Quantum-well photoemission spectroscopy of atomically-uniform films

Transcription

1 Journal of Electron Spectroscopy and Related Phenomena (001) locate/ elspec Quantum-well photoemission spectroscopy of atomically-uniform films a,b, a,b,1 a,b a,b T. Miller *, J.J. Paggel, D.-A. Luh, T.-C Chiang a Department of Physics, University of Illinois 1110 West Green Street, Urbana, IL , USA b Frederick Seitz Materials Research Laboratory, University of Illinois 104 South Goodwin Avenue, Urbana, IL , USA Received 8 August 000; received in revised form 0 September 000; accepted 3 October 000 Abstract Using a low-temperature growth technique and an Fe whisker sample, atomically-uniform films of Ag on Fe(100) are prepared. Extremely sharp quantum-well peaks are obtained in these films, as peak broadening from thickness variation is eliminated. The quality of the spectra allows the observation of quantum-well peaks in films over 100 monolayers thick. Quantum-well peaks from both the sp and d states have been observed and used to map the associated bands. The elimination of broadening from thickness variation allows for the interpretation of the peak linewidths in terms of the quasiparticle lifetime and interfacial reflectivity, and the phonon contribution can be deduced from the temperature dependence of the spectra. 001 Elsevier Science B.V. All rights reserved. Keywords: Photoelectron spectroscopy; Thin films 1. Introduction the values of the momentum still form a continuous spectrum characteristic of an ordinary bulk sample. In quantum-well photoemission, the specimen However those parallel components are conserved in takes the form of a thin film within which the the experiment and there is no problem in principle electrons are at least partially confined. Experimen- in determining them to any desired degree by using tally, such a sample provides the decisive advantage an electron analyzer of sufficient angular resolution. that the component of crystal momentum k perpen- So, it becomes possible to precisely select and dicular to the surface (k ') is quantized, and if the examine a particular electronic state in the valence film thickness is of atomic dimensions these in- bands. In particular, the spectral lineshape and dividual quantum states are easily resolved. In the directions parallel to the plane of the film, of course, linewidth can be interpreted in terms of the intrinsic properties of the material, such as the quasiparticle lifetime. In contrast, the lineshapes encountered in the more traditional type of experiment involving *Corresponding author. Present address: Institute for Experimental bulk photoelectric transitions are likely to appear Physics, Freie Universitat, Berlin, Germany. Tel.: complicated even for simple systems, and the width ; fax: address: tamille1@facstaff.wisc.edu (T. Miller). of a peak is likely to be much greater than the 1 Present address: Institute for Experimental Physics, Freie Uni- inverse lifetime of the photohole. For example, in versitat, Berlin, Arnimallee 14, Berlin, Germany. photoemission spectra from noble metal surfaces, / 01/ $ see front matter 001 Elsevier Science B.V. All rights reserved. PII: S (00)

2 514 T. Miller et al. / Journal of Electron Spectroscopy and Related Phenomena (001) direct-transition peaks from the sp band are decided- rate of about 0.5 monolayer (ML)/ min. The asly asymmetric. This is due to a quantum-mechanical grown sample did not show any quantum well peaks interference of two distinct photoexcitation channels: in the valence band, but after annealing the sample to one giving the direct transition in the bulk, and the above room temperature sharp quantum well peaks other due to the abrupt change in the photon field at appeared in the spectra. the surface. The result is a Fano-like line profile. The peak widths also contain a considerable contribution from final-state broadening, which obscures the 3. Results and discussion width due to the quasiparticle lifetime. Depending on the photon energy and the geometry of the measure- Fig. 1 shows normal-emission photoelectron specment, the sp-band peaks from this system may be tra from different thicknesses of Ag on Fe(100) broadened so severely by this effect as to be almost unrecognizable [1,]. In this paper results from quantum-well photoemission from thin films of Ag(100) on Fe(100) are summarized. Information on the band structure, quasiparticle lifetime, electron-phonon interaction, and defect scattering of the Ag material is obtained, as are properties of the quantum-well: the interface reflectivity and phase shift. Quantum-well states derived from both sp and d states are observed and analyzed, which demonstrates that the technique is not limited to nearly-free-electron states. It is emphasized, however, that the quality of the film is important if the data are to be readily interpreted.. Experimental All spectra were taken with a normal emission geometry using either the 4m NIM monochromator or the PGM undulator beam line at the Synchrotron Radiation Center of the University of Wisconsin in Stoughton, WI. Typical instrumental resolution was mev, and the angular acceptance was about Except as otherwise noted, all spectra presented here were taken at a sample temperature of 100 K. For the substrate, a single-crystal whisker of Fe was used. The details of sample preparation are as follows: a selected whisker is cleaned with numerous sputtering and annealing cycles with Ar ion energies between 1.5 kev and 500 ev. The sputtering was done at sample temperatures between 100 and about 850 K. After each sputtering cycle the sample was annealed at about 900 K. Sample quality was judged Fig. 1. Normal emission spectra for different coverages of Ag on Fe(100) as indicated. The data points are shown as dots, while the through the very contamination-sensitive Fe(100) fit and the background function are shown as curves. All of the surface state at the Fermi level E F [3]. Ag layers spectra are from atomically uniform films with an integer number were then grown at 100 K from an effusion cell at a of layers.

