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Light tuning of the image potential state electron-electron interactions
Surface Science 602 (2008) 2983–2988
Contents lists available at ScienceDirect
Surface Science journal homepage: www.elsevier.com/locate/susc
Light tuning of the image potential state electron-electron interactions Stefania Pagliara a, Gabriele Ferrini a, Gianluca Galimberti a, Emanuele Pedersoli a, Claudio Giannetti a, Carlo A. Rozzi b, Fulvio Parmigiani c,* a
Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore I-25121, Brescia National Centre on Nanostructures and Biosystems at Surfaces (S3) of INFM-CNR, Dipartimento di Fisica, Università di Modena e Reggio Emilia, 41100 Modena, Italy c Dipartimento di Fisica, Università di Trieste and Sincrotrone Trieste, Basovizza, I-34012 Trieste, Italy b
a r t i c l e
i n f o
Article history: Received 20 March 2008 Accepted for publication 18 July 2008 Available online 6 August 2008
a b s t r a c t We present the experimental evidence of the interplay between the variation of the linewidth and effective mass of electrons in image potential states on a Cu(1 1 1) surface induced by a selective alteration of the hot-electron gas density generated by ultra-short laser pulse excitations. Ó 2008 Elsevier B.V. All rights reserved.
Keywords: Angle resolved photoemission Visible and ultraviolet photoelectron spectroscopy Surface electronic phenomena (work function, surface potential, surface states, etc.)
1. Introduction Two-dimensional electronic surface states, such as the image potential states (IPS) and Shockley states (SS) at metal surfaces, are of increasing importance in surface science and nano-technology, since they represent a model system to study many-body electronic processes at solid surfaces and interfaces [1–5]. For these reasons, the electron dynamics of IPS and SS has attracted a significant attention in these last years. In a recent work [6,7], we have suggested that the effective mass of the image potential states could be modified by the interaction with the hot-electron gas generated by ultra-short light pulses at the metal surface. Nonetheless, a clear and unambiguous evidence of this interaction has never been given. Among different systems, the Cu(1 1 1) surface is particularly interesting since the binding energy (BE) of the SS (400 meV below the Fermi energy) and the BE of the IPS (180 meV below the vacuum level) are suitable for in resonance, quasi-resonance or out-of-resonance excitations using the second and fourth harmonics and the parametric conversion of the fundamental wavelength of the Ti:sapphire laser. In this work, we give the clear evidence of the interplay between the effective mass and linewidth of the Cu(1 1 1) IPS and the transient electronic density in the quasi-isoenergetic bulk states generated by intensity-controlled laser pulses. These findings, obtained from the analysis of the angle re* Corresponding author. E-mail address: [email protected] (F. Parmigiani). 0039-6028/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2008.07.029
solved photoemission spectra of Cu(1 1 1) IPS, are interpreted in terms of the penetration of the IPS wave function into the solid [15,16] and the transient hot-electron gas density generated by the pump light pulses. In agreement with our interpretation, the SS effective mass and linewidth, measured simultaneously to the IPS dispersions, are clearly less affected by the hot electron gas, suggesting a different interaction between the SS and the transient electronic density. These results represent a potential case study for the manybody theories of surface states. 2. Experimental The experiments are performed in ultrahigh vacuum conditions (pressure 5 1010 mbar) and at room temperature (300 K) on a Cu crystal cut along the (1 1 1) direction within ±0.5°. The clean and ordered Cu(1 1 1) surface is obtained by a standard procedure of sputtering and annealing. The light source is based on an amplified Ti:Sapphire laser system emitting 800 nm-120 fs light pulses at 1 kHz repetition rate. The two-color experiment is performed using photons with energy of hm = 3.14 eV and hm = 4.71 eV respectively, obtained from the second and the third harmonic of the fundamental laser emission. A Mach-Zehnder interferometer is used to bring into temporal coincidence the laser pulses. The kinetic energy of the photoemitted electrons was measured by a Time of Flight (ToF) spectrometer with an acceptance angle of 0.8°. The overall electronic noise of the system is less than 102 counts/sec, while the overall energy resolution is 35 meV at a kinetic energy of 2 eV. The work
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function measured using the fourth harmonic of the fundamental laser emission (hm = 6.28 eV) is 4.93 ± 0.1 eV. The parallel wavevector resolution is of the order of 0.01Å1. 3. Results and discussion We refer to a resonant excitation when the photon energy matches the SS–IPS transition energy at kk ¼ 0 (hm = 4.45 eV), quasi-resonant excitation when the mismatch between photon energy and SS-IPS transition energy is less than ±300 meV at kk ¼ 0, outof-resonance excitation in all the other cases. Fig. 1 shows schematically the two-photon quasi-resonant photoemission, at hm = 4.71 eV, from the Cu(1 1 1) surface. Fig. 1A reports the energy versus kk . Instead, Fig. 1B shows the k perpendicular cut along the CL direction, being the photon induced transitions at kk ¼ 0. As depicted in Fig. 1B the electrons from the occupied SS can be promoted to the bottom of the unoccupied bulk sp-bands, at kk ¼ 0. In the photoemission spectrum, the peak at higher energy (9 eV) is due to a two-photon emission from the occupied SS, whereas the peak at lower energy results from a one-photon emission from the transiently populated IPS via electron relaxation from the bulk bands. The photoemission at resonance (not shown) produces only a single peak at kk ¼ 0. As well known, by measuring angle resolved photoemission spectra (ARPES) it is possible to gain information about the bands dispersion, the effective mass m* (herewith reported in electron mass units) and the intrinsic linewidth versus the crystal momentum. Fig. 2 shows these band parameters for the IPS of the Cu(1 1 1)
Fig. 1. (A) Projected band structure of Cu(1 1 1) is shown together with a low energy electron diffraction (LEED) pattern. The measured spectral dispersions are also reported. Circles represent the Shockley states, squares the image potential state; triangles and diamonds the d-band states and the low energy peak dispersions, respectively. (B) Non-linear photoemission spectrum collected at kk ¼ 0 along the CL line, with a photon energy hm = 4.71 eV. The two peaks at the approximate energy of 9 eV are the surface state and image potential state, as indicated. The red lines represent the calculated electronic band structure (full lines the occupied bands, dashed lines the unoccupied bands) [8].
