Modification of Surface States in Ultrathin Films via Hybridization with ...

3 downloads 0 Views 2MB Size Report
Jan 24, 2006 - Frederick Seitz Materials Research Laboratory, University of Illinois at ... pecially those conducted by K. Horn's group, have re- vealed unusual ...
PRL 96, 036802 (2006)

PHYSICAL REVIEW LETTERS

week ending 27 JANUARY 2006

Modification of Surface States in Ultrathin Films via Hybridization with the Substrate: A Study of Ag on Ge S.-J. Tang, T. Miller, and T.-C. Chiang Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080, USA Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, 104 South Goodwin Avenue, Urbana, Illinois 61801-2902, USA (Received 18 July 2005; published 24 January 2006) The Shockley surface state of Ag(111) develops unusual band dispersion relations for Ag films of decreasing thicknesses on Ge(111), as observed by angle-resolved photoemission. Its parabolic dispersion in the thick-film limit shifts toward higher binding energies and splits into multiple bands with dispersions that reflect the valence band structure of Ge including the heavy-hole, light-hole, and split-off bands. The results are explained in terms of a hybridization interaction between the Ag surface state and the Ge substrate states. DOI: 10.1103/PhysRevLett.96.036802

PACS numbers: 73.21.Fg, 68.65.Fg, 79.60.Dp

Thin films can exhibit an electronic structure markedly different from the bulk counterpart. This is a research area of intense interest, and much recent work has focused on quantum-size effects related to the confinement of electrons in films forming standing-wave-like quantum-well states [1–3]. Such effects can lead to dramatic atomiclayer-by-atomic-layer variations in physical properties, such as the surface energy [4], thermal stability [5], work function [6], adsorption [7], superconducting transition temperature [8,9], etc. In this work, we explore a less familiar, but equally important subject matter, namely, the interaction of a surface state in a thin film with the substrate [10 –14]. Unlike quantum-well states which permeate throughout a film, the wave function of a surface state generally decays rapidly and exponentially away from the surface and thus remains largely unchanged in going from a semi-infinite crystal to films with thicknesses as small as 10 atomic layers. However, when the film thickness gets smaller yet, the tail of the surface-state wave function can reach and interact with the substrate. As shown by this angle-resolved photoemission study of a Shockley surface state in Ag(111) films grown on Ge(111), the result is a richly structured spectral weight function. The main effect is a hybridization interaction between the Ag surface state and the Ge substrate states, and the resulting complex dispersion relations reflect the valence band structure of Ge including the heavy-hole, light-hole, and split-off bands. A detailed analysis of this observation clarifies the basic electronic structure of ultrathin film systems, and suggests a powerful method for probing the band structure of solids. Accurate band mapping for arbitrary three-dimensional solids remains a challenge to this date, and the present work adds a valuable tool for this purpose. Our analysis is aided by the use of atomically uniform films [1,15]. As the results are sensitive to film thickness, a significant roughness can smear out details. This problem has undoubtedly affected some of the earlier studies [10 –12]. Previous work 0031-9007=06=96(3)=036802(4)$23.00

on surface states of thin films has generally focused on energy shifts as an indication of the interaction between the surface and substrate electronic structure [10 –13]. More recent studies of quantum-well states and resonances, especially those conducted by K. Horn’s group, have revealed unusual dispersion features that can be related to the substrate band structure [15–17]. In the present study, atomic-layer-resolved spectra reveal that the surface-state band actually splits as the film thickness decreases, and the resulting complex dispersion relations yield a wealth of information largely unexpected based on existing studies of thin films. Our experiment was performed at the Synchrotron Radiation Center, University of Wisconsin-Madison, using 50 eV photons. Dispersion relations were measured along the  K direction of the Ag(111) films. Photoelectron spectra were recorded as two-dimensional images with the energy and the polar emission angle  as two independent variables. Each image spans a range of  ’ 10 . The sample was rotated relative to the analyzer in steps of 5 to create a set of overlapping images, which were combined to create a wider angular span. A clean Ge(111)-c2  8 surface was prepared by sputtering at a substrate temperature of 500  C followed by annealing at 600  C. Ag was evaporated onto the Ge substrate maintained at 50 K. Subsequently, the sample was annealed at 300 K and cooled back to 50 K for the photoemission measurement. Additional Ag, if needed, was added by deposition at 50 K followed by annealing at 300 K. The resulting Ag films, with bulklike lattice constants, were oriented along 111 with the  K direction parallel to the same in the substrate. The large lattice mismatch between Ag and Ge resulted in an incommensurate interface and little strain in the substrate [18]. The absolute film thickness was determined by atomic layer counting [1,15]. Figure 1 shows photoemission results taken from Ag films of thicknesses N  20, 12, 9, 8, 7, and 6 monolayers (ML). The energy reference is the Fermi level. All of these