3 T. Miller et al. / Journal of Electron Spectroscopy and Related Phenomena (001) taken at a photon energy of 16 ev. With this experimental geometry only band states along the [100] direction are seen, and the energy range shown includes only emission from the sp band. This is a highly dispersive, nearly-free-electron like band that crosses the Fermi level along the [100] direction. Each peak in the spectra signals the existence of a standing wave state in the quantum well formed by the Ag overlayer, that is, a state satisfying the Bohr- Sommerfeld quantization condition.: pn 5 k(e)nt 1 F(E) (1) It is as if each of the four original peaks spawned a twin peak just to its right, with one of the new ones being slightly above the Fermi level and so it cannot be seen. In fact the new peaks correspond to a layer thickness one monolayer greater. This is verified by the top spectrum which is from a 39-ML thick film and now shows peaks only at locations corre- sponding to the added features in the middle spec-. The lowest curve in this figure is from a film 38 trum. ML thick. The vertical lines mark the positions of The spectra, then, show that these Ag overlayers four quantum-well peaks in that spectrum. Notice can be prepared so that they are of one thickness these peaks are sharp and baseline-resolved. Adding over the sample area used for measurement. This is 1/ ML to the sample results in the middle spec- in contrast to the more typical case of thin-film trum, which still shows the same four peaks as the quantum-well systems. Generally, one sees spectra bottom spectrum but also three more peaks as with relatively broad peaks which continuously shift marked by the vertical dashed lines above the curve. as additional submonolayer deposits are made, con- where k(e) is the electron wave number as a function of energy, F(E) is the total phase shift experienced by the electron wave at both interfaces, N is the number of monolayers of thickness t in the film, and n is an integer quantum number. In the language of the phase accumulation model [4] this expression says that an allowed state exists when the total phase shift suffered by the wave function in making a round trip through the film via reflections from both boundaries is some integer multiple of p. Eq. (1) is familiar from the solution to the one-dimensional particle-in-a-box problem in elementary quantum mechanics. It implies that the spacing of the allowed levels in k is inversely related to the thickness of the film, and it follows from the dispersion relation E(k) that the spacing of the peaks in the spectra are too. This is readily seen in the figure, which covers a range of coverages from 14 to 119 ML. Eventually, for very thick layers the peaks merge into the quasicontinuum characteristic of the bulk. Fig. 1 shows spectra from films with thicknesses that are each an exact integer number of monolayers as shown. In fact, each film is uniform over the area probed in the experiment. This atomic uniformity is a critical feature that facilitates interpretation of the spectra. This is emphasized by the close-up view of a sequence of submonolayer depositions given in Fig. Fig.. Normal emission spectra for a 38 ML (bottom), 38.5 ML (center), and 39 ML (top) Ag film on Fe(100) taken at a photon energy of 13 ev. The quantum well peak positions are indicated by vertical dashed lines. The spectrum for the 38.5-ML film shows two sets of quantum well peaks indicating the simultaneous presence of areas covered by 38 and 39 ML of Ag.