surface, as measured in the present experiment. We found that both the dispersion and the linewidth of the IPS, in the interval 0.12 Å1 < kk < 0.12 Å1, i.e., where the IPS is energetically separated from the bottom of the sp bulk-bands, depend on the photon energy. In particular, the IPS band dispersion measured at quasi-resonance, i.e. hm = 4.71 eV and hm = 4.28 eV has an effective mass of m* = 2.2 ± 0.1 and m* = 1.60 ± 0.07, respectively. These values largely exceed the expected effective mass value, i.e., m* = 1.3 ± 0.1, measured out of resonance at hm = 3.14 eV and in resonance at hm = 4.45 eV [9–11]. At the same time, the linewidth dispersion is quenched at a high value around kk ¼ 0 for quasi-resonant excitation, while the expected V-shaped dispersion profile is found for resonant and out-of-resonance excitations [13]. This finding is rather interesting since an increase of the IPS effective mass is associated with spatial localization of the electrons in the plane parallel to the sample surface. This corresponds to a spreading of the electron momentum spectrum and thus to a less sensitive dependence of the electron lifetime or dephasing rates on parallel momentum. In the experiments, the spatial localization manifests itself in the independence of the measured linewidth on the photoemission angle. In order to gain a qualitative insight into the mechanism that modify the IPS effective mass we have used the phase-shift model with two nearly-free electron bands [15,16]. The IPS energy is composed of three terms. The vacuum energy (E0), the kinetic energy of electron motion parallel to the surface (Ek ) and the image potential energy term (En). In this model, because of the IPS matching condition requirements at the surface, En depends on the parallel momentum [15,16]. To accomplish these matching conditions, the IPS wavefunction is expelled from the surface, into a region where the external Coulomb potential is weaker, determining a decrease in binding energy that is maximum at kk ¼ 0 and vanishes when the IPS band crosses the upper edge of the bulk bands (crossing point). As a result, the dispersion of the IPS vs kk is flattened at the center, resulting in an increased effective mass with respect to the free electron dispersion [9,10]. When a high electron density is injected in the bulk bands energetically close to the IPS, as in the case of hv ¼ 4:17 eV at kk ¼ 0, the wave function is further damped in the solid and expelled from the surface because of the scattering with hot electrons and Pauli exclusion principle, resulting in a further flattening of the IPS k-dispersion and increase of the IPS effective mass. In this qualitative picture it is not possible to discuss if the IPS expulsion is due to a pure final state effect (i.e., transient distortion of the unoccupied final bulk bands due to a high density population that modify the IPS potential) or to a pure scattering mechanism. In our opinion both mechanisms amount to the same physical picture when a strong scattering process is responsible of the coupling between the IPS and the hot-electrons population. The same effect is observed for quasi-resonant excitation at hv ¼ 4:28 eV, even if in this case it is not possible to populate the bulk bands at kk ¼ 0. To understand this result, we consider that the energy difference between the onset of bulk bands and the SS decreases for increasing kk because of the SS band dispersion. Consequently, a photon energy smaller than resonance can excite a high population density in the bulk bands at kk 6¼ 0. Due to the extremely rapid electron scattering toward band bottom, we expect the same effects observed by the direct population of the bulk bands at kk ¼ 0 with a photon energy higher than resonance. In both cases, a much rapidly decaying hot-electrons population continuously created during the laser pulse duration scatters with the quasi-isoenergetic electrons lying in the IPS states located outside the solid surface [1]. On the contrary, the effective masses measured at resonance and out-of-resonance are compatible with the expected values found in literature [9,10]. This can be rationalized by assuming that, at reso-
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Fig. 2. The binding energy with respect to the vacuum level (squares) and the intrinsic linewidth (circles) of the Cu(1 1 1) image potential state collected at different energies (at resonance hm = 4.45 eV, quasi-resonance hm = 4.71 eV, 4.28 eV and out of resonance 3.14 eV) are plotted versus the parallel momentum. The effective mass values are measured in the reduced kk range (between vertical dashed lines, 0.12 Å1 < kk < 0.12 Å1). The difference between parabolic fits in the reduced kk range and the entire kk range is shown in the hv ¼ 4:71 eV dispersion. The V-shaped lines in the linewidth dispersion plots are a guide to the eye.
