Bichromatic Two-Photon Photoemission Spectroscopy of Image Potential States on Ag(100)

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1 Appl. Phys. A 51, (1990) Applied,o,,,, Physics A Surfaces "' Springer-Verlag 1990 of Image Potential States on Ag(100) S. Schuppler, N. Fischer, Th. Fauster, and W. Steinmann Sektion Physik der Universit/it Miinchen, Schellingstrasse 4, D-8000 Miinchen 40, Fed. Rep. Germany Received 17 April 1990/Accepted 30 April 1990 Abstract. Bichromatic two-photon photoemission spectroscopy (Bi2PPES) leads to an increased signal-to-noise ratio compared to conventional two-photon photoemission spectroscopy and therefore allows the observation of the first four image potential states as well as a lineshape analysis with improved accuracy on Ag(100). The n = 2 image state with a measured linewidth of 37 mev FWHM is the narrowest unoccupied structure measured on any solid surface so far. The intrinsic linewidths of the first two image states were determined as 21 _ 4 mev and 5 _ 5 mev, respectively, in reasonable agreement with theoretical calculations. Disordered adsorption of oxygen on Ag(100) leads to a linewidth broadening of the first and - to a lesser extent - of the second image potential state. A quantitative analysis of the broadening suggests that the underlying mechanism is lifetime shortening due to scattering of the image state electrons by the adsorbate atoms. PACS: 73.20At, 79.60Cn, 79.20Ds Image potential states on metal surfaces have been a subject of growing interest over the past few years. They have their origin in the 1/4z potential of the image charge induced by an electron in front of the surface and in the reflection of the electron due to a band gap of the metal. Consequently, they form a hydrogen-like series converging toward the vacuum level. An extension to this crude picture is the phase analysis model [-1] which takes the view of multiple reflection between the image potential barrier and the crystal potential. The respective phase shifts upon reflection must sum up to a multiple of 2~ for an image state to occur. But the crystal phase shift depends on the position of the vacuum energy relative to the band gap, and in the simplest phase analysis model this is approximately accounted for by introducing a quantum defect a in the hydrogen-like formula for the binding energy: Eb(n ) = 0.85 ev/(n + a) 2. (1) For Ag(100) where the vacuum level is located in the middle of the band gap the quantum defect a is approximately 1/4 [2, 3]. Since the image states are localized in front of the surface one expects a long lifetime. Quite early a theoretical paper [-4] showed that the linewidth of the states should be proportional to 1In 3 so that the whole series could, in principle, be resolved by appropriate spectroscopies. A more recent theoretical analysis [-5] predicts that lifetimes for the first image state on fcc (100) faces should roughly be in the 50 fs range and the corresponding intrinsic linewidth therefore be around 10 mev. The first direct experimental verification of image states on metals was carried out with inverse photoemission [6]. But it was the development of two-photon photoemission spectroscopy (2PPES) which provided sufficient energy resolution not only to observe and measure the higher members of the Rydberg series but also to distinguish between different models for the binding energy and dispersion of the image states [2]. Recently the open problem concerning the binding energy and effective mass of image states on Ni(lll) could be settled using 2PPES, and the results show that a refined phase analysis model which accounts for the d-band effects on Ni is able to correctly describe image states [7]. The expected small intrinsic linewidth of image states requires a good energy resolution in order to perform lineshape analysis. 2PPES is therefore the only candidate for experimental investigations in this area and has already proven its ability for lineshape analysis in a study on Ni(111) [8]. Bichromatic 2PPES (Bi2PPES) is expected to further increase the signal-to-noise ratio in these measurements, making even better resolution possible.

