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Emergence of valence band structure in rare-gas clusters
Chemical Physics Letters 468 (2009) 148–152
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Emergence of valence band structure in rare-gas clusters D. Rolles a,b,c,*, H. Zhang a, Z.D. Pešic´ a,b, J.D. Bozek b,d, N. Berrah a a
Physics Department, Western Michigan University, Kalamazoo, MI 49008, USA Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Max Planck Advanced Study Group, Center for Free Electron Laser Science, 22761 Hamburg, Germany d Linac Coherent Light Source, Stanford Linear Accelerator Center, Menlo Park, CA 94025, USA b c
a r t i c l e
i n f o
Article history: Received 18 September 2008 In final form 4 December 2008 Available online 11 December 2008
a b s t r a c t The formation of electronic band structure by the valence-shell of Ar, Kr, and Xe clusters was studied for various cluster sizes using angle-resolved photoelectron spectroscopy. Different widths of the fine-structure components in the cluster spectra are attributed to a splitting of the outermost p3=2 levels due to valence-orbital overlap between neighboring atoms. Photoelectron angular distributions from the cluster differ from the atomic cases and vary substantially for different bands. The evolution of the electronic structure with increasing cluster size emulates the changes of the valence band structure in the transition from a condensed-phase monolayer to the bulk. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction Nanotechnological devices are reaching the size of few or even single molecules [1], motivating an increased need to study the electronic structure of mesoscopic systems that lie in between the traditional fields of atomic, molecular, and condensed matter physics, material science, and chemistry. Understanding the emergence of typical solid-state properties such as conductivity and magnetism on simple model systems is a crucial first step towards unraveling the properties and functionality of more complex systems with practical applications in material sciences and nanoengineering. In this sense, clusters are often touted as ‘bridging the gap’ between atoms and solids, and seem a perfect candidate for a ‘bottom-up’ approach, starting from a single atom and increasing their size until solid-state behavior is reached asymptotically [2]. Due to the simple control over their size or, more precisely, at least their average size, which can be varied from a single atom to several thousands or even millions of atoms, rare-gas clusters have received considerable attention. In the condensed-phase, rare gases are large-band-gap insulators that are well-studied by photoelectron spectroscopy [3–12]. Rare-gas clusters, as neutral species, are produced by supersonic expansion with a broad distribution of sizes around an average cluster size. Nevertheless, clear size effects have been observed in their photoelectron spectra, mostly for core levels, where a clear surface/bulk-splitting is the dominant spectral feature since these electrons are strongly localized [13–16]. Since atoms in rare-gas clusters are only weakly * Corresponding author. Address: Max Planck Advanced Study Group, Center for Free Electron Laser Science, 22761 Hamburg, Germany. E-mail address: [email protected] (D. Rolles). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.12.015
bound by van der Waals forces, the role of overlap and delocalization of the valence-orbitals is less established. The first valenceshell photoelectron spectroscopy of rare-gas clusters was performed on Ar, Kr, and Xe dimers [17–19], and later on larger clusters [20,21] using VUV-radiation from a He lamp. More recently, synchrotron radiation was used to investigate valence photoemission from pure [16,22–25] and mixed rare-gas clusters [26]. Several of these studies noted the different widths and shapes of the two fine-structure components in the cluster valence spectrum, but a consistent interpretation has not yet emerged. In the first study of the valence photoelectron spectra of different size rare-gas clusters [20,21], the peak shapes and widths were attributed to formation of small ionic cores (‘chromophores’) within the cluster. Later studies [16,23] noted a similarity of the cluster valence spectra to the band structure of rare-gas solids [3] and monolayers [4], but no clear experimental evidence of this interpretation has been provided thus far. Extensive investigations of band absorption and fluorescence in rare-gas clusters also stressed the similarities to solid-state band structure, but mostly focused on the evolution of surface and bulk excitons in the cluster [27–34]. In this Letter, we report an investigation of the photoemission of the outermost valence-orbitals of Ar, Kr and Xe clusters for different average cluster sizes using angle-resolved photoelectron spectroscopy (ARPES) to develop a clear understanding of the cluster valence spectra and the possible influence of band structure formation. ARPES is a successful tool used to study the band structure of surfaces, solids and interfaces [35,36], and hence well suited to provide specific insights into valence band structure effects in clusters. Our experimental data reveals the formation and evolution of the valence band for increasing average cluster size and establishes, for the first time, a clear link between the band structure of rare-gas clusters, monolayers and the bulk solid.
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D. Rolles et al. / Chemical Physics Letters 468 (2009) 148–152
2. Experimental method
13
12
11
5p1/2
The experiments were performed on beamline 10.0.1 of the Advanced Light Source at Lawrence Berkeley National Laboratory. The clusters were produced by supersonic expansion of rare gases through a liquid-nitrogen cooled nozzle [16]. The average cluster size in the beam was varied by changing the expansion pressure and the nozzle temperature according to common scaling laws based on the C formalism [37–39]. The skimmed cluster jet was crossed with tunable, linearly polarized synchrotron radiation, and the photoelectrons were detected in two time-of-flight (TOF) analyzers mounted at 0° and 54.7° with respect to the polarization vector in the plane perpendicular to the light propagation direction [16,40]. Simultaneous measurement of the photoelectron intensity at both angles allowed a determination of the asymmetry parameter b, which characterizes the photoelectron angular distribution of randomly oriented targets in the gas phase [41]. Spectrometer efficiencies and energy scales were calibrated using the atomic binding energies and asymmetry parameters [42] from the literature.
