were taken at different time delays between pump and probe pulses.The first two states with quantum numbers nϭ1 and nϭ2 are clearly resolved with binding energies of Ϫ0.65Ϯ0.05 and Ϫ0.16Ϯ0.05eV, respectively.The energy position of the first image potential state is close to the value of 0.63 eV obtained from IPS, 28 but is 0.13 eV smaller than that reported by Kinoshita et al. 18 With increasing delay time be-tween pump and probe pulses the relative intensities between both IPSs change.At a delay time of 340 fs only the nϭ2 IPS is still occupied whereas the first state is completely depopulated.This is clear evidence of a longer lifetime for the nϭ2 state.Another effect seen in the spectra especially for the nϭ2 image-potential state is the decrease in the spectral width with increasing delay time.This broadening at short delay times has been observed earlier on other surfaces 10 and was attributed to the contribution of a resonant two-photon photoemission process occurring when pump and probe pulses are in temporal overlap near zero time delay. 29The intrinsic linewidth of the IPSs has to be determined at sufficient delay between pump and probe pulse, when the pump pulse has already passed by.An analysis of the spectra at sufficient delay times gives the lifetime dominated linewidths of 30Ϯ15 and 18Ϯ12 meV for the n ϭ1 and nϭ2 state, respectively.
We determined the image potential state lifetimes by setting the energy analyzer to the photoelectron kinetic energy values corresponding to the IPS peaks in Fig. 2. Then the delay between pump and probe-pulse was varied.The results are shown in Fig. 3 for the Pt͑111͒ nϭ1 and nϭ2 IPS.The instrumental cross-correlation function was obtained on a contaminated Pt͑111͒ surface where all image potential states were quenched.The full width at half maximum of the cross-correlation trace was deduced to 152 fs by fitting a sech 2 function to the data ͑dashed line in Fig. 3͒.The maximum of the transient response of the nϭ1 IPS is shifted by 14 fs towards positive delay times.In addition the curve is slightly broadened indicating a clearly resolved finite lifetime of this state. 11A by far stronger effect is seen in the transient response of the nϭ2 state.The curve becomes significantly broader and shows an asymmetric line shape corroborating the longer lifetime seen in the 2PPE spectra of Fig. 2. In order to quantitatively evaluate the population of the IPSs one has to take into account the influence of the pumppulse laser field E(t)sin(t) as long as the excitation takes place.Here E(t) denotes the envelope of the pump pulse and is the frequency of light.This process is described by electronic transitions in a two-level system interacting with a time dependent oscillatory optical perturbation and can be described by using the optical Bloch equations in the rotating wave approximation. 30,31A pump pulse of sufficiently narrow bandwidth can generate coherent fluctuations of the IPS population.These oscillations, however, are smeared out in the case of a broad-band excitation when the frequencey spread of the light is larger than the linewidth of the excited final state. 30In our experiment the bandwidth of the laser pump-pulse can be estimated from the measured bandwidth of the 1.46 eV output ͑40 meV͒ of the Ti:sapphire laser system.Assuming that there are no energy cutoffs in the frequency spectrum of the laser pulse after frequency conversion 32,33 the estimated bandwidth exceeds the measured intrinsic linewidth of the nϭ1 image potential state.In this case the description of the IPS final-state population simplifies from solving the Bloch equations to a rate equation treatment. 30Using a sech 2 function to describe the temporal laser-pulse shape we obtain lifetimes of 1 ϭ26Ϯ7 fs and 2 ϭ62Ϯ7 fs for the nϭ1 and nϭ2 IPS on Pt͑111͒, respectively.The measured value of 1 is in good agreement with the calculated value of 1 ϭ29 fs while the theoretical lifetime 2 ϭ73 fs is slightly higher than the experimental one.This small descrepancy between the calculated and measured with TR2PPE lifetimes of the high order image states n ϭ2,3, . . ., is also obtained for Cu͑100͒ ͑Ref.12͒ and for Ag͑100͒. 34Despite this discrepancy the agreement between the experimental and theoretical lifetimes seems to be reasonably good.