nance, the high resonant cross section of the SS–IPS channel prevent the population of the bulk states. Similarly, at hm = 3.14 eV, the high transition rate between d-bands and states near the Fermi level at kk 6¼ 0 quenches the population of bulk states near the IPS, resulting in an effective reduction of the influence of the bulk electron density population on the IPS effective mass. To gain more consistency to our interpretation and to exclude experimental artifacts it is quite important to observe the dependence of the SS effective mass and linewidth on the transient hot electron gas density. In Fig. 3, the SS effective masses and linewidth dispersions are shown, with the direct photoemission measurements (hm = 6.28 eV) reported as reference. The SS electron effective mass value measured with hm = 4.71 eV in the interval 0.12 Å1 < kk < 0.12 Å1 results higher ðmSS ¼ 0:69 0:05me Þ with
respect to the value reported in the literature [18] and with respect to the value measured using the other photon energies ðmSS ¼ 0:50 0:05me Þ. In the case of SS, the increase of the effective mass, correlated to a quenching of the linewidth dispersion, is observed only at hm = 4.71 eV. At all the other photon energies, the SS effective mass is in agreement with the expected value and a Vshaped linewidth dispersion is shown. At hm = 4.28 eV we observe that the V-shaped linewidth dispersion is rather flat, probably due 1 to the resonance at about kk ¼ 0:15 Å between the SS–IPS energy difference and the photon energy. In Fig. 4 we report all the measured values for the IPS and SS effective masses at different photon energies [11,14]. The different results obtained for the IPS versus SS effective masses and linewidths can be rationalized considering that the
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Fig. 3. The binding energy with respect to the Fermi energy (squares) and the intrinsic linewidth (circles) of the Cu(1 1 1) surface state collected at different energies (at resonance hm = 4.45, quasi-resonance hm = 4.71 eV, 4.28 eV and out of resonance 3.14 eV) are plotted versus the parallel momentum. The effective mass values are measured in the reduced kk range (between vertical dashed lines, 0.12 Å1 < kk < 0.12 Å1). The difference between parabolic fits in the reduced kk range and the entire kk range is shown in the hv ¼ 4:71 eV dispersion. The V-shaped lines in the linewidth dispersion plots are a guide to the eye.
interaction processes between these two states and the transient electronic density in the quasi-isoenergetic bulk states are different. In fact the IPS and SS have, as well known, very different behavior. First of all, the SS is occupied, whereas the IPS is unoccupied, moreover the hybridization between the IPS wavefunction and the unoccupied bulk band is strong, whereas the overlap between the SS wavefunction and the bulk band below the vacuum level is negligible [12]. These differences could explain why the increase of the SS effective mass is observed only when the intermediate state is on the bulk band, i.e., where the transient hot electron density has been created. Instead, the IPS mass modification is due to the scattering with the hot electron population in the bulk. In both cases there is a dependence of the effective mass modification with the hot electron density. To test this hypothesis we have performed two-color photoemission experiments. By two-color photoemission measurements it is
possible to control the electron population excited into the sp-band by a variable intensity pump at photon energy hm = 4.71 and to photoemit the IPS transient electron population by the probe pulse. In Fig. 5, a two-color photoemission spectrum is shown. The feature A results from a one-photon emission at hm = 3.14 eV from the transiently populated IPS by electrons in the bulk bands excited by hm = 4.71 eV, whereas the feature B corresponds to the SS photoemitted by a two-photon absorption process with hm = 4.71 eV and hm = 3.14 eV. The two features (C and D) in the 4.5–5.5 eV energy range are ascribed to IPS and SS two-photon photoemission by 4.71 eV photons.1 1 The kinetic energy of the photoelectrons, reported in the figures, include the contact potential due to the work function difference between the sample and the ToF. For more details see Ref. [11].
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The kk dispersion of the IPS and SS energy extracted by hm = 3.14 eV photons is reported in Fig. 6. The IPS effective mass calculated in the 0.12 Å1 < kk < 0.12 Å1 range results
m* = 1.61 ± 0.07 and m* = 1.27 ± 0.07 for a pump pulse fluence of F = 7 lJ/cm2 and F = 4 lJ/cm2, respectively. However, the SS effective mass does not change so dramatically with the pump pulse
Fig. 4. The effective mass, calculated in the reduced kk -range (0.12 Å1 < kk < 0.12 Å1) (open markers) and considering the full kk -range of the measurements (full markers), is shown versus the photon energy for both the image potential state and the surface state.
Fig. 6. Kinetic energy versus kk dispersion for the image potential state and the surface state measured with two color photoemission by using two different incident fluence of the pump hm = 4.71 eV, F = 4 lJ/cm2 (large markers) and F = 7 lJ/ cm2 (small markers). The lines represent the best fit of the data in the reduced kk range (gray area).
Fig. 5. (a) Two color photoemission mechanisms from the Cu(1 1 1) surface state and image potential state. (b) A representative two color photoemission spectrum collected at kk ¼ 0 by using as a pump hm = 4.71 eV and as a probe hm = 3.14 eV. The A and B features are the image and the surface states, respectively, populated by a photon hm = 4.71 eV (red arrow) and photoemitted by hm = 3.14 eV (green arrow). The C and D features are the image and the surface states populated and photoemitted by two photons hm = 4.71 eV (red arrows). (c) The IPS and SS effective mass is reported versus the photon number per pulse of the pump. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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intensity. This behavior confirms different electron-scattering processes for the SS and IPS states with the hot electron gas generated by the pump pulse. In the single-color measurements reported in Fig. 2 the photon number per pulse on the Cu(1 1 1) was about 6.1 1010. Using pump–probe photoemission we are able to decrease the photon number per pump pulse to 3.3 1010 and 1.8 1010, respectively. The dependence of the SS and IPS effective mass on the pump photons per pulse is shown in Fig. 5. It is important to stress that also in the case of low incident intensity, the IPS is populated by an absorption of a photon of the pump (hm = 4.71 eV) and not by an absorption of two photons of the probe (hm = 3.14 eV). The constant intensity ratio between the IPS, extracted by a photon hm = 3.14 eV (A), and SS, photoemitted by two photons (hm = 4.71 plus hm = 3.14)(B) changing the pump intensity, assures that the IPS population mechanism (the absorption of a photon hm = 4.71 eV) is the same. Two photon absorption mechanism has, in fact, a much lower cross-section with respect a one-photon population. Therefore, we can conclude that the increase of the IPS effective mass depends on the electron density induced by the pump pulse into the unoccupied sp-bands. A hot-electron gas density close to the density of the available unoccupied states can significantly reduce the penetration of IPS wavefunction into the solid, modifying, in turn, the effective mass and the linewidth of the IPS. This interpretation can be strengthened by comparing the calculated available electron density in the unoccupied sp-band and the hot-electron gas density induced by the pump pulse at hm = 4.71 eV. The available empty states are those located in an energy interval ranging from the bottom of the unoccupied band at the L point, and the vacuum energy. Since the electrons are excited by a direct transition from the surface states, we are only interested to the states with jkj 6 0.2 Å1 (Fig. 1). These conditions together define the inside of a cylinder around the CL direction, having radius 0.2 Å1, and kx, ky, kz > 0. The holes density in this volume, and in an energy range of approximately 300 meV from the bottom of the unoccupied bulk band, can be estimated within the local density approximation using the tetrahedron integration with a proper reciprocal space grid. The calculation, for a 643 points grid in the full Brillouin zone, gives a number of 4 1018 states/cm3. The hot-electron gas density can be estimated starting from the photon density of the pump pulse.2 The determination of the electron density at the noble metal (1 1 1) surfaces has been addressed in Ref.[17]. The number of electrons in the SS at the Ag(1 1 1) surface has been measured with scanning tunnel microscopy, finding that SS constitute about 60% of the total surface electron density. We consider this value as representative also for the very similar surface of Cu(1 1 1). Assuming that the photons in the pump pulse are absorbed in the first surface layer in proportion to the surface density of states and that the totality of the SS excited electrons are promoted to the empty bulk states at the bottom of the gap, we estimate an upper limit for the hot-electron gas density in the bulk bands due to the
2 Considering the refractive index of Cu is ñ = 1.53 + i1.7 at a photon energy hm = 4.71 eV, the photons absorbed in the first layer (aCu = 3.61 Å) is about 8.2 103.
pump pulse. Under these approximations, a hot-electron gas density of the order of 1018 cm3 is calculated, which is consistent with the occupancy of a substantial fraction of the sp-bulk unoccupied states by the pump-pulse-induced electron density. This confirms the observed strong perturbing action of the pump pulse with respect to the IPS dynamics through the scattering by a high density hot-electron population. 4. Conclusions In conclusion we have reported a clear experimental evidence of the interplay between linewidth and effective mass of the Cu(1 1 1) surface states (IPS image potential state and SS Shockley state) and the hot electron gas density in the empty bulk states generated by an intensity-controlled laser pulse excitation. In particular, our experiment highlights the correlation between the effective mass of the IPS electrons and the hot-electron gas density. In the meantime we provide evidences that the mechanisms at the origin of the scattering processes between the surface state electrons and IPS electrons with the hot electron gas are different. This finding is consistent with the change of the penetration of the IPS wavefunction into the confining potential walls. Finally, we speculate that these results represent a potential case study for surface states many-body theories. References [1] P.M. Echenique, R. Berndt, E.V. Chulkov, Th. Fauster, A. Goldmann, U. Höfer, Surf. Sci. Rep. 52 (2004) 219. [2] N.-H. Ge, C.M. Wong, R.L. Lingle Jr., J.D. McNeill, K.J. Gaffney, C.B. Harris, Science 279 (1998) 202. [3] M. Roth, M. Pickel, W. Jinxiong, M. Weinelt, T. Fauster, Phys. Rev. Lett. 88 (2002) 096802. [4] F. Baumberger, M. Hengsberger, M. Muntwiler, M. Shi, J. Krempasky, L. Patthey, J. Osterwalder, T. Greber, Phys. Rev. Lett. 92 (2004) 196805. [5] A.D. Miller, I. Bezel, K.J. Gaffney, S. Garrett-Roe, S.H. Liu, P. Szymanski, C.B. Harris, Science 297 (2002) 1163. [6] G. Ferrini, C. Giannetti, G. Galimberti, S. Pagliara, D. Fausti, F. Banfi, F. Parmigiani, Phys. Rev. Lett. 92 (2004) 256802. [7] C. Giannetti, G. Ferrini, S. Pagliara, G. Galimberti, F. Banfi, E. Pedersoli, F. Parmigiani, Eur. Phys. J. B 53 (2006) 121. [8] G.A. Burdick, Phys. Rev. 129 (1963) 138. [9] M. Weinelt, Appl. Phys. A 71 (2000) 493. [10] A. Hotzel, M. Wolf, J.P. Gauyaeq, J. Phys. Chem. B 104 (2000) 8438. [11] S. Pagliara, G. Ferrini, G. Galimberti, E. Pedersoli, C. Giannetti, F. Parmigiani, Surf. Sci. 600 (2006) 4290. [12] J. Osma, I. Sarria, E.V. Chulkov, J.M. Pitarke, P.M. Echenique, Phys. Rev. B 59 (1999) 10591. [13] W. Berthold, U. Höfer, P. Feulner, E.V. Chulkov, V.M. Silkin, P.M. Echenique, Phys. Rev. Lett. 88 (2002) 056805. [14] S. Caravati, G. Butti, G.P. Brivio, M.I. Trioni, S. Pagliara, G. Ferrini, G. Galimberti, E. Pedersoli, F. Parmigiani, Surf. Sci. 600 (2006) 3901. [15] K. Giesen, F. Hage, F.J. Himpsel, H.J. Riess, W. Steinamnn, N.V. Smith, Phys. Rev. B 35 (1987) 975. [16] N.V. Smith, Phys. Rev. B 32 (1985) 3549. [17] L. Bürgi, N. Knorr, H. Brune, M.A. Schneider, K. Kern, Appl. Phys. A 75 (2002) 141. [18] F. Forster, G. Nicolay, F. Reinert, D. Ehm, S. Schmidt, S. Hufner, Surf. Sci. 160 (2003) 532.