atomic 5p1/2
5p3/2
cluster 5p1/2
bulk
Intensity (arb. units)
Xe solid (bulk)
atomic 5p3/2
surface
cluster 5p3/2
Xe cluster=8000
bulk bulk surface surface mj=+- 1/2 mj=+- 3/2
Xe cluster=2000
Xe cluster=500
3. Results and discussion Fig. 1 shows typical valence-shell photoelectron spectra of xenon clusters for different average cluster sizes hNi compared to the photoelectron spectra of solid (bulk) Xe (top) [3] and a Xe monolayer (bottom) [9]. The two strong and narrow peaks in the cluster spectra are due to contributions from uncondensed Xe atoms in the beam, while the broader features correspond to photoelectrons from the clusters. For hNi ¼ 500, the cluster peaks are remarkably similar to the monolayer spectra, whereas the appearance of new contributions, reminiscent of the Xe bulk spectrum, is evident for larger cluster sizes. While it has been argued previously that a surface/bulk-splitting was not visible for cluster valenceelectrons because of their delocalization [16,23], our spectra clearly show a splitting of the 5p1=2 fine-structure component and a variation of the intensities for increasing cluster size, demonstrating that such splitting does indeed occur. Furthermore, an increased width of the 5p3=2 peak as compared to the 5p1=2 peak can clearly be observed for all cluster sizes, suggesting an additional splitting of this peak related to band structure formation similar to the case of the condensed-phase spectra. When first observed in the late 1970s, the origin of the splitting of the p3=2 level in rare-gas monolayers was controversial [4,43,44]. However, a bounty of subsequent studies [9–11,45–47] confirmed the initial interpretation that the p3=2 level was split into the magnetic sublevels mj = 1/2 and mj = 3/2 due to lateral interaction between neighboring Xe atoms [4], leading to the formation of a twodimensional band structure [45,46]. Systematic studies of monoand multilayers [8,9] also established the gradual transition into the three-dimensional band structure of the bulk solid with a splitting of the p3=2 -derived bands in the crystal field [3,5]. Based on our observations, we hence conclude that the 5p3=2 cluster peak is split into two components consisting of the magnetic sublevels mj = 1/ 2 and mj = 3/2 due to symmetry-lowering of the cluster system by valence-orbital overlap of neighboring cluster atoms. In addition, each cluster peak is further split into a surface and bulk component, leading to a total of two components in the 5p1=2 cluster peak and four components in the 5p3=2 cluster peak, which we have separated by a least-square fit as shown in Fig. 1. Quantitative analysis confirms that the total width of the valence band increases with cluster size, mimicking a similar increase of the valence band width between the monolayer and bulk (see Table 1). When comparing angle-resolved gas-phase spectra to angle-resolved spectra of solids or thin films, an angular integration over
10
hν
θ
e- 5p 1/2
13
5p3/2 mj=+- 3/2 mj=+- 1/2
12
11
Xe monolayer
θ = 0O θ = 40O 10
Binding energy (eV) Fig. 1. Xe 5p cluster photoelectron spectra for three different average cluster sizes hNi compared to photoelectron spectra of solid (bulk) Xe [3] (top) and a Xe monolayer [9] (bottom). The cluster spectra were recorded at a photon energy of 20 eV for emission at 54.7° with respect to the light polarization direction. The bulk spectrum was taken at 13.8 eV at 0° with respect to the surface normal, and the monolayer spectra at 21.2 eV for emission at 0° (dashed line) and 40° (solid line). The monolayer and bulk spectra are shifted in binding energy to coincide with the 5p1=2 surface and bulk peak of the cluster, respectively.
both incidence and emission angle has to be taken into account due to the random orientation of the clusters in the gas phase. Hence, the gas-phase spectra correspond more closely to angleintegrated photoelectron spectra of solids. Band dispersion effects [45], as shown in the bottom panel of Fig. 1, result in a broadening of the cluster peaks, which smears out the splitting of the magnetic sublevels, and lead to an asymmetric shape of the cluster peaks with an extended tail towards lower binding energies. In order to account for the asymmetric peak shape due to band dispersion, we have employed asymmetric peak profiles for the least-square fit shown in Fig. 1. However, because of the strong overlap between the different components, especially in the 5p3=2 peak, as well as a possible mixing of the mj = 1/2 and mj = 3/2 bands at certain
Table 1 Total width of the valence band, W VB , and energy splitting DEmj of the 5p3=2 mj = 1/2 and 3/2 bands for monolayer, clusters with different average size hNi, and bulk.
Monolayer [4] Monolayer (calc.) [46] Cluster hNi ¼ 500 Cluster hNi ¼ 2000 Cluster hNi ¼ 8000 Bulk [3] a b
W VB (eV)
DEmj (eV)
2.3a
0.5a 0.44a 0.63 0.65b 0.8b 0.8
2.8 3.1 3.2 3.0
At C point. Averaged over the surface and bulk components.
