Femtosecond two-photon photoemission studies of image-potential states
Introduction
The existence of image-potential states at metal surfaces was predicted by Echenique and Pendry [1]and confirmed in inverse photoemission experiments a few years later 2, 3. Considerable progress has been made by two-photon photoelectron spectroscopy [4]which could identify several members of the Rydberg-like series of image-potential states. Since then extensive studies on clean and adsorbate-covered metal surfaces have been made which have been reviewed in several articles 5, 6, 7, 8. After the energies of image-potential states have been well understood the interest shifted to the linewidths and lifetimes of the states. Spectroscopic studies in the energy domain were limited by the available energy resolution 9, 10, whereas studies in the time domain were limited by the duration of the laser pulses 11, 12, 13. Due to the experimental difficulties with both types of experiments the comparison between linewidths and lifetimes was possible only in a few cases and the quantitative agreement was limited 6, 10.
With the introduction of Ti:sapphire lasers the generation of femtosecond pulses became relatively easy and was soon employed for the study of image-potential states in two-photon photoemission 14, 15. The improvement in count rate by three to four orders of magnitude opened up many new perspectives and possibilities. The most intriguing aspects and the current topics of research will be discussed in this article. These include the access to higher image-potential states by quantum beat spectroscopy (Section 5), the accurate determination of lifetimes down to 10 fs (Section 4), and the detailed comparison between linewidths and lifetimes (Section 4). This leads in turn to the study of dephasing processes (Section 5) and how they can be controlled by modifying the surface (Section 6). The final 7 Discussion, 8 Summary and outlookdiscuss the present state of the field and attempt an outlook into the future of femtosecond two-photon photoemission studies of image-potential states. Before starting we will review the main features of image-potential states (Section 2) and the experimental requirements for femtosecond time-resolved two-photon photoemission (Section 3).
Section snippets
Image-potential states
Since the quantum-mechanical theory of image-potential states is well developed 1, 16, we will present here a classical picture which helps to elucidate some of the issues regarding decay and dephasing rates in later sections. In Fig. 1 the attractive image potentialin front of a metal surface is shown. We consider the case of an electron in front of the surface. Its energy E is below the vacuum level Evac and within an energy gap of the band structure in the direction of the
Two-photon photoemission
The image-potential states are close to the vacuum level and are therefore normally unoccupied. Besides inverse photoemission 2, 3the most successful experimental method to probe image-potential states is two-photon photoemission [4]. The energy diagram for this process is shown in Fig. 2 where an electron from an occupied initial state with energy Ei is first excited into the image-potential state En by a photon of energy 3hν (this value corresponds to the frequency-tripled laser output used
Linewidths and lifetimes
Fig. 4 presents energy-resolved two-photon photoemission spectra from a Cu(100) sample for different delays between probe and pump pulse. In all spectra three peaks can be clearly identified which are assigned with increasing energy (here relative to the Fermi level EF) to the n=1, 2, and 3 image-potential states, respectively. From these data the energy En and intrinsic linewidth Γn can be extracted very accurately by lineshape analysis 9, 10. The results are in agreement with previous work [6]
Dephasing
The concept of dephasing can be most easily seen for the higher image-potential states n>3 which cannot be resolved energetically but still contribute to the two-photon photoemission intensity (see Fig. 4 for long delays at energies above the n=3 state). Time-resolved data in this energy range are shown in Fig. 6 and can be explained by the interference of the n=3 and 4 states coherently excited due to the large bandwidth of the pump pulse [15]. The data consist of an exponential decay and an
Controlling decay and dephasing rate
Having established the picture where population decay and pure dephasing are due to inelastic and quasielastic scattering, respectively, of the electrons in the image-potential state, one may attempt to control these processes by modifying the surface. The influence of temperature is predominantly via quasielastic scattering by phonons and has been studied by Wolf and co-workers for Cu(111) [22]. Adsorbate layers and in particular spacer layers of noble gases can change the coupling of the
Discussion
The previous section presented a plethora of results on the dependence of the decay and dephasing rates on quantum number of the image-potential states and on coverage of various adsorbates. We will first discuss the n dependence of these quantities. This will lead to the question how the differences between the various adsorbate systems may be explained.
The change of the decay rate with coverage as a function of quantum number n shown in Fig. 10 is independent of the adsorbate and is similar
Summary and outlook
The introduction of Ti:sapphire lasers into two-photon photoemission spectroscopy simultaneously led to an increase in the photoelectron count rate by three to four orders of magnitude and extended the time resolution into the femtosecond range. New experiments include the quantum beat spectroscopy which makes the higher image-potential states accessible. The effects of pure dephasing and population decay can be distinguished, which for the lower image-potential states can be identified from
Acknowledgements
Stimulating discussions with U. Höfer, A. Goldmann and F. Theilmann are gratefully acknowledged. This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG).
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