B. The Pt"111…-p"2x2…O surface
As mentioned above, after oxygen adsorption the work function increases to 6.16Ϯ0.03eV.Since image potential states are pinned to the vacuum level, their relative energy position with respect to E F is changed.The inset of Fig. 2 shows the energy position of the image-potential states relative to E F for the oxygen covered surface ͑solid circles͒ in comparison to those of the clean surface ͑line͒.We obtained binding energies of Ϫ0.67Ϯ0.05eV for the nϭ1 and Ϫ0.19 Ϯ0.05 eV for the nϭ2 IPS, respectively.Figure 4 shows the transient responses of the nϭ1 and nϭ2 IPSs on the oxygen covered surface.The instrumental cross correlation with a full width at half maximum of 270 fs is also shown.Unfortunately, this is larger than for the lower photon energy used on the clean Pt͑111͒ surface.However, we could reproduce the IPSs lifetimes on clean Pt͑111͒ for this higher photon energy.A lifetime of 32Ϯ10 fs for the nϭ2 state on Pt͑111͒-p(2ϫ2)O was deduced from a fit ͑solid line͒ to the data in Fig. 4 ͑curve C͒.The lifetime for the nϭ1 IPS is much shorter as can be seen from the transient response which follows directly the instrumental cross-correlation trace.We estimate an upper limit of 20 fs for the lifetime of this state keeping in mind that the temporal resolution is reduced due to the relatively broad cross-correlation trace at this photon energy .
Additional measurements have been performed to investigate the influence of oxygen adsorption on the valence electronic structure.For this purpose we generated laser pulses with a photon energy of 4.47 eV by sum-frequency mixing of the 1.49 eV output of the Ti:sapphire laser system and the frequency-doubled radiation.Figure 5 shows the energy distribution curves of the valence band from the clean ͑solid line͒ and oxygen covered ͑dashed line͒ Pt͑111͒ surface obtained with 2PPE.A feature at an energy of 0.52Ϯ0.05eV below E F is seen for the clean surface ͑marked by an arrow in Fig. 5͒ which is quenched under oxygen adsorption.This structure was also observed by Roos et al. 17 who assigned it to an occupied surface resonance.Such a surface resonance is also apparent in the band structure calculations of Fig. 1 near ⌫ ¯at energy slightly lower than that observed in the experiments.In addition the DOS near E F is considerably enhanced by oxygen adsorption.