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emission angles [4], a precise, quantitative analysis of the fit results is extremely difficult without further theoretical guidance. Qualitatively, the spectra in Fig. 1 show an increasing splitting of the magnetic sublevels with cluster size (see Table 1), which can be rationalized by a growing valence-orbital overlap as the cluster sizes increases. The maximum splitting appears in the bulk spectra, where the most overlap occurs. Further support for our interpretation of the breadth of the p3=2 cluster peak as due to splitting into its magnetic sublevel components is provided by a measurement of the photoelectron angular distribution, which has proven to be sensitive to cluster size effects [16]. Fig. 2 shows the photoelectron spectra of different sized Xe clusters measured at two different angles with respect to the light polarization direction together with the angular distribution parameter b calculated across the cluster peaks from the ratio of the two simultaneous measurements [40]. A positive or negative b represents an anisotropic photoelectron angular distribution peaked parallel or perpendicular to the light polarization direction, respectively, while a b close to zero reflects an isotropic distribution [41]. The b spectra in Fig. 2 show that the angular distributions of the cluster photoelectrons are not only considerably more isotropic than those of the atomic photoelectrons, but also vary strongly across the cluster peaks. In particular, b decreases for lower binding energies and approaches zero towards the end of the cluster valence band, suggesting that the angular distributions of electrons from the bulk of the cluster are more isotropic than those from the surface, and that the angular distribution of the mj = 3/2 band is more isotropic than the mj = 1/2 band. In a previous study on variable size Xe clusters [16], we found the photoelectron angular distribution of 4d inner-shell photoelectrons to differ for cluster surface and bulk, and, for the latter, to vary as a function of cluster size towards more isotropic distributions for bigger clusters. Accompanying multiple-scattering calculations traced the origin of this effect to elastic electron scattering that randomized the emission direction of the cluster photoelectrons. While elastic scattering certainly also substantially affects the valence-electron angular distribution, our new and more detailed results suggest that in addition to the final-state scattering effects, initial-state contributions such as the formation of delocalized valence bands may play an important role. A more detailed study investigating the photon energy dependence of the valence-shell angular distribu-
Asymmetry parameter β
Intensity (arb. units)
13
12
11
10
13
tion parameters for Ar, Kr, and Xe clusters and the dependence of elastic scattering on the photoelectron kinetic energy and the electron escape depth will be presented in a forthcoming publication [48]. Inelastic scattering [22], however, does not influence the PAD parameter, since the inelastically scattered electrons do not appear in the main photoline. In order to test our band structure hypothesis on other cluster species, we have measured the valence spectra of Kr and Ar clusters as well as their photoelectron angular distributions, both shown in Fig. 3. Because of the smaller spin-orbit splitting in Kr and Ar compared to Xe, the corresponding cluster peaks are not as clearly separated from one another. Furthermore, a decreased splitting of the magnetic sublevels is evident for the lighter atoms, since the covalent radii of the atoms decreases much faster than the interatomic distances in the cluster and the solid, thus forming less overlap between neighboring atoms [46]. As noted above for Xe, the splitting of the magnetic sublevels in Kr and Ar clusters seems to also lie between the cases of the monolayer [9] and the bulk [7], shown in Fig. 3. While the assignment of surface and bulk components within the Xe cluster peaks was unambiguous based on the comparison with the monolayer and bulk spectra and the different cluster sizes, the situation is less straightforward for Kr and Ar. In the latter case, we tentatively suggest that the first two components of the 3p3=2 may actually correspond to the mj = 1/2 and mj = 3/2 surface peaks and the latter two to the two bulk peaks. In order to unambiguously assign the contributions across the breadth of the unresolved cluster peak, spin-resolved photoemission experiments would be very helpful. Different spin polarizations of the photoelectrons from the different magnetic sublevels [10–12,47], observed by spin-resolved measurements would reveal their position within the cluster peak. In the absence of such measurements, significant evidence is provided by the angular distribution measurements shown in the bottom panels of Fig. 3. As already noted for Xe clusters, we again observe a considerably more isotropic angular distribution of the cluster photoelectrons compared to the atomic ones, with an almost complete isotropy (b ¼ 0) for low binding energies. Especially in the case of Ar, the decrease of the asymmetry parameter is more abrupt, reinforcing our assignment of the higher binding energy part of the 3p3=2 band to the two surface bands, while the second half, below roughly 15 eV binding energy, contains the bulk bands.
12
atomic Xe 5p3/2 hν=20 eV
atomic 5p1/2
10
13
12
Xe hν=20 eV=2000
=500
cluster 5p1/2
11
10
Xe hν=20 eV=8000 surface bulk
cluster 5p3/2
11
mj=+- 1/2 + surface mj= - 3/2 bulk surface bulk
1.5 1.0 0.5 0.0 13
12
11
Binding energy (eV)
10
13
12
11
Binding energy (eV)
10
13
12
11
10
Binding energy (eV)
Fig. 2. (Top) Xe 5p cluster photoelectron spectra for different cluster sizes recorded at 0° (solid line) and 54.7° (dotted line) with respect to the light polarization direction. (Bottom) spectral variation of the angular distribution parameter b computed from the ratio of the spectra above. The solid circles represent the atomic values [42].
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Intensity (arb. units)
Intensity (arb. units)
14.5
4p
14.0
13.5
13.0
12.5
16.0
Kr hν=25 eV=500
1/2
4p mj=+- 1/2
15.5
15.0
14.5
Ar
3p
3/2 hν=26 eV mj=+- 1/2 mj=+- 3/2=250 3p 1/2 surface mj=+ - 1/2 mj=+- 3/2
3/2
bulk
mj=+- 3/2
4p
1/2
4p
monolayer solid (bulk)
3/2
3p
3p
3/2
1/2
1.1
Asymmetry parameter β
1.5
0.4
1.0
0.3 0.2
0.5 0.1 0.0
0.0
-0.1 14.5
14.0 13.5 13.0 Binding energy (eV)
12.5
16.0
15.5
15.0 14.5 Binding energy (eV)
Fig. 3. (Top) Kr 4p and Ar 3p cluster photoelectron spectra measured at 54.7° with a tentative fit of the mj = 1/2 and 3/2 bands for cluster surface (solid lines) and bulk (dotted lines). (Middle) monolayer [9] and bulk [7] spectra at 21.2 eV measured at 40° and 50°, respectively, with respect to the surface normal. (Bottom) spectral variation of the angular distribution parameter b for the cluster spectra; the atomic values are shown as solid circles [42].
