Electron Dynamics at Metal Surfaces Università degli Studi di Trieste Dipartimento di Fisica and Sincrotrone Trieste (Trieste, Italy) Fulvio Parmigiani

The study of the electron dynamics at surfaces and interfaces relays on the ability to time-resolve the ultra-rapid scattering processes which result in energy and momentum relaxation, recombination and diffusion. In typical experiments a short-pulsed ( fs) laser can be used for photoemission experiments in the time-domain, whereas longer laser pulses (1-5 ps) provided by FT limited coherent sources can be used for photoemission experiments in the frequency (energy) domain with unrecorded resolving power. Experimental techniques must be brought to bear in which band- structure specificity are combined with time resolution. Angle resolved photoemission is particularly suited for such experiments. Introduction

A rather interesting system to study the electron dynamics at the solid surfaces is represented by the Surface States (SS) Image Potential States (IPS). The SS-IPS represents a paradigmatic two-levels system in solids and can be seen as a playground to study, in the momentum space,the optical transitions in semiconductors, insulators and superconducting systems. band dispersion direct versus indirect population mechanisms polarization selection rules effective mass ( in the plane of the surface) electron scattering processes and lifetime Introduction

ToF LINEAR PHOTOEMISSION ( h >  band mapping of OCCUPIED STATES TIME RESOLVED MULTI-PHOTON PHOTOEMISSION ( h <  band mapping of UNOCCUPIED STATES and ELECTRON SCATTERING PROCESSES mechanisms

PHOTOEMISSION SPECTRA ON Ag(100) Log Scale 10 6 sensitivity I abs =13  J/cm 2 p -polarized incident radiation 30° incidence and 150 fs pulse. Multiphoton on Ag(100) M-B distribution “temperature” in a typical range of eV. G. P. Banfi et al., PRB 67, (2003). n=1 n=2 h = 3.14 eV Linear photoemission on Ag(100) h =6.28 eV F-D distribution at the RT energy Introduction

Linear Photoemission Process

Experimental Set-up   -metal UHV chamber  residual magnetic field < 10 mG  Base pressure < 2 · mbar  photoemitted electrons detector: Time of Flight (ToF) spectrometer Acceptance angle:  0.83° Energy resolution: 10 2eV Detector noise: <10 -4 counts/s ToF PC GPIB Multiscaler FAST 7887 PS1PS2PS3PS4 start stop Preamplifier Discriminator Laser sampledetector G. Paolicelli et al. Surf. Rev. and Lett. 9, 541 (2002)

Non-Linear Photoemission Process PHOTOEMISSION PROCESS PROBLEMS: E fermi E vac occupied states empty states Φ n=1 Upon the absorption of two photon the electron is already free. Which is the absorption mechanism responsible of the free-free transition? Keldysh parameter  1500>>1, perturbative regime Evidence of ABOVE THRESHOLD PHOTOEMISSION in solids ? 

ATP 2 and 3 photon Fermi Edge: -  E = h - Fermi-Dirac edge Energy-shift with photon energy:  E 3PFE = 3·h  3-Photon Fermi Edge: Three experimental evidences... Non-linearity order: 3-photon Fermi edge vs 2-photon Fermi edge n=2 n=3

ATP PHOTOEMISSION PROCESS RESULTS: To evaluate the cross section for an n -photon absorption involving the initial and final states: E fermi E vac occupied states empty states Φ n=1 is proportional to the Transition Matrix Element in the DIPOLE APPROXIMATION In this calculation we have to consider the mixing of the final free electron state with all the unperturbed Hamiltonian eigenstates but is it difficult to evaluate the contribution of this mixing to T (3). Rough Estimate T (3) /T (2)  Experimental Value T (3) /T (2)  Is another mechanism involved?

ATP

Image Potential States In most metals exists a gap in the bulk bands projection on the surface. When an electron is taken outside the solid it could be trapped between the Coulomb-like potential induced by the image charge into the solid, and the high reflectivity barrier due the band gap at the surface. Ag(100) U. Hofer et al., Science 277, 1480 (1997).

k // Dispersion LEED n = 1 E n = 2 k // m/m*=0.97  0.02 m/m*=1.03  0.06 G. Ferrini et al., Phys. Rev. B 67, (2003) Image Potential States dispersion measured via two- photon resonant ARPES on Ag(100) along  X n=1 n=2 IPS n=1: h =4.32 eV, p pol.