2 S. Schuppler et al. 323 Evac n=l - E F -- 2h~ 2hv 2PPES PROCESSES hv conventional bichromatic Fig. 1. Energy diagram of the excitation processes in conventional and bichromatic 2PPES with the first image potential state as intermediate state. Conventional 2PPES uses frequency-doubled laser light ("2hv") for both excitation steps, whereas in bichromatic 2PPES the second excitation step is performed with the fundamental photon energy hv. The arrow thicknesses symbolize light intensities. The energy distribution curve shown as an example in the upper right hand edge is recorded with a 2hv intensity reduced by a factor of 15 in the "bichromatic" part as compared to the"conventional" part. The corresponding increase in signal-to-noise ratio of the two peaks is one order of magnitude In a conventional 2PPE process [2] an electron from an occupied state below the Fermi energy Er is excited into an unoccupied intermediate state by absorption of one photon. By absorbing a second photon within the lifetime of this state it is lifted to the final state above the vacuum energy E,,~ where it can be analyzed. In practice, frequency-doubled laser light with a photon energy 2hv is used for these two excitation steps. The situation is illustrated in the left part of Fig. 1 with the n = 1 image state as the intermediate state. Unfortunately, however, the experimentally usable photon energies for the first excitation step often have to lie very close to the sample work function ~ where the onset of the much more intense one-photon photoemission (1PPE) causes problems by generating space charge and spectral background. Bichromatic 2PPES (Bi2PPES), which was introduced by Schoenlein et al. [9] for their time-resolved measurements of image state lifetimes on Ag(100), circumvents this problem by performing the second excitation step using the fundamental wavelength of the laser at the energy hv which is obviously harmless in this respect. As in the ease of ordinary 2PPE, the signal counting rate is proportional to the product of the light intensities involved. Since the M-intensity is chosen much higher, the 2hv-intensity needed for the first step can be reduced for obtaining the same signal counting rate as in conventional 2PPE, resulting in reduced background and space charge distortion. Furthermore, the excitation in the second step is more efficient for the lower photon energy [9]. In the right hand part of Fig. 1 the Bi2PPES process is depicted together with a resulting experimental spectrum showing both the 2PPES and the Bi2PPES peak corresponding to the n = 1 image state. Note that the 2hv-intensity for the Bi2PPES part of the spectrum was reduced by a factor of 15 and still gives a higher signal counting rate as compared to the 2PPES signal. Obviously Bi2PPES is indeed a way to significantly improve the signal-to-noise ratio in the spectroscopy of unoccupied states, in this case by one order of magnitude. 1. Experimental We used a tunable three-stage dye laser pumped by an excimer laser as the light source for the Bi2PPES experiments. Pulse lengths are about 10 ns. The dye laser light is frequency doubled in a/%bab20 4 crystal. Since the polarization of the frequency-doubled wave is perpendicular to that of the fundamental, the ratio of the two corresponding intensities can be varied continuously in a certain range by a set of two Glan-Thompson polarizers in the light path after the frequency doubling crystal. We used p-polarization for both excitation steps in the Bi2PPES process. The photoelectrons are analyzed in a sectoral hemispherical analyzer equipped with three-lens entrance and exit electron optics. The system achieves an angular resolution better than +_ 2 and a relative energy resolution of about 2.5%. The pass energy is kept constant for each spectrum. In the present experiments analyzer resolutions between 27 mev and 55 mev were used. The experiments were performed at normal emission. The UHV chamber in addition contains a noble gas discharge lamp which allows the recording of onephoton photoemission 0PPE) spectra using the same analyzer. The Ag(100) surface was cleaned in the usual way by argon sputtering and heating cycles. A LEED unit was used to check the quality of the surface structure. 2. Clean Ag(100) Information about analyzer resolution and work function can be obtained from the low-energy edge of both 1PPE and 2PPE spectra. We regularly controlled the parameters in both ways with equal results, but the discussion below will concentrate on the 2PPE measurements. Figure 2 shows in both panels the peak around zero kinetic energy in 2PPES. The intrinsic lineform was taken to be a step function centered at the position of the is fitted to the data by varying E... AE, ~, and the vacuum level Ewo in the spectrum multiplied by an exponentially decreasing function exp[-/~(e-evj]. After convoluting this function with the Gaussian apparatus function with energy width AE, the resulting function amplitude of the step function. The result of the fit is shown as a continuous curve in both panels. Details of this fitting procedure can be found in [8]. In this way the work function ~ of the sample could be determined as = ev, in accordance with earlier measurements [3]. The energy resolution of the analyzer was found to be AE = 27 mev in the lower and - due to the higher pass energy - 47 mev in the upper panel. Note that these Gaussian widths, as well as all linewidths given below, are to be understood as the full width at half maximum (FWHM). The parameter//in the ansatz function could also be given physical meaning. We verified in all spectra taken that it is equal to 1/kT, where k is the Boltzmann constant and T the absolute temperature, in most cases room temperature. An interesting example is shown in the upper panel of Fig. 2. This spectrum was recorded during a heating cycle in order to desorb oxygen from the sample