4. Conclusions In summary, angle-resolved photoemission measurements have provided strong experimental evidence for the formation of electronic band structure in van der Waals-bound rare-gas clusters. We observe striking spectral similarities between the valence photoemission of clusters of different average sizes with the monolayer and bulk spectra. The valence electrons from the atoms on the cluster surface appear to form a two-dimensional band structure similar to the one observed in rare-gas monolayers, while the electronic structure corresponding to bulk atoms resembles the three-dimensional band structure known from rare-gas solids. As the cluster size increases, the total width of the valence band increases and the electronic structure of the cluster becomes dominated by the band structure of the bulk, undergoing a transition similar to that in rare-gas multilayers [8,9]. Although state-ofthe-art band structure calculations are needed in order to fully explain the spectral shape and angular distribution of the cluster photoemission, experimental investigations of variable size cluster systems such as the ones reported here serve as model systems to elucidate the electronic structure of small solid-state system. These new measurements also provide a motivation as well as an excellent test case for the accuracy of advanced calculations. Acknowledgements We acknowledge E. Kukk for providing the IgorPro macros for multi-peak fitting, and thank K. Horn for helpful discussions concerning the band structure of rare-gas monolayers and solids. We
also thank the staff at the ALS for their assistance during the experiments. The work was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division. D.R. acknowledges support from the Alexander von Humboldt foundation. References [1] K. Jensen, J. Weldon, H. Garcia, A. Zettl, Nano Lett. 7 (2007) 3508. [2] O. Kostko, B. Huber, M. Moseler, B.v. Issendorff, Phys. Rev. Lett. 98 (2007) 043401. [3] N. Schwentner, F.-J. Himpsel, V. Saile, M. Skibowski, W. Steinemann, E.E. Koch, Phys. Rev. Lett. 34 (1975) 528. [4] K. Horn, M. Scheffler, A.M. Bradshaw, Phys. Rev. Lett. 41 (1978) 822. [5] K. Horn, A.M. Bradshaw, Solid State Commun. 30 (1979) 545. [6] K. Jacobi, Y. Hsu, H.H. Rotermund, Surf. Sci. 114 (1982) 683. [7] K. Jacobi, H.H. Rotermund, Surf. Sci. 116 (1982) 435. [8] T. Mandel, G. Kaindl, M. Domke, W. Fischer, W.D. Schneider, Phys. Rev. Lett. 55 (1985) 1638. [9] K. Jacobi, Phys. Rev. B 38 (1988) 5869. [10] G. Schönhense, A. Eyers, U. Friess, F. Schäfer, U. Heinzmann, Phys. Rev. Lett. 54 (1985) 547. [11] G. Schönhense, A. Eyers, U. Heinzmann, Phys. Rev. Lett. 56 (1986) 512. [12] B. Kessler, A. Eyers, K. Horn, N. Müller, B. Schmiedeskamp, G. Schönhense, U. Heinzmann, Phys. Rev. Lett. 59 (1987) 331. [13] O. Björneholm, F. Federmann, F. Fössing, T. Möller, Phys. Rev. Lett. 74 (1995) 3017. [14] O. Björneholm, F. Federmann, F. Fössing, T. Möller, P. Stampfli, J. Chem. Phys. 104 (1996) 1846. [15] M. Tchaplyguine et al., J. Chem. Phys. 120 (2004) 345. [16] D. Rolles et al., Phys. Rev. A 75 (2007) 031201(R). [17] P.M. Dehmer, J.L. Dehmer, J. Chem. Phys. 67 (1977) 1774. [18] P.M. Dehmer, J.L. Dehmer, J. Chem. Phys. 68 (1978) 3462. [19] P.M. Dehmer, J.L. Dehmer, J. Chem. Phys. 69 (1978) 125. [20] F. Carnovale, J.B. Peel, R.G. Rothwell, J. Valldorf, P.J. Kuntz, J. Chem. Phys. 90 (1989) 1452.
152
D. Rolles et al. / Chemical Physics Letters 468 (2009) 148–152
[21] F. Carnovale, J.B. Peel, R.G. Rothwell, J. Chem. Phys. 95 (1991) 1473. [22] U. Hergenhahn, A. Kolmakov, M. Riedler, A.R.B. de Castro, O. Löfken, T. Möller, Chem. Phys. Lett. 351 (2002) 235. [23] R. Feifel et al., Eur. Phys. J. D 30 (2004) 343. [24] S. Joshi, S. Barth, S. Marburger, V. Ulrich, U. Hergenhahn, Phys. Rev. B 73 (2006) 235404. [25] J.D. Bozek, B.S. Rude, A.L.D. Kilcoyne, AIP Conf. Proc. 811 (2006) 54. [26] M. Lundwall et al., J. Chem. Phys. 125 (2006) 014305. [27] J. Stapelfeld, J. Wörmer, G. Zimmerer, T. Möller, Z. Phys. D. 12 (1989) 435. [28] J. Stapelfeld, J. Wörmer, T. Möller, Phys. Rev. Lett. 62 (1989) 98. [29] J. Wörmer, V. Guzielski, J. Stapelfeld, T. Möller, Chem. Phys. Lett. 159 (1989) 321. [30] J. Wörmer, V. Guzielski, J. Stapelfeld, G. Zimmerer, T. Möller, Phys. Scr. 41 (1990) 490. [31] J. Wörmer, M. Joppien, G. Zimmerer, T. Möller, Phys. Rev. Lett. 67 (1991) 2053. [32] R. Müller, M. Joppien, T. Möller, Z. Phys. D 26 (1993) 370. [33] J. Wörmer, R. Karnbach, M. Joppien, T. Möller, J. Chem. Phys. 104 (1996) 8269. [34] T. Laarmann, K. von Haeften, A. Kanaev, H. Wabnitz, T. Möller, Phys. Rev. B 66 (2002) 205407.