Fermi Edge Direct Photoemission 2-Photon Photoemission with P -polarized light 2-P Fermi Edge h  = 6.28eV E kin = h -  h  = 3.14eV E kin = 2 h -  h E fermi E vac occupied states empty states  n=1 Photoemission Spectra on Ag(100) single crystal Log Scale 10 6 sensitivity I abs =13  J/cm 2 p -polarized incident radiation ? Undirectly Populated IPS on Ag(100)

Image Potential State E kin = h -E bin E bin  0.5 eV n=1 Ag(100) K || =0 Shifting with photon energy h  =3.15eV h  =3.54eV  E kin =0.39 eV

k // -dispersion of non-resonantly populated IPS 2DEG effective mass (ARPES) m/m* = 0.88  0.04, h = 3.14 eV non resonant excitation both in p and s polarizations m/m*= 0.97  0.02, h = 4.28 eV resonant excitation, p-polarization 9% change of IPS effective mass suggests that the photoemission process is mediated by scattering with the hot electron gas created by the laser pulse. G. Ferrini et al., Phys. Rev. Lett. 92, (2004).

EVEV n=2 Cu(111) LEED pattern KK MM Shockley state d-band Tamm states Cu(111)

EFEF VL ≈ ≈ IPS is located at k // =0 close to the upper edge of the bulk unoccupied sp-band (~200meV) The energy separation between the IPS and the occupied surface state n=0 (Shockley)is about 4.45 eV

Goldmann Smith Giesen Schoenlein Padowitz IPS (n=1) m*/m measurements on Cu(111) and Ag(111) Haight m*/m measurements

In the phase-analysis model treats the states as electron waves undergoing multiple reflection between the crystal and image potential. Phase shift model - P.M. Echenique, J.B. Pendry- Bohr-like quantization condition on the round trip phase accumulation a pole in this expression denotes a bound states of the surface, i.e. a surface states Reflected wave from the crystal surface: Reflected wave from the image potential barrier: Summing the repeated scattering gives the total amplitude of  : the condition for a surface state is For the flux conservation N.V. Smith, PRB, 32,3549(1985) J.Phys.C:Solid State Phys., 11, 2065 (1978) Phase shift model

Even though completely reflected, the wave does extend to the far side of the boundary as the evanescent wave wave function inside the crystal wave function outside the crystal momentum perpendicular to the surface where q is the damping factor The wave functions N.V. Smith, PRB, 32,3549(1985) Phase shift model GAP Unoccupied bands

For a pure image potential, the barrier phase change may be written In the nearly-free- electron two band model  is the electron momentum at k // =0 z 0 is the position of the image potential plane The phase  B change respect to the energy is connected to the penetration of the wave on the vacuum side of the boundary. The phases The phase  C change respect to the energy is connected to the penetration of the wave in the crystal The phase  B for an image barrier diverges equation is satisfied ad infinitum, Rydberg series are generated, converging on the vacuum level Phase shift model

EnEn The  C phase If  C is treated as a constant over the range of the Rydberg series the energies are given by is the quantum defect When Ev is in the gap non perfect reflectivity  C <  a ≠ 0 For infinite crystal barrier perfect reflectivity  C =  a = 0 m free electron mass; n =1, 2, 3… K. Giesen, et al., PRB, 35, 975 (1987) K // ( Å -1 ) P.M. Echenique, Chemical Physics, 251, 1 (2000) Phase shift model

IPS effective mass on Cu(111) in the phase shift model An effective mass m*/m different from unit results when the phase  C and, consequently En, depends on k //. At different k // the electron reflected by the surface experiences different phase change K. Giesen, et al., PRB, 35, 975 (1987) K // ( Å -1 ) on Ag(111) on Cu(111) Phase shift model

60 meV Fermi Energy Vacuum level Resonant Case The effective mass of the IPS and SS states are in agreement with the litterature. h =4.45 eV Cu(111)

h  = 4.71 eV h =4.71 eV m*/m=2.17 ± 0.07 in k // [-0.12, 0.12] m*/m=1.28 ± 0.07 in k // [-0.2, 0.2] Changing  C To be submitted

Cu(111) FWHM 3-PPE

Fermi Energy Vacuum level h =4.28 eV Cu(111) h =4.28 eV

Cu(111) Dependence of m/m* on the pump intensity h =4.71 eV h =3.14 eV To be submitted

A B IPS k// unoccupied sp bands  A B IPS k// unoccupied sp bands  h =4.71 eV Cu(111)

Conclusions ATP on solid was demonstrated Indirect population of the IPS was shown The origin of anomalous electron effective mass for the IPS has been clarified The possibility to photo-induced changes of the electron effective mass in solids has been demonstrated.

Co-workers: G. Ferrini C. Giannetti S. Pagliara F. Banfi (Univ. of Geneve) G. Galimberti E. Pedersoli D. Fausti (Univ. of Groningen)