Journal of Electron Spectroscopy and Related Phenomena 129 (2003) 97–104 www.elsevier.com / locate / elspec Lifetime of holes and electrons at metal surfaces; electron–phonon coupling a, b c c b,d d * B. Hellsing , A. Eiguren , F. Reinert , G. Nicolay , E.V. Chulkov , V.M. Silkin , c b,d ¨ S. Hufner , P.M. Echenique a ¨ Experimental Physics, Chalmers University of Technology and Goteborg University, S-412 96 Gothenburg, Sweden b ´ ´ Departmento de Fısica de Materiales and Centro Mixto CSIC-UPV/ EHU, Facultad de Ciencias Quımicas, Universidad del Pais ´ Vasco / Euskal Herriko Unibertsitatea, Apdo. 1072, 20018 San Sebastian / Donostia, Basque Country, Spain c ¨ ¨ Fachrichtung Experimentalphysik, Universitat des Saarlandes, 66041 Saarbrucken, Germany d ´ Donostia International Physics Center ( DIPC), Paseo de Manuel Lardizabal, 4, 20018 San Sebastian / Donostia, Basque Country, Spain Abstract Surface chemical reactions are influenced by inherent dissipative processes which involve energy transfer between the conduction electrons and the ionic motion. We will discuss how it is possible to model this electron–phonon coupling in order to estimate its importance. A relevant quantity for this investigation is the lifetime of surface localized electron states. A surface state, quantum-well state or surface image state is located in a surface projected band gap and becomes relatively sharp in energy. This makes a comparison between calculations and experimental data most attractive, with a possibility to resolve the origin of the lifetime broadening. We point out the importance of taking into account the phonon spectrum, electron surface state wave functions and the screening of the electron–ion potential.  2003 Elsevier Science B.V. All rights reserved. Keywords: Electron-phonon coupling; Electron excitations; Lifetime broadening; Surface state lifetime; Phonon induced decay 1. Introduction chemistry, a reaction often proceeds via an inter- mediate electronically excited state. A relevant ques- Lately, experimental surface science techniques tion is then if the lifetime of this intermediate state is have been used to reveal the fundamental interac- compatible with the time it takes for the reactants to tions in solids, such as the electron–electron ( e – e) complete the reaction, or at least long enough that a and the electron–phonon ( e – p) interactions. An significant fraction will. For this reason, it is im- understanding of these interactions is important in portant to find the parameters that determine the nanoscale physics, as quantum size effects become lifetime of the excitation. The decay channel of an important and the e – e and e – p interactions will limit excited electronic state via excitations of secondary the lifetime of excited one-electron states. In surface electrons has been investigated theoretically in detail for many systems [1–3]. In this paper, we summarize some calculations of lifetimes of surface localized *Corresponding author. Tel.: 146-31-772-5042; fax: 146-31- states with focus on the e – p scattering mechanism. 772-3367. E-mail address: hellsing@fy.chalmers.se (B. Hellsing). In addition, we discuss the possibility to obtain 0368-2048 / 03 / $ – see front matter  2003 Elsevier Science B.V. All rights reserved. doi:10.1016 / S0368-2048(03)00056-2