[35] S.D. Kevan (Ed.), Angle-Resolved Photoemission – Theory and Current Applications, Elsevier, Amsterdam, 1992. [36] A. Damascelli, Phys. Scr. T 109 (2004) 61. [37] O.F. Hagena, Z. Phys. D 4 (1987) 291. [38] O.F. Hagena, Rev. Sci. Instrum. 63 (1992) 2374. [39] U. Buck, R. Krohne, J. Chem. Phys. 105 (1996) 5408. [40] N. Berrah, B. Langer, A.A. Wills, E. Kukk, J.D. Bozek, A. Farhat, T.W. Gorczyca, J. Electron Spectrosc. Relat. Phenom. 101–103 (1999) 1. [41] J. Cooper, R.N. Zare, J. Chem. Phys. 48 (1968) 942. [42] K.-N. Huang, W.R. Johnson, K.T. Cheng, At. Data Nucl. Data Tables 26 (1981) 33. [43] B.J. Waclawski, J.F. Herbst, Phys. Rev. Lett. 35 (1975) 1594. [44] P.R. Antoniewicz, Phys. Rev. Lett. 38 (1977) 374. [45] M. Scheffler, K. Horn, A.M. Bradshaw, K. Kambe, Surf. Sci. 80 (1979) 69. [46] K. Hermann, J. Noffke, K. Horn, Phys. Rev. B 22 (1980) 1022. [47] B. Vogt, B. Kessler, N. Müller, G. Schönhense, B. Schmiedeskamp, U. Heinzmann, Phys. Rev. Lett. 67 (1991) 1318. [48] H. Zhang, D. Rolles, N. Berrah, et al., in preparation.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Emergence of valence band structure in rare-gas clusters D. Rolles a,b,c,*, H. Zhang a, Z.D. Pešic´ a,b, J.D. Bozek b,d, N. Berrah a a
Physics Department, Western Michigan University, Kalamazoo, MI 49008, USA Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Max Planck Advanced Study Group, Center for Free Electron Laser Science, 22761 Hamburg, Germany d Linac Coherent Light Source, Stanford Linear Accelerator Center, Menlo Park, CA 94025, USA b c
a r t i c l e
i n f o
Article history: Received 18 September 2008 In final form 4 December 2008 Available online 11 December 2008
a b s t r a c t The formation of electronic band structure by the valence-shell of Ar, Kr, and Xe clusters was studied for various cluster sizes using angle-resolved photoelectron spectroscopy. Different widths of the fine-structure components in the cluster spectra are attributed to a splitting of the outermost p3=2 levels due to valence-orbital overlap between neighboring atoms. Photoelectron angular distributions from the cluster differ from the atomic cases and vary substantially for different bands. The evolution of the electronic structure with increasing cluster size emulates the changes of the valence band structure in the transition from a condensed-phase monolayer to the bulk. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction Nanotechnological devices are reaching the size of few or even single molecules [1], motivating an increased need to study the electronic structure of mesoscopic systems that lie in between the traditional fields of atomic, molecular, and condensed matter physics, material science, and chemistry. Understanding the emergence of typical solid-state properties such as conductivity and magnetism on simple model systems is a crucial first step towards unraveling the properties and functionality of more complex systems with practical applications in material sciences and nanoengineering. In this sense, clusters are often touted as ‘bridging the gap’ between atoms and solids, and seem a perfect candidate for a ‘bottom-up’ approach, starting from a single atom and increasing their size until solid-state behavior is reached asymptotically [2]. Due to the simple control over their size or, more precisely, at least their average size, which can be varied from a single atom to several thousands or even millions of atoms, rare-gas clusters have received considerable attention. In the condensed-phase, rare gases are large-band-gap insulators that are well-studied by photoelectron spectroscopy [3–12]. Rare-gas clusters, as neutral species, are produced by supersonic expansion with a broad distribution of sizes around an average cluster size. Nevertheless, clear size effects have been observed in their photoelectron spectra, mostly for core levels, where a clear surface/bulk-splitting is the dominant spectral feature since these electrons are strongly localized [13–16]. Since atoms in rare-gas clusters are only weakly * Corresponding author. Address: Max Planck Advanced Study Group, Center for Free Electron Laser Science, 22761 Hamburg, Germany. E-mail address: [email protected] (D. Rolles). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.12.015
bound by van der Waals forces, the role of overlap and delocalization of the valence-orbitals is less established. The first valenceshell photoelectron spectroscopy of rare-gas clusters was performed on Ar, Kr, and Xe dimers [17–19], and later on larger clusters [20,21] using VUV-radiation from a He lamp. More recently, synchrotron radiation was used to investigate valence photoemission from pure [16,22–25] and mixed rare-gas clusters [26]. Several of these studies noted the different widths and shapes of the two fine-structure components in the cluster valence spectrum, but a consistent interpretation has not yet emerged. In the first study of the valence photoelectron spectra of different size rare-gas clusters [20,21], the peak shapes and widths were attributed to formation of small ionic cores (‘chromophores’) within the cluster. Later studies [16,23] noted a similarity of the cluster valence spectra to the band structure of rare-gas solids [3] and monolayers [4], but no clear experimental evidence of this interpretation has been provided thus far. Extensive investigations of band absorption and fluorescence in rare-gas clusters also stressed the similarities to solid-state band structure, but mostly focused on the evolution of surface and bulk excitons in the cluster [27–34]. In this Letter, we report an investigation of the photoemission of the outermost valence-orbitals of Ar, Kr and Xe clusters for different average cluster sizes using angle-resolved photoelectron spectroscopy (ARPES) to develop a clear understanding of the cluster valence spectra and the possible influence of band structure formation. ARPES is a successful tool used to study the band structure of surfaces, solids and interfaces [35,36], and hence well suited to provide specific insights into valence band structure effects in clusters. Our experimental data reveals the formation and evolution of the valence band for increasing average cluster size and establishes, for the first time, a clear link between the band structure of rare-gas clusters, monolayers and the bulk solid.
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D. Rolles et al. / Chemical Physics Letters 468 (2009) 148–152
2. Experimental method
13
12
11
5p1/2
The experiments were performed on beamline 10.0.1 of the Advanced Light Source at Lawrence Berkeley National Laboratory. The clusters were produced by supersonic expansion of rare gases through a liquid-nitrogen cooled nozzle [16]. The average cluster size in the beam was varied by changing the expansion pressure and the nozzle temperature according to common scaling laws based on the C formalism [37–39]. The skimmed cluster jet was crossed with tunable, linearly polarized synchrotron radiation, and the photoelectrons were detected in two time-of-flight (TOF) analyzers mounted at 0° and 54.7° with respect to the polarization vector in the plane perpendicular to the light propagation direction [16,40]. Simultaneous measurement of the photoelectron intensity at both angles allowed a determination of the asymmetry parameter b, which characterizes the photoelectron angular distribution of randomly oriented targets in the gas phase [41]. Spectrometer efficiencies and energy scales were calibrated using the atomic binding energies and asymmetry parameters [42] from the literature.