036802-1

© 2006 The American Physical Society

PHYSICAL REVIEW LETTERS

PRL 96, 036802 (2006) 0

Energy (eV)

SS Q1 Q2 … 8 ML 0

20 ML

-1

-1

-2

-2

-3

-3

0

-10ML -5 12

0

5

10 7-10 ML -5 0

-1

-1

-2

-2

-3

-3

0

9-10 ML -5

0

5

10 6-10 ML -5 0

-1

-1

-2

-2

-3

-3 -10

week ending 27 JANUARY 2006

-5

0

5 10 -10 -5 Emission Angle (deg)

0

5

10

0

5

10

0

5

10

FIG. 1 (color online). Angle-resolved photoemission data presented as gray scale images as a function of energy and emission angle for 20, 12, 9, 8, 7, and 6 ML of Ag on Ge(111). The labels SS and Q1, Q2, . . . indicate a surface-state band and quantumwell subbands.

FIG. 2 (color online). (a) Close-up of angle-resolved photoemission data for 6 ML Ag on Ge(111) with the horizontal axis converted to k. (b) The same after intensity renormalization to show details. (c) A model fit for the region between the two vertical lines in (b).

films are atomically uniform; a slight increase of coverage from integer N results in additional emission features corresponding to the thickness N  1. At 20 ML, the image shows a Shockley surface-state band, labeled SS, and several quantum-well subbands, labeled Q1, Q2, etc. All of these exhibit approximately parabolic dispersion relations. The SS band is mostly unoccupied, and only a small portion near its band bottom is visible by photoemission. The results are very similar to what have been reported for bulk single-crystal Ag(111) [19], suggesting that the decay length of the surface state is much shorter than 20 ML [10,11]. As reported in prior studies, the quantum-well subbands exhibit subtle ‘‘kinks’’ as they cross the Ge band edges [15–17]. Figure 1 shows that, as the film thickness decreases, the SS band shifts downward. A greater portion of its dispersion becomes visible. Simultaneously, the quantum-well subbands move apart and away from the Fermi level due to a changing quantization condition. As the SS band shifts downward, it develops complex features, and this is most evident in the 6 ML case. The portion of the image near the Fermi level, with the horizontal axis converted to in-plane momentum, k, is enlarged and shown in Fig. 2(a) for the 6 ML case. The central portion of the image shows three concave bands, which bear no resemblance to the original Ag surface band, but rather correspond well to the bulk Ge

valence bands along the 110 direction (-K-X line in the Brillouin zone) [20 –22]. Portions of the convex surfacestate band are seen at larger k. Some of the emission features in Fig. 2(a) are weak and hard to see, but become apparent if the image intensity is amplified (at the expense of saturation in other areas). Figure 2(b) is the same data processed for easier visual analysis. First, the image, asymmetric about k  0 due to geometric effects, is symmetrized. Next, the image is normalized such that its average intensity over k is the same for all energies below the Fermi level. The appearance of the normalized image suggests that the surfacestate band ‘‘disappears’’ as it approaches the Ge bands from larger k and transfers its spectral weight to features reflecting the Ge bulk band edges. The two vertical lines in Fig. 2(b) indicate a region where the spectral weight is Gelike. Figure 2(c) is a fit to Fig. 2(b) within this region. The fit is based on the following considerations. The electronic states in Ag are characterized by a Bloch wave vector k. The component along the surface normal, k? , is given by the Bohr-Sommerfeld quantization rule 2k? Nt    2n;

(1)

for the quantum-well states, where t is the monolayer

036802-2

PRL 96, 036802 (2006)

thickness,  is the boundary phase shift, and n is a quantum number [1]. For the surface state,  (2) k?  iq: t

Energy (eV)

0.0

This is a complex quantity, and the imaginary part is related to the decay length of the surface state [10]. For a semi-infinite solid, q, as well as the energy of the surface state, is uniquely determined by the boundary condition that the state must decay into the bulk. Depending on the coordinate system, the imaginary part of k? is either iq or iq, but not both. For a thin film, however, the interface presents another boundary, and states with iq and iq are both allowed. The result is a continuum of surface states, S q or S E, with a smooth spectral weight distribution within the substrate continuum. By contrast, quantum-well states or resonances give rise to periodic structures in their spectral weight as a function of E due to interference effects governed by Eq. (1). Such periodic variations and interference effects are absent for the surface state because the real part of the surface-state wave vector is a fixed number, as given by Eq. (2). Within the substrate continuum, the wave function of the system, E, involves hybridization of the Ag surface state and the Ge states. The photoemission intensity is given by IE / jh

S Ej

Eij2 gE  jMj2 gE;

(3)

where the matrix element M is expected to be a smooth function as explained above. The function g is the density of states of the system, and is given by gE 