4 516 T. Miller et al. / Journal of Electron Spectroscopy and Related Phenomena (001) sistent with a film that is rough on an atomic scale [5]. Atomic uniformity of the layer removes uncertainty caused by layer-thickness variations, and makes possible the interpretation of the peak widths as quasiparticle inverse lifetimes [6]. It is still necessary to take into account some broadening due to imperfect reflectivity of the film s interfaces. Fortunately, this effect becomes less significant for larger film thicknesses and it can be separated out of the data by analyzing spectra from films of different thicknesses. In the method used here, the film is treated as a Fabry Perot interferometer [7] for electrons [8]. Each spectrum is modeled with the following function: 1 I~ ]]]]]]] A(E) 1 B(E) () 4f F 1 1] sinsknt 1] D p with A(E) and B(E) being smooth functions, and f is the finesse of the interferometer. The finesse (ratio of peak separation to peak width) is given by: pœ ] Re Nt/l f 5 ]]]] (3) 1 Re Nt/l Fig. 3. Fabry Perot model results. (a) Dispersion relation for the Ag sp band. (b) Quasiparticle inverse lifetime as a function of binding energy. (c) Total reflectivity of the quantum well boundaries. (d) Total phase shift for electron reflection in units of p. where l is the mean free path and R is the combined reflectivity of the two boundaries of the well. The exponential factor describes the attenuation of the wavefunction due to the finite quasiparticle lifetime in the well. Eq. () has peaks where the argument to 1 K [10]. Some of the discrepancy here can be the sine function vanishes; this reproduces the Bohr attributed to the temperature difference between the Sommerfeld quantization condition. To fit the data, two measurements. k 5 k(e) (the dispersion relation) is parameterized in From Fig. 3b it can be seen that the inverse the two-band model, and R, l and F are expressed lifetime increases with binding energy, in accordance as polynomial functions of E. Because spectra from with the general expectation that the probability for the films are atomic-layer-resolved, the number of the hole state to decay increases the deeper the layers N can be determined precisely by layer energy of the state. In a Fermi liquid, the lifetime is counting [9]. infinite at the Fermi level. Ag is a good candidate for A set of spectra of different coverages is fit Fermi liquid behavior, but the lifetime width evidentsimultaneously, as shown by the solid curves in Fig. ly does not vanish at EF. Other channels contributing 1. The resulting band structure and quasiparticle to the width include scattering by phonons and lifetime as a function of binding energy are shown in defects. Considering these contributions, the width Fig. 3, along with the quantum-well reflectivity and can be expressed as: phase shift. The accuracy of this band structure determination allows comparison of the measured G(E,T ) 5 G0 1 G 1(E,T ) 1 be (4) Fermi wave vector (k F /kg X ) to a de Haas van Alphen result of obtained at where G0 comes from defects, G 1(E,T ) from phonon

5 T. Miller et al. / Journal of Electron Spectroscopy and Related Phenomena (001) scattering, and the term be represents electron- fit using Eqs. (4) and (5) with l as a fitting electron scattering. The temperature dependence of parameter. A value of is obtained for l; the spectra may be used to isolate the phonon theoretical estimates are about half as large. l contribution. This can be described by [11]: characterizes the strength of the electron phonon interaction. This measured value puts Ag near the D E9 range seen for a number of superconducting simple G 1(E,T ) 5 pl E SD ] [1 f(e E9) 1 b(e9) E metals. The constant contribution to the width, 8 D 0 mev, corresponds to a quasiparticle coherence length 1 f(e 1 E9)] de9 (5) of 1000 A limited by defect scattering. It may at first seem surprising that the d bands of where ED is the Debye energy, and f and b are the Ag can also be studied with quantum-well photo- Fermi Dirac and Bose Einstein distributions, re- emission. Compared to the nearly free-electron sp spectively. In keeping with common usage, in this band, the d bands are much less dispersive and the context l is the electron-phonon mass-enhancement wave functions are more localized, such that they parameter [1]. Data (not shown) taken over a range have been compared to shallow core levels [14]. The of temperatures from 100 to 400 K show a definite relatively flat bands imply low group velocities, broadening of the quantum-well peaks as the tem- which in turn give rise to short mean free paths. For perature increases [13]. Fig. 4 shows the phonon and a film to work effectively as an interferometer, the defect parts of the total peak widths, obtained from a mean free path must not be small in comparison to Fabry Perot analysis of spectra from films 14 and 19 the film thickness. The observation of d band quan- ML thick, as a function of temperature. The elec- tum well states is complicated by the multiplicity of tron electron contribution (determined earlier, see bands in a small energy range: a 0-ML film might Fig. 3b) has been subtracted off. The solid curve is a support up to 100 peaks in an energy range of 4 ev. On the other hand, atomically uniform films are free from broadening due to film-thickness variation and have very narrow spectral peaks that can be resolved, even for these d band states. The upper panel of Fig. 5 shows spectra from four different thicknesses of Ag on Fe(100) over a range of binding energies occupied by the Ag d bands. The peaks are quantumwell states derived from those bands. It turns out that in any given spectrum only a fraction of the possible states are seen, partially because of a matrix-element effect which strongly emphasizes certain peaks while suppressing the others. Different peaks may be brought out by taking spectra at different photon energies. In this way, many peaks, coming from different bands in the d manifold, may be tracked as a function of film thickness. This feature can be used to amass peak-position data from which a map of the structure of the d bands can be made [14]. An accurate determination of the band structure is possible, as this kind of mapping is immune to the Fig. 4. Temperature dependence of the contributions to the problem of final-state lifetime broadening encounquasiparticle inverse lifetime from scattering by defects and tered in the usual type of photoemission experiment phonons. The dots are obtained from experimental widths by subtracting the electron electron contribution. The solid line is a from bulk samples. fit as described in the text. The dashed curves indicate the separate In the spectra of Fig. 5, the peaks at the top of the contributions from defects and phonons. d manifold (lowest binding energies) are noticeably