atomic 5p1/2
5p3/2
cluster 5p1/2
bulk
Intensity (arb. units)
Xe solid (bulk)
atomic 5p3/2
surface
cluster 5p3/2
Xe cluster
bulk bulk surface surface mj=+- 1/2 mj=+- 3/2
Xe cluster
Xe cluster
3. Results and discussion Fig. 1 shows typical valence-shell photoelectron spectra of xenon clusters for different average cluster sizes hNi compared to the photoelectron spectra of solid (bulk) Xe (top) [3] and a Xe monolayer (bottom) [9]. The two strong and narrow peaks in the cluster spectra are due to contributions from uncondensed Xe atoms in the beam, while the broader features correspond to photoelectrons from the clusters. For hNi ¼ 500, the cluster peaks are remarkably similar to the monolayer spectra, whereas the appearance of new contributions, reminiscent of the Xe bulk spectrum, is evident for larger cluster sizes. While it has been argued previously that a surface/bulk-splitting was not visible for cluster valenceelectrons because of their delocalization [16,23], our spectra clearly show a splitting of the 5p1=2 fine-structure component and a variation of the intensities for increasing cluster size, demonstrating that such splitting does indeed occur. Furthermore, an increased width of the 5p3=2 peak as compared to the 5p1=2 peak can clearly be observed for all cluster sizes, suggesting an additional splitting of this peak related to band structure formation similar to the case of the condensed-phase spectra. When first observed in the late 1970s, the origin of the splitting of the p3=2 level in rare-gas monolayers was controversial [4,43,44]. However, a bounty of subsequent studies [9–11,45–47] confirmed the initial interpretation that the p3=2 level was split into the magnetic sublevels mj = 1/2 and mj = 3/2 due to lateral interaction between neighboring Xe atoms [4], leading to the formation of a twodimensional band structure [45,46]. Systematic studies of monoand multilayers [8,9] also established the gradual transition into the three-dimensional band structure of the bulk solid with a splitting of the p3=2 -derived bands in the crystal field [3,5]. Based on our observations, we hence conclude that the 5p3=2 cluster peak is split into two components consisting of the magnetic sublevels mj = 1/ 2 and mj = 3/2 due to symmetry-lowering of the cluster system by valence-orbital overlap of neighboring cluster atoms. In addition, each cluster peak is further split into a surface and bulk component, leading to a total of two components in the 5p1=2 cluster peak and four components in the 5p3=2 cluster peak, which we have separated by a least-square fit as shown in Fig. 1. Quantitative analysis confirms that the total width of the valence band increases with cluster size, mimicking a similar increase of the valence band width between the monolayer and bulk (see Table 1). When comparing angle-resolved gas-phase spectra to angle-resolved spectra of solids or thin films, an angular integration over
10
hν
θ
e- 5p 1/2
13
5p3/2 mj=+- 3/2 mj=+- 1/2
12
11
Xe monolayer
θ = 0O θ = 40O 10
Binding energy (eV) Fig. 1. Xe 5p cluster photoelectron spectra for three different average cluster sizes hNi compared to photoelectron spectra of solid (bulk) Xe [3] (top) and a Xe monolayer [9] (bottom). The cluster spectra were recorded at a photon energy of 20 eV for emission at 54.7° with respect to the light polarization direction. The bulk spectrum was taken at 13.8 eV at 0° with respect to the surface normal, and the monolayer spectra at 21.2 eV for emission at 0° (dashed line) and 40° (solid line). The monolayer and bulk spectra are shifted in binding energy to coincide with the 5p1=2 surface and bulk peak of the cluster, respectively.
both incidence and emission angle has to be taken into account due to the random orientation of the clusters in the gas phase. Hence, the gas-phase spectra correspond more closely to angleintegrated photoelectron spectra of solids. Band dispersion effects [45], as shown in the bottom panel of Fig. 1, result in a broadening of the cluster peaks, which smears out the splitting of the magnetic sublevels, and lead to an asymmetric shape of the cluster peaks with an extended tail towards lower binding energies. In order to account for the asymmetric peak shape due to band dispersion, we have employed asymmetric peak profiles for the least-square fit shown in Fig. 1. However, because of the strong overlap between the different components, especially in the 5p3=2 peak, as well as a possible mixing of the mj = 1/2 and mj = 3/2 bands at certain
Table 1 Total width of the valence band, W VB , and energy splitting DEmj of the 5p3=2 mj = 1/2 and 3/2 bands for monolayer, clusters with different average size hNi, and bulk.
Monolayer [4] Monolayer (calc.) [46] Cluster hNi ¼ 500 Cluster hNi ¼ 2000 Cluster hNi ¼ 8000 Bulk [3] a b
W VB (eV)
DEmj (eV)
2.3a
0.5a 0.44a 0.63 0.65b 0.8b 0.8
2.8 3.1 3.2 3.0
At C point. Averaged over the surface and bulk components.