Contents lists available at ScienceDirect
Surface Science journal homepage: www.elsevier.com/locate/susc
Light tuning of the image potential state electron-electron interactions Stefania Pagliara a, Gabriele Ferrini a, Gianluca Galimberti a, Emanuele Pedersoli a, Claudio Giannetti a, Carlo A. Rozzi b, Fulvio Parmigiani c,* a
Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore I-25121, Brescia National Centre on Nanostructures and Biosystems at Surfaces (S3) of INFM-CNR, Dipartimento di Fisica, Università di Modena e Reggio Emilia, 41100 Modena, Italy c Dipartimento di Fisica, Università di Trieste and Sincrotrone Trieste, Basovizza, I-34012 Trieste, Italy b
a r t i c l e
i n f o
Article history: Received 20 March 2008 Accepted for publication 18 July 2008 Available online 6 August 2008
a b s t r a c t We present the experimental evidence of the interplay between the variation of the linewidth and effective mass of electrons in image potential states on a Cu(1 1 1) surface induced by a selective alteration of the hot-electron gas density generated by ultra-short laser pulse excitations. Ó 2008 Elsevier B.V. All rights reserved.
Keywords: Angle resolved photoemission Visible and ultraviolet photoelectron spectroscopy Surface electronic phenomena (work function, surface potential, surface states, etc.)
1. Introduction Two-dimensional electronic surface states, such as the image potential states (IPS) and Shockley states (SS) at metal surfaces, are of increasing importance in surface science and nano-technology, since they represent a model system to study many-body electronic processes at solid surfaces and interfaces [1–5]. For these reasons, the electron dynamics of IPS and SS has attracted a significant attention in these last years. In a recent work [6,7], we have suggested that the effective mass of the image potential states could be modified by the interaction with the hot-electron gas generated by ultra-short light pulses at the metal surface. Nonetheless, a clear and unambiguous evidence of this interaction has never been given. Among different systems, the Cu(1 1 1) surface is particularly interesting since the binding energy (BE) of the SS (400 meV below the Fermi energy) and the BE of the IPS (180 meV below the vacuum level) are suitable for in resonance, quasi-resonance or out-of-resonance excitations using the second and fourth harmonics and the parametric conversion of the fundamental wavelength of the Ti:sapphire laser. In this work, we give the clear evidence of the interplay between the effective mass and linewidth of the Cu(1 1 1) IPS and the transient electronic density in the quasi-isoenergetic bulk states generated by intensity-controlled laser pulses. These findings, obtained from the analysis of the angle re* Corresponding author. E-mail address: [email protected] (F. Parmigiani). 0039-6028/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2008.07.029
solved photoemission spectra of Cu(1 1 1) IPS, are interpreted in terms of the penetration of the IPS wave function into the solid [15,16] and the transient hot-electron gas density generated by the pump light pulses. In agreement with our interpretation, the SS effective mass and linewidth, measured simultaneously to the IPS dispersions, are clearly less affected by the hot electron gas, suggesting a different interaction between the SS and the transient electronic density. These results represent a potential case study for the manybody theories of surface states. 2. Experimental The experiments are performed in ultrahigh vacuum conditions (pressure 5 1010 mbar) and at room temperature (300 K) on a Cu crystal cut along the (1 1 1) direction within ±0.5°. The clean and ordered Cu(1 1 1) surface is obtained by a standard procedure of sputtering and annealing. The light source is based on an amplified Ti:Sapphire laser system emitting 800 nm-120 fs light pulses at 1 kHz repetition rate. The two-color experiment is performed using photons with energy of hm = 3.14 eV and hm = 4.71 eV respectively, obtained from the second and the third harmonic of the fundamental laser emission. A Mach-Zehnder interferometer is used to bring into temporal coincidence the laser pulses. The kinetic energy of the photoemitted electrons was measured by a Time of Flight (ToF) spectrometer with an acceptance angle of 0.8°. The overall electronic noise of the system is less than 102 counts/sec, while the overall energy resolution is 35 meV at a kinetic energy of 2 eV. The work
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function measured using the fourth harmonic of the fundamental laser emission (hm = 6.28 eV) is 4.93 ± 0.1 eV. The parallel wavevector resolution is of the order of 0.01Å1. 3. Results and discussion We refer to a resonant excitation when the photon energy matches the SS–IPS transition energy at kk ¼ 0 (hm = 4.45 eV), quasi-resonant excitation when the mismatch between photon energy and SS-IPS transition energy is less than ±300 meV at kk ¼ 0, outof-resonance excitation in all the other cases. Fig. 1 shows schematically the two-photon quasi-resonant photoemission, at hm = 4.71 eV, from the Cu(1 1 1) surface. Fig. 1A reports the energy versus kk . Instead, Fig. 1B shows the k perpendicular cut along the CL direction, being the photon induced transitions at kk ¼ 0. As depicted in Fig. 1B the electrons from the occupied SS can be promoted to the bottom of the unoccupied bulk sp-bands, at kk ¼ 0. In the photoemission spectrum, the peak at higher energy (9 eV) is due to a two-photon emission from the occupied SS, whereas the peak at lower energy results from a one-photon emission from the transiently populated IPS via electron relaxation from the bulk bands. The photoemission at resonance (not shown) produces only a single peak at kk ¼ 0. As well known, by measuring angle resolved photoemission spectra (ARPES) it is possible to gain information about the bands dispersion, the effective mass m* (herewith reported in electron mass units) and the intrinsic linewidth versus the crystal momentum. Fig. 2 shows these band parameters for the IPS of the Cu(1 1 1)
Fig. 1. (A) Projected band structure of Cu(1 1 1) is shown together with a low energy electron diffraction (LEED) pattern. The measured spectral dispersions are also reported. Circles represent the Shockley states, squares the image potential state; triangles and diamonds the d-band states and the low energy peak dispersions, respectively. (B) Non-linear photoemission spectrum collected at kk ¼ 0 along the CL line, with a photon energy hm = 4.71 eV. The two peaks at the approximate energy of 9 eV are the surface state and image potential state, as indicated. The red lines represent the calculated electronic band structure (full lines the occupied bands, dashed lines the unoccupied bands) [8].