6 518 T. Miller et al. / Journal of Electron Spectroscopy and Related Phenomena (001) the Fabry Perot model with imperfect reflectivity. In a thinner film an electron in the well reflects off the boundaries more frequently, and so the reflection losses are comparatively greater. The solid curve in the figure is the result of fitting the width data to the Fabry Perot model with a reflectivity R50.68 and a quasiparticle lifetime width G 513 mev as fitting parameters. This lifetime width measurement is extremely narrow for a bulk state at such a high binding energy. In comparison, a previous measurement of the width of the uppermost d band state from Cu(100) at ev was 5 mev [15]. 4. Summary Fig. 5. (a) Normal-emission spectra for atomically uniform films of Ag on Fe(100) with different thicknesses as indicated. The photon energy was 1 ev. The energy region shown is occupied by Ag d bands. (b) The circles represent the Lorentzian linewidths (left vertical axis) of the least-bound d band quantum-well peak as a function of film thickness, after taking the instrumental res- olution into account. Points at the same thickness are from spectra at different photon energies. The solid curve is a fit to the points using a Fabry Perot model. The dashed curve shows the mean free path as a function of energy (right vertical axis). With the development of metal films with atomic uniformity, the utility of quantum-well photoemission spectroscopy for the study of valence electronic states, as was proposed long ago [16], has been demonstrated. Accurate determinations of band structure as well as quasiparticle lifetimes are obtained using this method, and the different contributions to the lifetime width can be isolated by a temperature- and thickness-dependent study. The film quality is important to eliminate broadening due to film-thickness variation, so it is not known now to what extent this technique may be generalized to other material systems. However, it is not necessary to use a nearly free-electron band in the film, nor is an actual band gap needed in the substrate. So, there are exciting possibilities for further research and applications. Acknowledgements sharper and better resolved than the deeper states. This is expected on general grounds, but particularly This material is based upon work supported by the for the highest-energy peak because of the lack of a US National Science Foundation, under Grant Nos. d d sp Coster Kronig Auger decay channel for that DMR and An acknowledgement state. The Lorentzian width of this peak as a function is made to the Donors of the Petroleum Research of film thickness is plotted as circles in the lower Fund, administered by the American Chemical Socipanel of Fig. 5. These values were obtained from a ety, and to the US Department of Energy, Division fit of a Voigt lineshape to the peak, with the Gaussian of Materials Sciences, (Grant No. DEFG0- width set to the instrumental resolution as deduced 91ER45439) for partial support of the synchrotron from lineshape of the Fermi edge. The Lorentzian beamline operation and for support of the central width is seen to decrease with increasing film facilities of the Materials Research Laboratory. The thickness. This can be understood in the context of Synchrotron Radiation Center of the University of

7 T. Miller et al. / Journal of Electron Spectroscopy and Related Phenomena (001) Wisconsin is supported by the National Science [8] J.J. Paggel, T. Miller, T.-C. Chiang, Science 83 (1999) Foundation under Grant No. DMR [9] J.J. Paggel, T. Miller, D.-A. Luh, T.-C. Chiang, Appl. Surf. Sci. 78 (000) 16. [10] P.T. Coleridge, I.M. Templeton, Phys. Rev. B 5 (198) References [11] B.A. McDougall, T. Balasubramanian, E. Jensen, Phys. Rev. [1] A. Samsavar, T. Miller, T.-C. Chiang, J. Phys.: Condens. B51 (1995) Matter (1990) [1] G. Grimvall, in: The Electron-Phonon Interaction in Metals, [] E.D. Hansen, T. Miller, T.-C. Chiang, Phys. Rev. Lett. 80 North-Holland, New York, (1998) [13] J.J. Paggel, T. Miller, T.-C. Chiang, Phys. Rev. Lett. 83 [3] M. Turner, J.L. Erskine, Phys. Rev. B 30 (1984) (1999) [4] N.V. Smith, N.B. Brookes, Y. Chang, P.D. Johnson, Phys. [14] D.-A. Luh, J.J. Paggel, T. Miller, T.-C. Chiang, Phys. Rev. Rev. B 49 (1994) 33. Lett. 84 (000) [5] T. Miller, A. Samsavar, G.E. Franklin, T.-C. Chiang, Phys. [15] R. Matzdorf, A. Gerlach, F. Theilmann, G. Meister, A. Rev. Lett. 61 (1988) Goldmann, Appl. Phys. B 68 (1999) 393. [6] J.J. Paggel, T. Miller, T.-C. Chiang, Phys. Rev. Lett. 81 [16] P.D. Loly, J.B. Pendry, J. Phys. C 16 (1983) 43. (1998) 563. [7] M. Born, E. Wolf, in: Principles of Optics, 6th Edition, Pergamon, New York, 1980.