3 324 ~ Ag(100) ~ from fit: ~ T = 320 C e- n o AE = room t. = 27 mev Kinetic energy (ev) Fig. 2. Energy distribution curves of the low-energy peak in 2PPES. From the fitting procedure described in the text we obtain the work function and the energy resolution. The exponential decrease with energy can be used to determine the sample temperature. Upper panel: Sample heated to 320 C, resulting in broadened exponential decrease; energy resolution set to 47 mev, Lower panel: Analyzer set to the best resolution used in our experiments (27 mev). Sample at room temperature (the corresponding adsorption experiments will be discussed in the next section). We took care to heat the sample just above the desorption temperature which was taken from Ref. [10] to be 300 C. Indeed, the parameter fl resulting from the fit is equivalent to a temperature of 320 C. From this exp(-e/kt)-dependence of the photoelectron signal and measurements on Ni(111) reported in a previous paper [7] we conclude that the low-energy electrons in 2PPE are mainly a result of one-photon photoemission from thermally occupied states above E F and not caused by secondary electrons as in 1PPE. The upper part of Fig. 3 shows a Bi2PPE energy distribution curve recorded at a photon energy hv=2.218ev for the second excitation step and 2hv =4.436 ev for the first excitation step, slightly above the work function. This means, on the one hand, that the whole series of image potential states can be excited from states at or below EF. On the other hand, it leads to strong 1PPE, but obviously this does not affect the spectrum much, which illustrates the potential of Bi2PPES quite well. In addition to the first three image peaks, the spectrum shows a shoulder above the third peak, interpreted as the fourth image peak. It is a consequence of the excitation of the whole series but can be seen here for the first time. The continuous curve is obtained by convoluting four Lorentzians modelling the first four image states on Ag(100) with a Gaussian as an approximation to the apparatus function and is fitted to the data by minimizing Z 2 [11]. It should be noted that the last two structures are indeed fitted significantly better (99.8% confidence level) by two peaks than by one broad peak as might be suggested by a first inspection of the enlarged section shown in the figure. In this way the binding energies of the image state series on a metal surface could be determined up to n--4. In Table 1 these binding energies are compared to the simplest phase analysis model of image states where the LU fit. O. xl J E O t.. t- o / Binding energy relative to Eva c (mev) Fig. 3. Upper panel: Bi2PPE spectrum recorded with a photon energy 2hv slightly above the work function. The first four members of the image state series are modelled by a convolution of four Lorentzians with a Gaussian, shown as the continuous curve. Lower panel: Bi2PPE spectrum at a lower photon energy and improved analyzer resolution Table 1. Binding Energies of Image States on Ag(lO0) State E b [mev] Theory Experiment n = _+ 15 n= n= _+15 n=4 47 ~ 31 Comparison of experimental and theoretical binding energies for the first four image states on Ag(100). Theoretical values are obtained using (1) and the fitted value for the quantum defect a = 0.26 (see text). The difference for n = 4 is due to the contribution of image states with n>4 quantum defect a is used as the parameter in a fitting procedure for the first three image states. Obviously the series is described well by this model with the resulting value a = 0.264, which in turn lies close to the approximate value a = 1/4 mentioned earlier. The significantly bigger difference for the n = 4 state can be qualitatively explained by the contribution of even higher members of the Rydberg series. A spectrum recorded with the analyzer resolution 27 mev taken from the corresponding 2PPES low-energy cutoff of Fig. 2 is shown in the lower panel of Fig. 3. The photon energy 2hv was decreased by 86 mev and therefore only the first two image states were fully excited from states below EF. The n = 3 state can also be seen but is

4 s. Schuppler et al. slightly distorted by Fermi edge effects and thus cannot be taken into consideration. Obviously the two main peaks are very narrow: we measured 47 mev and 37 mev FWHM for the first and second states, respectively. This means that the n = 2 state on Ag(100) represents the narrowest unoccupied structure so far observed on any solid surface. Thanks to the Bi2PPES process, signal statistics allow a lineshape analysis with narrow limits of error. The two peaks are fitted by a convolution of two Lorentzians with intrinsic linewidths meV and 5_ 5 mev, respectively, with a Gaussian of width 35meV. As in the case of Ni(lll) [8], the measured linewidth of the n = 2 state forms a strict upper limit for the Gaussian width in the lineshape analysis, and this adds further significance to the simultaneous fitting of both states. In the time-resolved 2PPE measurement mentioned above [9], the lifetime of the first image state on Ag(100) was investigated. It used 55 fs pulses and had to introduce Bi2PPES in order to measure the lifetime by applying a variable time delay between the first and second excitation step. In this way the authors determined the lifetime to be in the range 15-35fs, equivalent to an intrinsic linewidth of 19-44meV. Another conventional 2PPE measurement [12] finds an intrinsic linewidth for the n = 1 state of 35 ± 9 mev, using an energy resolution of 70 mev. Theory [5] predicts linewidths that are about one-half of our experimental intrinsic linewidths: <10meV and < 2meV for the n = 1 and n = 2 state, respectively. Our result has the smallest error limits and lies closer to the theoretical prediction than the other measurements. The comparison with theory should be viewed in the light of the results on Ni(111) 1-8] where the present theory is definitely not able to describe the experimental intrinsic linewidths. 