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emission angles [4], a precise, quantitative analysis of the fit results is extremely difficult without further theoretical guidance. Qualitatively, the spectra in Fig. 1 show an increasing splitting of the magnetic sublevels with cluster size (see Table 1), which can be rationalized by a growing valence-orbital overlap as the cluster sizes increases. The maximum splitting appears in the bulk spectra, where the most overlap occurs. Further support for our interpretation of the breadth of the p3=2 cluster peak as due to splitting into its magnetic sublevel components is provided by a measurement of the photoelectron angular distribution, which has proven to be sensitive to cluster size effects [16]. Fig. 2 shows the photoelectron spectra of different sized Xe clusters measured at two different angles with respect to the light polarization direction together with the angular distribution parameter b calculated across the cluster peaks from the ratio of the two simultaneous measurements [40]. A positive or negative b represents an anisotropic photoelectron angular distribution peaked parallel or perpendicular to the light polarization direction, respectively, while a b close to zero reflects an isotropic distribution [41]. The b spectra in Fig. 2 show that the angular distributions of the cluster photoelectrons are not only considerably more isotropic than those of the atomic photoelectrons, but also vary strongly across the cluster peaks. In particular, b decreases for lower binding energies and approaches zero towards the end of the cluster valence band, suggesting that the angular distributions of electrons from the bulk of the cluster are more isotropic than those from the surface, and that the angular distribution of the mj = 3/2 band is more isotropic than the mj = 1/2 band. In a previous study on variable size Xe clusters [16], we found the photoelectron angular distribution of 4d inner-shell photoelectrons to differ for cluster surface and bulk, and, for the latter, to vary as a function of cluster size towards more isotropic distributions for bigger clusters. Accompanying multiple-scattering calculations traced the origin of this effect to elastic electron scattering that randomized the emission direction of the cluster photoelectrons. While elastic scattering certainly also substantially affects the valence-electron angular distribution, our new and more detailed results suggest that in addition to the final-state scattering effects, initial-state contributions such as the formation of delocalized valence bands may play an important role. A more detailed study investigating the photon energy dependence of the valence-shell angular distribu-
Asymmetry parameter β
Intensity (arb. units)
13
12
11
10
13
tion parameters for Ar, Kr, and Xe clusters and the dependence of elastic scattering on the photoelectron kinetic energy and the electron escape depth will be presented in a forthcoming publication [48]. Inelastic scattering [22], however, does not influence the PAD parameter, since the inelastically scattered electrons do not appear in the main photoline. In order to test our band structure hypothesis on other cluster species, we have measured the valence spectra of Kr and Ar clusters as well as their photoelectron angular distributions, both shown in Fig. 3. Because of the smaller spin-orbit splitting in Kr and Ar compared to Xe, the corresponding cluster peaks are not as clearly separated from one another. Furthermore, a decreased splitting of the magnetic sublevels is evident for the lighter atoms, since the covalent radii of the atoms decreases much faster than the interatomic distances in the cluster and the solid, thus forming less overlap between neighboring atoms [46]. As noted above for Xe, the splitting of the magnetic sublevels in Kr and Ar clusters seems to also lie between the cases of the monolayer [9] and the bulk [7], shown in Fig. 3. While the assignment of surface and bulk components within the Xe cluster peaks was unambiguous based on the comparison with the monolayer and bulk spectra and the different cluster sizes, the situation is less straightforward for Kr and Ar. In the latter case, we tentatively suggest that the first two components of the 3p3=2 may actually correspond to the mj = 1/2 and mj = 3/2 surface peaks and the latter two to the two bulk peaks. In order to unambiguously assign the contributions across the breadth of the unresolved cluster peak, spin-resolved photoemission experiments would be very helpful. Different spin polarizations of the photoelectrons from the different magnetic sublevels [10–12,47], observed by spin-resolved measurements would reveal their position within the cluster peak. In the absence of such measurements, significant evidence is provided by the angular distribution measurements shown in the bottom panels of Fig. 3. As already noted for Xe clusters, we again observe a considerably more isotropic angular distribution of the cluster photoelectrons compared to the atomic ones, with an almost complete isotropy (b ¼ 0) for low binding energies. Especially in the case of Ar, the decrease of the asymmetry parameter is more abrupt, reinforcing our assignment of the higher binding energy part of the 3p3=2 band to the two surface bands, while the second half, below roughly 15 eV binding energy, contains the bulk bands.
12
atomic Xe 5p3/2 hν=20 eV
atomic 5p1/2
10
13
12
Xe hν=20 eV
cluster 5p1/2
11
10
Xe hν=20 eV
cluster 5p3/2
11
mj=+- 1/2 + surface mj= - 3/2 bulk surface bulk
1.5 1.0 0.5 0.0 13
12
11
Binding energy (eV)
10
13
12
11
Binding energy (eV)
10
13
12
11
10
Binding energy (eV)
Fig. 2. (Top) Xe 5p cluster photoelectron spectra for different cluster sizes recorded at 0° (solid line) and 54.7° (dotted line) with respect to the light polarization direction. (Bottom) spectral variation of the angular distribution parameter b computed from the ratio of the spectra above. The solid circles represent the atomic values [42].
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Intensity (arb. units)
Intensity (arb. units)
14.5
4p
14.0
13.5
13.0
12.5
16.0
Kr hν=25 eV
1/2
4p mj=+- 1/2
15.5
15.0
14.5
Ar
3p
3/2 hν=26 eV mj=+- 1/2 mj=+- 3/2
3/2
bulk
mj=+- 3/2
4p
1/2
4p
monolayer solid (bulk)
3/2
3p
3p
3/2
1/2
1.1
Asymmetry parameter β
1.5
0.4
1.0
0.3 0.2
0.5 0.1 0.0
0.0
-0.1 14.5
14.0 13.5 13.0 Binding energy (eV)
12.5
16.0
15.5
15.0 14.5 Binding energy (eV)
Fig. 3. (Top) Kr 4p and Ar 3p cluster photoelectron spectra measured at 54.7° with a tentative fit of the mj = 1/2 and 3/2 bands for cluster surface (solid lines) and bulk (dotted lines). (Middle) monolayer [9] and bulk [7] spectra at 21.2 eV measured at 40° and 50°, respectively, with respect to the surface normal. (Bottom) spectral variation of the angular distribution parameter b for the cluster spectra; the atomic values are shown as solid circles [42].