V. DISCUSSION
The lifetimes of the image potential states on the clean surface reflect the localization of their wave functions with respect to the metal.The wave function maximum of the n ϭ2 state is located further into the vacuum region, thus, resulting in a reduced wave function overlap with energetically adjacent bulk states.A comparison between the experimental data for the binding energies of the image potential states and the calculated band structure seen in Fig. 1 implies that both states are still located inside the bulk band gap.The good agreement for the obtained lifetimes of the image potential states on the clean surface between experiment and theory supports this interpretation since the band structure data from Fig. 1 were taken for the calculation of the image potential state lifetimes.However, the agreement between the measured linewidths and the lifetimes is only satisfying for the first image potential state.The linewidth can be affected by defects of the crystal lattice or dephasing processes.This has also been observed on Pd͑111͒ for the first image potential state. 16The lifetime value for the first image potential state on Pt͑111͒ of 26 fs is close to the value of 24 fs for the nϭ1 state on Pd͑111͒.That result might be surprising since on Pd͑111͒ the vacuum level and the image potential states lie close to the middle of the bulk band gap.For the decay rate ប/ of the nϭ2 state on Pd͑111͒ no experimental value is available.But the theoretical value of 7.4 meV ͑Ref.16͒ is close to that of Pt͑111͒ of 9 meV.
The adsorption of oxygen results in a well ordered Pt͑111͒-p(2ϫ2)-O surface structure that was found to involve a slight rearrangement of the Pt substrate atoms. 20ompared to the clean surface, the lifetime of the nϭ2 state is reduced by a factor of 2, whereas for the lifetime of the first image-potential state only an upper limit can be estimated.Several effects can be responsible for the observed effect.
Schuppler et al. had observed a linewidth broadening of image potential states on a Ag͑100͒ surface under oxygen adsorption. 35The linewidths of the image potential states were observed to increase linearly with oxygen exposure indicating shorter lifetimes because of more effective scattering of electrons in image potential states with O atoms.This may play a role on a surface with disordered adatoms, but is expected to be negligible on surfaces with well ordered layers of adatoms. 36,37ue to the increased work function especially the second image-potential state could be shifted out of the band gap.Therefore its wave function would penetrate deeper into the crystal leading to a stronger coupling with adjacent bulk bands and hence to a shorter lifetime.Such a behavior would mainly affect the nϭ2 image potential state as was observed on Cu͑111͒. 37However, on the Pt͑111͒-(2ϫ2)O surface this effect is unlikely since all image potential state lifetimes are reduced in a similar way.
For the decay of image potential state electrons into electron-hole pairs other surface states play a dominant role.Since image potential states are strongly localized in the vacuum region, they couple mainly to other surface states while the coupling to bulk bands is relatively smaller.For example, the unoccupied s-p band derived S 1 surface state is therefore assumed to be one reason for the relatively broad linewidth of the nϭ1 state on Ni͑111͒. 15As mentioned above, under oxygen adsorption the surface resonance observed 0.52 eV below E F is quenched.It is presently not clear whether this state is simply depopulated and shifted above E F ͑Ref. 1͒ or whether a major reorganizazion of the valence DOS occurs.The latter seems more likely since a small oxygen indiced buckling reconstruction of the Pt substrate was observed. 20Figure 5 provides evidence that this leads to an increase in the DOS around E F .This could also create additional unoccupied states that influence the relaxation process, hence accelerating the decay of the image potential states.Since image potential states are pinned to the vacuum level the work function increase for the oxygen covered surface increases the number of available final states for the decay process.This is also expected to shorten the image potential state lifetime.More dramatic change can take place for the nϭ2 IPS because on the O covered surface this state degenerates in energy with bulk states that leads to strong overlap with bulk states.

VI. CONCLUSIONS
In summary we have investigated the population dynamics of IPS on the clean and oxygen covered Pt͑111͒ surface.We have shown that experimental and theoretical data are in good agreement.After oxygen adsorption a Pt͑111͒-p(2 ϫ2)-O structure is formed leading to a quenching of the occupied surface resonance and a major rearrangement of the surface DOS.This is in turn mainly responsible for a faster depopulation of the IPS's due to an increased number of available final states.

FIG. 1 .
FIG. 1. Projected bulk bandstructure ͑grey symbols͒ and states localized at the surface ͑black symbols͒ along the K ¯-⌫ ¯-M ¯direction.E F denotes the Fermi level, e v o the vacuum level of the film calculation.The ⌫ point corresponds to k ϭ 0. From the Pt͑111͒ film calculation we plot only the states up to e vo that had either more than 50% of their charge localized in the surface layer or more than 10% in the vacuum.Surface states appear in the gaps of the projected bulk band structure.

FIG. 2 .
FIG. 2. Energy distribution curves for the two resolved image potential states on the clean Pt͑111͒ surface at different delay times after excitation.The inset shows the energy shift of the image potential states with respect to E F after oxygen adsorption ͑dotted line͒.The image potential states on the clean surface are also shown ͑solid line͒.

FIG. 3 .
FIG. 3. Transient responses of the nϭ1 ͑middle panel͒ and n ϭ2 ͑bottom panel͒ image potential states ͑solid symbols͒.The cross correlation trace ͑open squares, top panel͒ reflects the instrumental function described by a sech 2 function ͑dashed lines͒.From fits to the data lifetimes of 26Ϯ7 fs and 62Ϯ7 fs were obtained for the nϭ1 and nϭ2 state, respectively.

FIG. 5 .
FIG. 5. Energy distribution curves for transitions of the clean ͑solid line͒ and oxygen covered ͑dashed line͒ occupied states close to E F obtained with a photon energy of 4.47 eV.The occupied surface resonance on the clean surface is marked by the arrow.