3. Oxygen on Ag(100) Finally, we investigated the influence of the disordered adsorption of oxygen on linewidths. The additional oxygen atoms should act as scattering centers for the electrons in image states and therefore lower the lifetime of these states. This leads to a broadened linewidth of the image states and also to a reduced signal intensity, since the lifetime of the intermediate state in the 2PPE process directly affects the efficiency of the process. We investigated oxygen exposures between 80L and 2400L (1 L= 10-6 Torr-s) and found both predictions to hold. We note that even at an oxygen dose of 7800 L the n = ] state can still be detected which illustrates the sensitivity of Bi2PPES. Lineshape analysis of several spectra shows that the broadening has mainly Lorentzian shape (as is expected for lifetime effects), so that information about broadening can be obtained to a good approximation by linear subtraction of the measured linewidth at the clean surface from the linewidth at the oxygen-exposed surface instead of performing a full lineshape analysis for each spectrum. A double-logarithmic plot of this line broadening versus oxygen dose is shown in Fig. 4. The data points can be fitted quite well by straight lines of nearly the same c~ I00 _Z Z < a_ z A loo, I OXYGEN EXPOSUBE (10-8 tort*s) Fig. 4. Linewidth broadening of the first two image states on Ag(100) upon disordered oxygen adsorption slope. Consequently, a power law between the oxygeninduced line broadening and oxygen dose holds: A Eacls(n ) -- A Eelean(rt ) = ~(n)" (dose) c, (2) where c was determined to be c = The sticking coefficient of oxygen on Ag(100) is small but unfortunately unknown. We assume that it is constant over the range of oxygen doses studied, and therefore the coverage should be proportional to the oxygen exposure. It follows then from (2) that the linewidth broadening due to oxygen adsorption is proportional to the square root of the coverage. On the other hand, the oxygen-induced kll-uncertainty which is equal to the inverse average nearest-neighbour distance between two adsorbate atoms is also proportional to the square root of the coverage. Consequently, the line broadening is inversely proportional to the linear scale introduced by disordered adsorption. Our results confirm the view that oxygen adsorbate atoms on Ag(100) act as scattering centers for electrons in the image states and thus confine these states laterally. The energetic broadening is therefore a consequence of the decrease in lifetime due to scattering by the adsorbate atoms. The n=2 state is obviously less influenced by the oxygen adsorption than the n = 1 state. From Fig. 4 the ratio of the amplitudes in (2) can be deduced as e(l)/~(2) = (3) This result can be made plausible by recalling that the second image state is located further away from the metal surface than the first one by roughly a factor of four. 4. Summary Bichromatic 2PPES was successfully applied to the investigation of the Rydberg series of image potential states on Ag(100). The signal-to-noise ratio could be improved by an order of magnitude by this method. The binding energies of the first four members of the image state series were measured for the first time. Exploiting this method we were able to determine the intrinsic linewidths of the first two image states and found reasonable agreement with theory. Disordered oxygen adsorption on Ag(100) causes a linewidth broadening which can be interpreted in the picture of adsorbate atoms acting as scattering centers. Linewidths are under further investigation. Bi2PPES has proven to be significantly more sensitive to weak struc-

5 326 tures than conventional 2PPES and thus enhances the possibilities for studying unoccupied states. Acknowledgement. This work was supported by the Deutsche Forschungsgemeinschaft. References 1. N.V. Smith: Phys. Rev. B32, 3549 (1985) 2. W. Steinmann: Appl. Phys. A49, 365 (1989) and references therein 3. K. Giesen, F. Hage, F.J. Himpsel, H.J. Riess, W. Steinmann: Phys. Rev. B35, 971 (1987) 4. P.M. Echenique, J.B. Pendry: J. Phys. C 11, 2065 (1978) 5. P.M. Echenique, F. Flores, F. Sols: Phys. Rev. Lett. 55, 2348 (1985) P.L. de Andres, P.M. Echenique, F. Flores: Phys. Rev. B39, (1989) 6. V. Dose, W. Altmann, A. Goldmann, U. Kolac, J. Rogozik: Phys. Rev. Lett. 52, 1919 (1984) D. Straub, F.J. Himpsel: Phys. Rev. Lett. 52, 1922 (1984) 7. S. Schuppler, N. Fischer, W. Steinmann, R. Schneider, E. Bertel: Submitted to Phys. Rev. B 8. N. Fischer, S. Schuppler, Th. Fauster, W. Steinmann: To be published 9. R.W. Schoenlein, J.G. Fujimoto, G.L. Eesley, T.W. Capehart: Phys. Rev. Lett. 61, 2596 (1988) 10. H.A. Engelhardt, D. Menzel: Surf. Sci. 57, 591 (1976) 11. W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterlin: Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, Cambridge 1989) 12. H.B. Nielsen, G. Brostroem, E. Matthias: Z. Phys. B 77, 91 (1989) Note added in proof. In the meantime we became aware of the work by R.W. Schoenlein et al. [Phys. Rev. B41, 5436 (1990)] who find for the n=2 state on Ag(100) a lifetime of fs. This is equivalent to an intrinsic linewidth of mev and agrees well with our result.