3 X

week ending 27 JANUARY 2006

PHYSICAL REVIEW LETTERS

A p i ; E Ei E E i i1

(4)

where  is the unit step function, and each Ai is a constant. The summation is over the three Ge band edges at Ei k within the energy range of interest. The corresponding bulk bands are commonly referred to as the heavy-hole (HH), light-hole (LH), and split-off (SO) bands [23]. Equations (3) and (4), with the addition of a smooth background function and lifetime and instrumental broadenings, are used to fit the data. Additionally, a broadening in k is found necessary for a good fit, which accounts for scattering caused by lattice mismatch and possibly other imperfections. The quantities jMj2 , Ai , and Ei are taken to be low-order smooth functions of k. The best-fit intensity pattern, shown in Fig. 2(c), is dominated by the density of states. At each k, there is a peak at each band edge. Thus, the image is essentially a map of the dispersion relations of the HH, LH, and SO bands. The band dispersion relations derived from the fit are shown in Fig. 3(a); the band shapes are generally nonparabolic. A distinctive feature of the LH band is a small peak at the zone center riding on top of a broader peak. This feature is apparent in both the data and the fit. Its origin is spin-orbit coupling caused by relativistic effects [20 –

Expt

(a) HH

-0.2

LH

-0.4 SO -0.6

Energy (eV)

0.0

Expt Theory

(b)

-0.2 -0.4 -0.6 -0.2

-0.1

0.0

0.1

0.2

-1 k|| (Å ) FIG. 3 (color online). (a) Dispersion relations for the HH, LH, and SO bands of Ge deduced from a fit. The dotted lines indicate an anticrossing gap and positions of extra intensity seen in the data. (b) Comparison of the experimental dispersion relations with a relativistic band structure calculation.

22]. Without such coupling, all three Ge bands are nested at the zone center and are approximately parabolic, but with different curvatures. With the coupling included, the middle band shifts downward by an energy approximately equal to the spin-orbit splitting of atomic Ge. A second effect of the spin-orbit coupling is that the shifted middle band interacts with the bottom band, resulting in an anticrossing gap. Thus, the small peak of the LH band as seen in Fig. 3(a) is really a remnant of the bottom (SO) band after gap opening. The dotted lines in Fig. 3(a) suggest what one would expect if the anticrossing interaction is set to zero. A careful examination of the images such as those shown in Figs. 2(a) and 2(b) with various brightness and contrast settings shows that there is significant emission intensity at locations corresponding to the dashed lines in Fig. 3(a). We do not have a quantitative interpretation for this observation. Qualitatively, the aforementioned shift of the LH band is mostly an atomic effect, and the anticrossing is mostly a solid state effect (depending on k). The interface causes a symmetry reduction relative to bulk Ge, and perhaps this is the reason for the extra intensity bridging the anticrossing gap. This extra intensity, not built into our model, can affect the fitting, mostly for the SO band. The spin-orbit splitting at the zone center is 0.301 eV from our fit, which equals within 10 meV those deduced

036802-3

PRL 96, 036802 (2006)

PHYSICAL REVIEW LETTERS

from optical measurements [24] and relativistic band structure calculations [20,21]. The effective masses deduced from the fit are 0.30, 0.034, and 0.21 for the HH, LH, and SO bands, respectively, in terms of the free electron mass. These compare well with the (direction-averaged) values 0.33, 0.043, and 0.095 deduced from cyclotron resonance and magnetoreflectance measurements [25,26]. The SO band shows the largest discrepancy. As discussed above, the extra intensity bridging the anticrossing gap can affect our fitting. It can make the SO band emission to appear broader on the sides, thus possibly leading to a larger effective mass from the fit. Figure 3(b) compares our dispersion relations with those obtained from a relativistic band structure calculation [20]. The experimental and theoretical curvatures near the zone center are very similar for the HH and LH bands. The larger discrepancy for the SO band may be attributed to the extra intensity in the anticrossing gap mentioned above. At larger k, the theoretical band dispersion curves are narrower than the experimental results. At even larger k values beyond the range of Fig. 3(b), experimental band dispersion curves can be determined from the distortions of the quantum-well subband dispersions as seen in Fig. 1 [15–17]. Overall, the relativistic calculation is in agreement with the experiment if one allows theoretical energy uncertainties 0:2 eV and momentum uncertainties 10% of the Brillouin zone size. While modern electronic structure calculations can yield critical point energies as accurate as 0:1 eV or better, the present results suggest that the detailed band shapes can stand further scrutiny. The discrepancies can also be attributed in part to inaccuracies introduced by the approximations in our model. In summary, our analysis shows that the surface electronic structure of an ultrathin atomically uniform film can be a source of valuable information about the substrate. The Shockley surface state of Ag(111) shifts, splits, and develops complex dispersions in films, with decreasing thicknesses, on Ge(111). The result is a display of the Ge band structure including the HH, LH, and SO bands with unprecedented detail. Effects pertaining to spin-orbit coupling are clearly visible, including the band splitting and anticrossing gap. Note that photoemission, limited by the photoelectron mean free path, has a probing depth of only a ˚ ngstroms, and yet this study illustrates a powerful few A method for probing the bulk band structure of materials covered under a film with a thickness much greater than the mean free path. The authors wish to thank Timothy Boykin and Niels E. Christensen for supplying theoretical Ge band dispersion relations. This work is supported by the U.S. National Science Foundation (Grant No. DMR-05-03323). We acknowledge the Petroleum Research Fund, administered by the American Chemical Society, and the U.S. Department of Energy, Division of Materials Sciences (Grant No. DEFG02-91ER45439), for partial support of the syn-