4. Conclusions In summary, angle-resolved photoemission measurements have provided strong experimental evidence for the formation of electronic band structure in van der Waals-bound rare-gas clusters. We observe striking spectral similarities between the valence photoemission of clusters of different average sizes with the monolayer and bulk spectra. The valence electrons from the atoms on the cluster surface appear to form a two-dimensional band structure similar to the one observed in rare-gas monolayers, while the electronic structure corresponding to bulk atoms resembles the three-dimensional band structure known from rare-gas solids. As the cluster size increases, the total width of the valence band increases and the electronic structure of the cluster becomes dominated by the band structure of the bulk, undergoing a transition similar to that in rare-gas multilayers [8,9]. Although state-ofthe-art band structure calculations are needed in order to fully explain the spectral shape and angular distribution of the cluster photoemission, experimental investigations of variable size cluster systems such as the ones reported here serve as model systems to elucidate the electronic structure of small solid-state system. These new measurements also provide a motivation as well as an excellent test case for the accuracy of advanced calculations. Acknowledgements We acknowledge E. Kukk for providing the IgorPro macros for multi-peak fitting, and thank K. Horn for helpful discussions concerning the band structure of rare-gas monolayers and solids. We
also thank the staff at the ALS for their assistance during the experiments. The work was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division. D.R. acknowledges support from the Alexander von Humboldt foundation. References [1] K. Jensen, J. Weldon, H. Garcia, A. Zettl, Nano Lett. 7 (2007) 3508. [2] O. Kostko, B. Huber, M. Moseler, B.v. Issendorff, Phys. Rev. Lett. 98 (2007) 043401. [3] N. Schwentner, F.-J. Himpsel, V. Saile, M. Skibowski, W. Steinemann, E.E. Koch, Phys. Rev. Lett. 34 (1975) 528. [4] K. Horn, M. Scheffler, A.M. Bradshaw, Phys. Rev. Lett. 41 (1978) 822. [5] K. Horn, A.M. Bradshaw, Solid State Commun. 30 (1979) 545. [6] K. Jacobi, Y. Hsu, H.H. Rotermund, Surf. Sci. 114 (1982) 683. [7] K. Jacobi, H.H. Rotermund, Surf. Sci. 116 (1982) 435. [8] T. Mandel, G. Kaindl, M. Domke, W. Fischer, W.D. Schneider, Phys. Rev. Lett. 55 (1985) 1638. [9] K. Jacobi, Phys. Rev. B 38 (1988) 5869. [10] G. Schönhense, A. Eyers, U. Friess, F. Schäfer, U. Heinzmann, Phys. Rev. Lett. 54 (1985) 547. [11] G. Schönhense, A. Eyers, U. Heinzmann, Phys. Rev. Lett. 56 (1986) 512. [12] B. Kessler, A. Eyers, K. Horn, N. Müller, B. Schmiedeskamp, G. Schönhense, U. Heinzmann, Phys. Rev. Lett. 59 (1987) 331. [13] O. Björneholm, F. Federmann, F. Fössing, T. Möller, Phys. Rev. Lett. 74 (1995) 3017. [14] O. Björneholm, F. Federmann, F. Fössing, T. Möller, P. Stampfli, J. Chem. Phys. 104 (1996) 1846. [15] M. Tchaplyguine et al., J. Chem. Phys. 120 (2004) 345. [16] D. Rolles et al., Phys. Rev. A 75 (2007) 031201(R). [17] P.M. Dehmer, J.L. Dehmer, J. Chem. Phys. 67 (1977) 1774. [18] P.M. Dehmer, J.L. Dehmer, J. Chem. Phys. 68 (1978) 3462. [19] P.M. Dehmer, J.L. Dehmer, J. Chem. Phys. 69 (1978) 125. [20] F. Carnovale, J.B. Peel, R.G. Rothwell, J. Valldorf, P.J. Kuntz, J. Chem. Phys. 90 (1989) 1452.
152
D. Rolles et al. / Chemical Physics Letters 468 (2009) 148–152
[21] F. Carnovale, J.B. Peel, R.G. Rothwell, J. Chem. Phys. 95 (1991) 1473. [22] U. Hergenhahn, A. Kolmakov, M. Riedler, A.R.B. de Castro, O. Löfken, T. Möller, Chem. Phys. Lett. 351 (2002) 235. [23] R. Feifel et al., Eur. Phys. J. D 30 (2004) 343. [24] S. Joshi, S. Barth, S. Marburger, V. Ulrich, U. Hergenhahn, Phys. Rev. B 73 (2006) 235404. [25] J.D. Bozek, B.S. Rude, A.L.D. Kilcoyne, AIP Conf. Proc. 811 (2006) 54. [26] M. Lundwall et al., J. Chem. Phys. 125 (2006) 014305. [27] J. Stapelfeld, J. Wörmer, G. Zimmerer, T. Möller, Z. Phys. D. 12 (1989) 435. [28] J. Stapelfeld, J. Wörmer, T. Möller, Phys. Rev. Lett. 62 (1989) 98. [29] J. Wörmer, V. Guzielski, J. Stapelfeld, T. Möller, Chem. Phys. Lett. 159 (1989) 321. [30] J. Wörmer, V. Guzielski, J. Stapelfeld, G. Zimmerer, T. Möller, Phys. Scr. 41 (1990) 490. [31] J. Wörmer, M. Joppien, G. Zimmerer, T. Möller, Phys. Rev. Lett. 67 (1991) 2053. [32] R. Müller, M. Joppien, T. Möller, Z. Phys. D 26 (1993) 370. [33] J. Wörmer, R. Karnbach, M. Joppien, T. Möller, J. Chem. Phys. 104 (1996) 8269. [34] T. Laarmann, K. von Haeften, A. Kanaev, H. Wabnitz, T. Möller, Phys. Rev. B 66 (2002) 205407.
[35] S.D. Kevan (Ed.), Angle-Resolved Photoemission – Theory and Current Applications, Elsevier, Amsterdam, 1992. [36] A. Damascelli, Phys. Scr. T 109 (2004) 61. [37] O.F. Hagena, Z. Phys. D 4 (1987) 291. [38] O.F. Hagena, Rev. Sci. Instrum. 63 (1992) 2374. [39] U. Buck, R. Krohne, J. Chem. Phys. 105 (1996) 5408. [40] N. Berrah, B. Langer, A.A. Wills, E. Kukk, J.D. Bozek, A. Farhat, T.W. Gorczyca, J. Electron Spectrosc. Relat. Phenom. 101–103 (1999) 1. [41] J. Cooper, R.N. Zare, J. Chem. Phys. 48 (1968) 942. [42] K.-N. Huang, W.R. Johnson, K.T. Cheng, At. Data Nucl. Data Tables 26 (1981) 33. [43] B.J. Waclawski, J.F. Herbst, Phys. Rev. Lett. 35 (1975) 1594. [44] P.R. Antoniewicz, Phys. Rev. Lett. 38 (1977) 374. [45] M. Scheffler, K. Horn, A.M. Bradshaw, K. Kambe, Surf. Sci. 80 (1979) 69. [46] K. Hermann, J. Noffke, K. Horn, Phys. Rev. B 22 (1980) 1022. [47] B. Vogt, B. Kessler, N. Müller, G. Schönhense, B. Schmiedeskamp, U. Heinzmann, Phys. Rev. Lett. 67 (1991) 1318. [48] H. Zhang, D. Rolles, N. Berrah, et al., in preparation.