surface, as measured in the present experiment. We found that both the dispersion and the linewidth of the IPS, in the interval 0.12 Å1 < kk < 0.12 Å1, i.e., where the IPS is energetically separated from the bottom of the sp bulk-bands, depend on the photon energy. In particular, the IPS band dispersion measured at quasi-resonance, i.e. hm = 4.71 eV and hm = 4.28 eV has an effective mass of m* = 2.2 ± 0.1 and m* = 1.60 ± 0.07, respectively. These values largely exceed the expected effective mass value, i.e., m* = 1.3 ± 0.1, measured out of resonance at hm = 3.14 eV and in resonance at hm = 4.45 eV [9–11]. At the same time, the linewidth dispersion is quenched at a high value around kk ¼ 0 for quasi-resonant excitation, while the expected V-shaped dispersion profile is found for resonant and out-of-resonance excitations [13]. This finding is rather interesting since an increase of the IPS effective mass is associated with spatial localization of the electrons in the plane parallel to the sample surface. This corresponds to a spreading of the electron momentum spectrum and thus to a less sensitive dependence of the electron lifetime or dephasing rates on parallel momentum. In the experiments, the spatial localization manifests itself in the independence of the measured linewidth on the photoemission angle. In order to gain a qualitative insight into the mechanism that modify the IPS effective mass we have used the phase-shift model with two nearly-free electron bands [15,16]. The IPS energy is composed of three terms. The vacuum energy (E0), the kinetic energy of electron motion parallel to the surface (Ek ) and the image potential energy term (En). In this model, because of the IPS matching condition requirements at the surface, En depends on the parallel momentum [15,16]. To accomplish these matching conditions, the IPS wavefunction is expelled from the surface, into a region where the external Coulomb potential is weaker, determining a decrease in binding energy that is maximum at kk ¼ 0 and vanishes when the IPS band crosses the upper edge of the bulk bands (crossing point). As a result, the dispersion of the IPS vs kk is flattened at the center, resulting in an increased effective mass with respect to the free electron dispersion [9,10]. When a high electron density is injected in the bulk bands energetically close to the IPS, as in the case of hv ¼ 4:17 eV at kk ¼ 0, the wave function is further damped in the solid and expelled from the surface because of the scattering with hot electrons and Pauli exclusion principle, resulting in a further flattening of the IPS k-dispersion and increase of the IPS effective mass. In this qualitative picture it is not possible to discuss if the IPS expulsion is due to a pure final state effect (i.e., transient distortion of the unoccupied final bulk bands due to a high density population that modify the IPS potential) or to a pure scattering mechanism. In our opinion both mechanisms amount to the same physical picture when a strong scattering process is responsible of the coupling between the IPS and the hot-electrons population. The same effect is observed for quasi-resonant excitation at hv ¼ 4:28 eV, even if in this case it is not possible to populate the bulk bands at kk ¼ 0. To understand this result, we consider that the energy difference between the onset of bulk bands and the SS decreases for increasing kk because of the SS band dispersion. Consequently, a photon energy smaller than resonance can excite a high population density in the bulk bands at kk 6¼ 0. Due to the extremely rapid electron scattering toward band bottom, we expect the same effects observed by the direct population of the bulk bands at kk ¼ 0 with a photon energy higher than resonance. In both cases, a much rapidly decaying hot-electrons population continuously created during the laser pulse duration scatters with the quasi-isoenergetic electrons lying in the IPS states located outside the solid surface [1]. On the contrary, the effective masses measured at resonance and out-of-resonance are compatible with the expected values found in literature [9,10]. This can be rationalized by assuming that, at reso-
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Fig. 2. The binding energy with respect to the vacuum level (squares) and the intrinsic linewidth (circles) of the Cu(1 1 1) image potential state collected at different energies (at resonance hm = 4.45 eV, quasi-resonance hm = 4.71 eV, 4.28 eV and out of resonance 3.14 eV) are plotted versus the parallel momentum. The effective mass values are measured in the reduced kk range (between vertical dashed lines, 0.12 Å1 < kk < 0.12 Å1). The difference between parabolic fits in the reduced kk range and the entire kk range is shown in the hv ¼ 4:71 eV dispersion. The V-shaped lines in the linewidth dispersion plots are a guide to the eye.
