Multiphoton electron emission from Cu and W: An angle-resolved study Andrea Damascelli Solid State Physics Laboratory, Groningen University, Nijenborgh 4, 9747 AG, Groningen, The Netherlands Giuseppe Gabetta and Alberto Lumachi Materials Division, Centro Informazioni Studi Esperienze Tecnologie Innovative S.p.A., P.O. Box 12081, I-20134 Milan, Italy Lorenzo Fini Department of Physics and European Laboratory for Nonlinear Spectroscopy, University of Florence, Largo Enrico Fermi 2, I-50125 Florence, Italy Fulvio Parmigiani Istitoto Nazionale per la Fisica della Materia and Department of Physics, Polytechnic of Milan, Piazza Leonardo da Vinci 32, I-20134 Milan, Italy ~Received 27 March 1996! The experimental results of multiphoton electron emission from Cu and W induced by 2-eV 100-fs laser pulses with s and p polarizations at incidence angles between 0° and 85° and different intensities are reported. The data show a third-order nonlinear photoemission process for Cu and a fourth-order behavior for W. For both metals the electron emission is higher for the polarization in the incidence plane, with a maximum value at the pseudo-Brewster angle, while the electron yield as a function of the incidence angle exhibits an unam- biguous dependence on the bulk absorption coefficient and it can be accounted for on the basis of the Fresnel equations. @S0163-1829~96!02233-3# Since the early models developed by Fowler 1 and Dubridge, 2 several theoretical and experimental investiga- tions have been carried out on photoelectron emission from metal surfaces, and nowadays this subject represents an im- portant branch of modern surface science. In particular, the advent of powerful ultrashort laser pulses has allowed the investigation of the nonlinear case on time scales comparable to electron-phonon relaxation times 3–6 and has highlighted several similarities between multiphoton electron emission from a metal surface and the multiphoton ionization of free atoms. 7,8 Multiphoton electron emission processes have been inter- preted by Bechtel, Smith, and Bloembergen 3 ~BSB model!, extending to the nonlinear case the Fowler-Dubridge theory. 1,2 However, when pulses are shorter than the electron-phonon relaxation time, a decoupling between the electrons and lattice temperatures can take place, generating the so-called anomalous heating effect. This effect, postu- lated by Bechtel and Bloembergen, 3,9 was observed by Fujimoto and co-workers 5 on a polycrystalline W sample using a 620-nm 75-fs laser source. In alternative, extending the model proposed by Broudy 10 for the linear case to mul- tiphoton processes, a surface-enhanced optical absorption ~SEOA! should be expected. 10 This mechanism takes into account the role played by the surface states in favoring the electron emission for the p -polarized light and in contrast to what expected by the BB model, the total electron yield Y versus the light beam incidence angles and polarization should deviate from that expected on the basis of the bulk absorption coefficient and Fresnel equations. Girardeau- Montaut et al. 11 have reported the evidence of a possible SEOA effect, in the single-photon emission case, on a Au sample irradiated by a 248-nm 450-fs laser source at 82° and 86° angles of incidence. Moreover, Srinivasan-Rao et al. 12 observed an enhancement of the multiphoton emission for p -polarized light up to 75 times larger than for the s polar- ization on Cu mirrors at 72.5° incidence and 10 11 W/cm 2 intensity, assigning this behavior to optical field effects. With the aim to explain these behaviors, Aeschlimann et al. 13 have tried to correlate the surface enhancement with the surface roughness, while Fann et al. 14 have suggested that image-potential surface states could give rise to resonant enhancements in the multiphoton photoemission electron distribution. On the other hand, as reported by Elsayed-Ali et al. 15 the electron-phonon transfer time was observed to be 1–4 ps for Cu and is expected to be similar for W. Therefore, operating at 120 fs only e - e interaction mechanisms should be ob- served and effects originating from electron-phonon scatter- ing processes should be excluded. Using these experimental conditions, nonlinear photoemission processes on metals, such as W and Cu, should be simplified, the electron gas being decoupled from the lattice. To clarify the origin of multiphoton electron emission, angle-resolved experiments by s - and p -polarized subpico- second laser pulses are required. This paper reports the non- linear photoemission data obtained on Cu and W polycrys- talline samples as a function of incidence angle, light polarization, and beam intensity, using 120-fs pulses at 600 nm with energies up to 100 mJ. It is shown that the changes of the photoemission current as a function of polarization, intensity, and laser beam incidence angle u are well de- scribed for both Cu and W by the bulk absorption coefficient and Fresnel equations, despite the fact that in Cu a third- PHYSICAL REVIEW B 1 SEPTEMBER 1996-I VOLUME 54, NUMBER 9 54 0163-1829/96/54~9!/6031~4!/$10.00 6031 © 1996 The American Physical Society