week ending 27 JANUARY 2006

chrotron beam line operations and the central facilities of the Frederick Seitz Materials Research Laboratory. The Synchrotron Radiation Center of the University of Wisconsin-Madison is supported by the U.S. National Science Foundation (Grant No. DMR-00-84402).

[1] T.-C. Chiang, Surf. Sci. Rep. 39, 181 (2000). ˚ . Lindgren and L. Wallde´n, Handbook of Surface [2] S.-A Science, edited by S. Holloway, N. V. Richardson, K. Horn, and M. Scheffler, Electronic Structure Vol. 2 (Elsevier, New York, 2000). [3] M. Milun, P. Pervan, and D. P. Woodruff, Rep. Prog. Phys. 65, 99 (2002). [4] P. Czoschke, L. Basile, H. Hong, and T.-C. Chiang, Phys. Rev. Lett. 93, 036103 (2004). [5] D.-A. Luh, T. Miller, J. J. Paggel, M. Y. Chou, and T.-C. Chiang, Science 292, 1131 (2001). [6] J. J. Paggel, C. M. Wei, M. Y. Chou, D.-A. Luh, T. Miller, and T.-C. Chiang, Phys. Rev. B 66, 233403 (2002). [7] L. Aballe, A. Barinov, A. Locatelli, S. Heun, and M. Kiskinova, Phys. Rev. Lett. 93, 196103 (2004). [8] Y. Guo, Y.-F. Zhang, X.-Y. Bao, T.-Z. Han, Z. Tang, L.-X. Zhang, W.-G. Zhu, E. G. Wang, Q. Niu, Z. Q. Qiu, J.-F. Jia, Z.-X. Zhao, and Q.-K. Xue, Science 306, 1915 (2004). [9] T.-C. Chiang, Science 306, 1900 (2004). [10] T. C. Hsieh, T. Miller, and T. C. Chiang, Phys. Rev. Lett. 55, 2483 (1985). [11] T. C. Hsieh and T. C. Chiang, Surf. Sci. 166, 554 (1986). [12] A. L. Wachs, A. P. Shapiro, T. C. Hsieh, and T. C. Chiang, Phys. Rev. B 33, 1460 (1986). [13] L. Aballe, C. Rogero, and K. Horn, Phys. Rev. B 65, 125319 (2002). [14] G. Neuhold and K. Horn, Phys. Rev. Lett. 78, 1327 (1997). A shift in surface-state energy is attributed to a strain effect. [15] S.-J. Tang, L. Basile, T. Miller, and T.-C. Chiang, Phys. Rev. Lett. 93, 216804 (2004). [16] L. Aballe, C. Rogero, P. Kratzer, S. Gokhale, and K. Horn, Phys. Rev. Lett. 87, 156801 (2001). [17] I. Matsuda, T. Ohta, and H. W. Yeom, Phys. Rev. B 65, 085327 (2002). [18] L. Basile, H. Hong, P. Czoschke, and T.-C. Chiang, Appl. Phys. Lett. 84, 4995 (2004). [19] G. Nicolay, F. Reinert, S. Hu¨fner, and P. Blaha, Phys. Rev. B 65, 033407 (2002). [20] U. Schmid, N. E. Christensen, and M. Cardona, Phys. Rev. B 41, 5919 (1990). [21] M. S. Hybersten and S. G. Louis, Phys. Rev. B 34, 2920 (1986). [22] M. Rohlfing, P. Kruger, and J. Pollmann, Phys. Rev. B 48, 17 791 (1993). [23] G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures (Halsted, New York, 1988). [24] D. E. Aspnes, Phys. Rev. B 12, 2297 (1975). [25] R. N. Dexter, H. J. Zeiger, and B. Lax, Phys. Rev. 104, 637 (1956). [26] R. L. Aggarwal, Phys. Rev. B 2, 446 (1970).

036802-4