nance, the high resonant cross section of the SS–IPS channel prevent the population of the bulk states. Similarly, at hm = 3.14 eV, the high transition rate between d-bands and states near the Fermi level at kk 6¼ 0 quenches the population of bulk states near the IPS, resulting in an effective reduction of the influence of the bulk electron density population on the IPS effective mass. To gain more consistency to our interpretation and to exclude experimental artifacts it is quite important to observe the dependence of the SS effective mass and linewidth on the transient hot electron gas density. In Fig. 3, the SS effective masses and linewidth dispersions are shown, with the direct photoemission measurements (hm = 6.28 eV) reported as reference. The SS electron effective mass value measured with hm = 4.71 eV in the interval 0.12 Å1 < kk < 0.12 Å1 results higher ðmSS ¼ 0:69 0:05me Þ with
respect to the value reported in the literature [18] and with respect to the value measured using the other photon energies ðmSS ¼ 0:50 0:05me Þ. In the case of SS, the increase of the effective mass, correlated to a quenching of the linewidth dispersion, is observed only at hm = 4.71 eV. At all the other photon energies, the SS effective mass is in agreement with the expected value and a Vshaped linewidth dispersion is shown. At hm = 4.28 eV we observe that the V-shaped linewidth dispersion is rather flat, probably due 1 to the resonance at about kk ¼ 0:15 Å between the SS–IPS energy difference and the photon energy. In Fig. 4 we report all the measured values for the IPS and SS effective masses at different photon energies [11,14]. The different results obtained for the IPS versus SS effective masses and linewidths can be rationalized considering that the
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Fig. 3. The binding energy with respect to the Fermi energy (squares) and the intrinsic linewidth (circles) of the Cu(1 1 1) surface state collected at different energies (at resonance hm = 4.45, quasi-resonance hm = 4.71 eV, 4.28 eV and out of resonance 3.14 eV) are plotted versus the parallel momentum. The effective mass values are measured in the reduced kk range (between vertical dashed lines, 0.12 Å1 < kk < 0.12 Å1). The difference between parabolic fits in the reduced kk range and the entire kk range is shown in the hv ¼ 4:71 eV dispersion. The V-shaped lines in the linewidth dispersion plots are a guide to the eye.
interaction processes between these two states and the transient electronic density in the quasi-isoenergetic bulk states are different. In fact the IPS and SS have, as well known, very different behavior. First of all, the SS is occupied, whereas the IPS is unoccupied, moreover the hybridization between the IPS wavefunction and the unoccupied bulk band is strong, whereas the overlap between the SS wavefunction and the bulk band below the vacuum level is negligible [12]. These differences could explain why the increase of the SS effective mass is observed only when the intermediate state is on the bulk band, i.e., where the transient hot electron density has been created. Instead, the IPS mass modification is due to the scattering with the hot electron population in the bulk. In both cases there is a dependence of the effective mass modification with the hot electron density. To test this hypothesis we have performed two-color photoemission experiments. By two-color photoemission measurements it is
possible to control the electron population excited into the sp-band by a variable intensity pump at photon energy hm = 4.71 and to photoemit the IPS transient electron population by the probe pulse. In Fig. 5, a two-color photoemission spectrum is shown. The feature A results from a one-photon emission at hm = 3.14 eV from the transiently populated IPS by electrons in the bulk bands excited by hm = 4.71 eV, whereas the feature B corresponds to the SS photoemitted by a two-photon absorption process with hm = 4.71 eV and hm = 3.14 eV. The two features (C and D) in the 4.5–5.5 eV energy range are ascribed to IPS and SS two-photon photoemission by 4.71 eV photons.1 1 The kinetic energy of the photoelectrons, reported in the figures, include the contact potential due to the work function difference between the sample and the ToF. For more details see Ref. [11].
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The kk dispersion of the IPS and SS energy extracted by hm = 3.14 eV photons is reported in Fig. 6. The IPS effective mass calculated in the 0.12 Å1 < kk < 0.12 Å1 range results
m* = 1.61 ± 0.07 and m* = 1.27 ± 0.07 for a pump pulse fluence of F = 7 lJ/cm2 and F = 4 lJ/cm2, respectively. However, the SS effective mass does not change so dramatically with the pump pulse
Fig. 4. The effective mass, calculated in the reduced kk -range (0.12 Å1 < kk < 0.12 Å1) (open markers) and considering the full kk -range of the measurements (full markers), is shown versus the photon energy for both the image potential state and the surface state.
Fig. 6. Kinetic energy versus kk dispersion for the image potential state and the surface state measured with two color photoemission by using two different incident fluence of the pump hm = 4.71 eV, F = 4 lJ/cm2 (large markers) and F = 7 lJ/ cm2 (small markers). The lines represent the best fit of the data in the reduced kk range (gray area).
Fig. 5. (a) Two color photoemission mechanisms from the Cu(1 1 1) surface state and image potential state. (b) A representative two color photoemission spectrum collected at kk ¼ 0 by using as a pump hm = 4.71 eV and as a probe hm = 3.14 eV. The A and B features are the image and the surface states, respectively, populated by a photon hm = 4.71 eV (red arrow) and photoemitted by hm = 3.14 eV (green arrow). The C and D features are the image and the surface states populated and photoemitted by two photons hm = 4.71 eV (red arrows). (c) The IPS and SS effective mass is reported versus the photon number per pulse of the pump. