Background subtraction enhances the contrast between QWSs for odd and even N see Supplementary Information.ĭelaying the two laser pulses at energies h ν 1 and h ν 2 employed in 2PPE with respect to each other enables us to study the decay of hot quasiparticles directly in the time domain in a pump–probe experiment.
The data are fitted by Lorentzian peaks and an exponentially decaying background (BG) and convoluted with a Gaussian instrument function. b, 2PPE spectra for three exemplary values of N. The image is composed from three overlapping data sets in total, 109 spectra have been analysed for this figure. The 2 ML oscillation period of the binding energy of the luQWS is emphasized by a dotted line. The horizontal dashed lines indicate the positions of the valence- and conduction-band edges (VBE/CBE). The binding energies are determined from a Lorentzian line fit as explained in b and the Supplementary Information.
Red (blue) circles indicate the binding energies of the luQWS for even (odd) N yellow circles indicate higher-lying QWSs. The requirement that the sample work function is smaller than h ν in 2PPE prevented us from accessing energies E− E F<300 meV in these particular experiments. The 2PPE intensity is shown on a logarithmic scale, whereas the 1PPE intensity is plotted on a linear scale. The thickness-dependent 1PPE results probe the quantized occupied electronic states 21, 23, confirm our earlier laser photoemission observations 24 and are used as a thickness reference.Ī, Photoemission intensity in a colour map as a function of Pb thickness N in ML for the occupied and unoccupied states analysed by 1PPE and 2PPE, respectively. In contrast, for odd N the luQWS is degenerate with Si bands. Hence, the study of electron dynamics of the luQWS is especially interesting because this state resides in the Si bandgap for even N and is confined to the film. Simultaneously, the QWS peaks exhibit a high intensity contrast owing to an efficient electron confinement to the film at energies of the Si bandgap. The binding energies ( E− E F) of the lowest unoccupied QWS (luQWS) oscillate between 1.65 and 0.6 eV by 45–165% on variation by one monolayer (1 ML) in thickness from N to N+1 ML and form the two lowest branches of unoccupied QWSs. The data exhibit three branches of occupied quantum-well states (QWSs) and five branches of unoccupied QWSs that disperse towards E F with increasing coverage. In Fig. 1b the fitting results are shown for three exemplary Pb thicknesses details are given in the Supplementary Information. Symbols denote the peak positions of Lorentzian line fits. These linear and nonlinear methods of photoemission are illustrated in Fig. 1, left. We probe occupied states at energies below the Fermi level E F by one-photon photoemission (1PPE) with a photon energy h ν larger than the work function E F− E vac and unoccupied states above E F by two-photon photoemission (2PPE), where the sum of both photon energies h ν 1+ h ν 2 is larger than the work function. Figure 1a shows the photoemission intensity in a colour map as a function of Pb film thickness. We begin the discussion by analysing the quantized electronic structure in epitaxially grown Pb films. Thereby we demonstrate that for understanding electronic decay in nanostructures coupling to the environment is essential, and that even for electron confinement to a few ångströms Fermi-liquid theory for bulk can remain valid. For states resonant with Si bands, extra decay channels open for electron transfer to Si, resulting in lifetimes shorter than expected for bulk. For electronic states confined to the film by the Si bandgap we find quantitative agreement with Fermi-liquid theory and ab initio calculations 4, 7 for bulk Pb, which we attribute to efficient screening. Here, we lift this discrepancy by investigating Pb quantum-well structures on Si(111), a two-dimensional model system 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29. In contrast, quasiparticle lifetimes of metal bulk 5, 9, 10, 11, 12 and films 11, 13, 14, 15 are not well understood because electronic transport 10, 16, 17 leads to experimental lifetimes shorter than expected theoretically 13, 15, 18. Such lifetimes are widely studied by time-resolved two-photon photoemission 5, 6, which led to understanding of electronic decay at surfaces 6, 7, 8. Relaxation of hot electrons is governed by inelastic electron–electron scattering, which occurs on femtosecond timescales owing to the large scattering phase space competing with screening effects 4.
#THOMAS FERMI SCREENING LENGTH COPPER FREE#
Quasiparticle lifetimes in metals as described by Fermi-liquid theory 1 are essential in surface chemistry 2 and determine the mean free path of hot carriers 3.
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