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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intensity. This behavior confirms different electron-scattering processes for the SS and IPS states with the hot electron gas generated by the pump pulse. In the single-color measurements reported in Fig. 2 the photon number per pulse on the Cu(1 1 1) was about 6.1 1010. Using pump–probe photoemission we are able to decrease the photon number per pump pulse to 3.3 1010 and 1.8 1010, respectively. The dependence of the SS and IPS effective mass on the pump photons per pulse is shown in Fig. 5. It is important to stress that also in the case of low incident intensity, the IPS is populated by an absorption of a photon of the pump (hm = 4.71 eV) and not by an absorption of two photons of the probe (hm = 3.14 eV). The constant intensity ratio between the IPS, extracted by a photon hm = 3.14 eV (A), and SS, photoemitted by two photons (hm = 4.71 plus hm = 3.14)(B) changing the pump intensity, assures that the IPS population mechanism (the absorption of a photon hm = 4.71 eV) is the same. Two photon absorption mechanism has, in fact, a much lower cross-section with respect a one-photon population. Therefore, we can conclude that the increase of the IPS effective mass depends on the electron density induced by the pump pulse into the unoccupied sp-bands. A hot-electron gas density close to the density of the available unoccupied states can significantly reduce the penetration of IPS wavefunction into the solid, modifying, in turn, the effective mass and the linewidth of the IPS. This interpretation can be strengthened by comparing the calculated available electron density in the unoccupied sp-band and the hot-electron gas density induced by the pump pulse at hm = 4.71 eV. The available empty states are those located in an energy interval ranging from the bottom of the unoccupied band at the L point, and the vacuum energy. Since the electrons are excited by a direct transition from the surface states, we are only interested to the states with jkj 6 0.2 Å1 (Fig. 1). These conditions together define the inside of a cylinder around the CL direction, having radius 0.2 Å1, and kx, ky, kz > 0. The holes density in this volume, and in an energy range of approximately 300 meV from the bottom of the unoccupied bulk band, can be estimated within the local density approximation using the tetrahedron integration with a proper reciprocal space grid. The calculation, for a 643 points grid in the full Brillouin zone, gives a number of 4 1018 states/cm3. The hot-electron gas density can be estimated starting from the photon density of the pump pulse.2 The determination of the electron density at the noble metal (1 1 1) surfaces has been addressed in Ref.[17]. The number of electrons in the SS at the Ag(1 1 1) surface has been measured with scanning tunnel microscopy, finding that SS constitute about 60% of the total surface electron density. We consider this value as representative also for the very similar surface of Cu(1 1 1). Assuming that the photons in the pump pulse are absorbed in the first surface layer in proportion to the surface density of states and that the totality of the SS excited electrons are promoted to the empty bulk states at the bottom of the gap, we estimate an upper limit for the hot-electron gas density in the bulk bands due to the
2 Considering the refractive index of Cu is ñ = 1.53 + i1.7 at a photon energy hm = 4.71 eV, the photons absorbed in the first layer (aCu = 3.61 Å) is about 8.2 103.
pump pulse. Under these approximations, a hot-electron gas density of the order of 1018 cm3 is calculated, which is consistent with the occupancy of a substantial fraction of the sp-bulk unoccupied states by the pump-pulse-induced electron density. This confirms the observed strong perturbing action of the pump pulse with respect to the IPS dynamics through the scattering by a high density hot-electron population. 4. Conclusions In conclusion we have reported a clear experimental evidence of the interplay between linewidth and effective mass of the Cu(1 1 1) surface states (IPS image potential state and SS Shockley state) and the hot electron gas density in the empty bulk states generated by an intensity-controlled laser pulse excitation. In particular, our experiment highlights the correlation between the effective mass of the IPS electrons and the hot-electron gas density. In the meantime we provide evidences that the mechanisms at the origin of the scattering processes between the surface state electrons and IPS electrons with the hot electron gas are different. This finding is consistent with the change of the penetration of the IPS wavefunction into the confining potential walls. Finally, we speculate that these results represent a potential case study for surface states many-body theories. References [1] P.M. Echenique, R. Berndt, E.V. Chulkov, Th. Fauster, A. Goldmann, U. Höfer, Surf. Sci. Rep. 52 (2004) 219. [2] N.-H. Ge, C.M. Wong, R.L. Lingle Jr., J.D. McNeill, K.J. Gaffney, C.B. Harris, Science 279 (1998) 202. [3] M. Roth, M. Pickel, W. Jinxiong, M. Weinelt, T. Fauster, Phys. Rev. Lett. 88 (2002) 096802. [4] F. Baumberger, M. Hengsberger, M. Muntwiler, M. Shi, J. Krempasky, L. Patthey, J. Osterwalder, T. Greber, Phys. Rev. Lett. 92 (2004) 196805. [5] A.D. Miller, I. Bezel, K.J. Gaffney, S. Garrett-Roe, S.H. Liu, P. Szymanski, C.B. Harris, Science 297 (2002) 1163. [6] G. Ferrini, C. Giannetti, G. Galimberti, S. Pagliara, D. Fausti, F. Banfi, F. Parmigiani, Phys. Rev. Lett. 92 (2004) 256802. [7] C. Giannetti, G. Ferrini, S. Pagliara, G. Galimberti, F. Banfi, E. Pedersoli, F. Parmigiani, Eur. Phys. J. B 53 (2006) 121. [8] G.A. Burdick, Phys. Rev. 129 (1963) 138. [9] M. Weinelt, Appl. Phys. A 71 (2000) 493. [10] A. Hotzel, M. Wolf, J.P. Gauyaeq, J. Phys. Chem. B 104 (2000) 8438. [11] S. Pagliara, G. Ferrini, G. Galimberti, E. Pedersoli, C. Giannetti, F. Parmigiani, Surf. Sci. 600 (2006) 4290. [12] J. Osma, I. Sarria, E.V. Chulkov, J.M. Pitarke, P.M. Echenique, Phys. Rev. B 59 (1999) 10591. [13] W. Berthold, U. Höfer, P. Feulner, E.V. Chulkov, V.M. Silkin, P.M. Echenique, Phys. Rev. Lett. 88 (2002) 056805. [14] S. Caravati, G. Butti, G.P. Brivio, M.I. Trioni, S. Pagliara, G. Ferrini, G. Galimberti, E. Pedersoli, F. Parmigiani, Surf. Sci. 600 (2006) 3901. [15] K. Giesen, F. Hage, F.J. Himpsel, H.J. Riess, W. Steinamnn, N.V. Smith, Phys. Rev. B 35 (1987) 975. [16] N.V. Smith, Phys. Rev. B 32 (1985) 3549. [17] L. Bürgi, N. Knorr, H. Brune, M.A. Schneider, K. Kern, Appl. Phys. A 75 (2002) 141. [18] F. Forster, G. Nicolay, F. Reinert, D. Ehm, S. Schmidt, S. Hufner, Surf. Sci. 160 (2003) 532.