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Adsorption structure of germanium on the Ru(0 0 0 1) surface
Applied Surface Science 254 (2007) 431–435 www.elsevier.com/locate/apsusc
Adsorption structure of germanium on the Ru(0 0 0 1) surface Y.H. Lu a, Y. Jia b, H.J. Zhang a, B. Song a, H.Y. Li a, S.N. Bao a, P. He a,* b
a Department of Physics, Zhejiang University, Hangzhou 310027, China School of Physics and Engineering, Zhengzhou University, Zhengzhou 450052, China
Received 31 March 2007; received in revised form 25 May 2007; accepted 27 May 2007 Available online 17 June 2007
Abstract Coverage-dependent adsorption energy of the Ge/Ru(0 0 0 1) growth system and the geometrical distortions of the most stable adsorption structure are investigated through first-principles calculations density functional theory. A local minimum in adsorption energy is found to pffiffiffiffiffiwithin pffiffiffiffiffi be at a Ge coverage of 1/7 monolayer with a Ru(0 0 0 1)- 21 21-3Ge symmetry. Based on this stale superstructure, the scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) p images are ffiffiffiffiffi p ffiffiffiffiffisimulated by means of surface local-density of states (LDOS). The results are consistent well with the STM measurements on the 21 21 phase for Ge overlayer on Ru(0 0 0 1). From this stimulation, the relations between the STM images and the lattice distortion are also clarified. # 2007 Published by Elsevier B.V. PACS : 71.15.Mb; 68.37.Ef; 68.03.Hj Keywords: Ge/Ru growth system; Adsorption structure; Ab initio DFT calculation; Scanning tunneling microscopy
1. Introduction Film growth and interface behavior of metals on semiconductor surfaces have been intensively explored in the past [1–4], whereas there are only a few studies on the reverse systems, i.e. semiconductors on metal surfaces, especially on the transition metal substrate [5–10]. Such systems also involve fundamental issues, such as adsorption structures, growth mechanism, novel surface electronic structures, and formation of surface alloy/compound. Understanding of the adsorption geometries and growth mechanism is helpful to the applications of these systems in catalysis and possibly electronics in the future [11,12]. Germanium, as a typical semiconductor, shows very interesting behaviors on closed packed substrate of transition metal. On the (1 1 1) surfaces of noble metals (Cu and Ag) [5,7], a sub-monolayer of Ge deposited at room temperature forms surface alloy pffiffiffi layers pffiffiffi through replacement reaction, while on Pt(1 1 1), a 5 5 dilute surface alloy is formed after two monolayer (ML) Ge deposition followed with a 1300 K
annealing [9]. Ruthenium is a very important transition metal in the catalysis industry, and the close packed Ru(0 0 0 1) surface have some special electronic structure [14–16]. Ge growth on Ru(0 0 0 1) can be considered as a model system for well understanding growth behavior of semiconductors on close packed surface of transition metal. Recently scanning tunneling microscopy (STM) investigations of germanium growth on the Ru(0 pffiffiffiffiffi 0 0p1)ffiffiffiffiffisurface was reported, and the results showed a ð 21 21ÞR10:9 superstructure in the sub-monolayer regime [13]. In this paper, we report on coverage-dependent adsorption energy of germanium on the Ru(0 0 0 1) surface by using the state-of-the art DFT calculation method, pffiffiffiffiffi andpwith ffiffiffiffiffi a relatively stable model structure of Ruð0 0 0 1Þ-ð 21 21ÞR10:9 -3Ge, The scanning tunneling microscopy (STM) images and the scanning tunneling spectra (STS) images are well simulated, pffiffiffiffiffi consisting well with the STM measurements on the ð 21 pffiffiffiffiffi 21ÞR10:9 superstructure of Ge/Ru(0 0 0 1) system in the monolayer regime [13]. 2. Calculational details
* Corresponding author. Tel.: +86 571 87953256; fax: +86 571 87951328. E-mail address: [email protected] (P. He). 0169-4332/$ – see front matter # 2007 Published by Elsevier B.V. doi:10.1016/j.apsusc.2007.05.084
The first-principle density-functional-theory (DFT) calculations for the Ge/Ru(0 0 0 1) system were performed by using
432
Y.H. Lu et al. / Applied Surface Science 254 (2007) 431–435
the Vienna ab initio simulation package (VASP) [17]. The generalized gradient approximation (PBE) [18] is used for exchange-correlation energy functional. We used PAW [19] potential and plane-waves basis with a cutoff energy of 400 eV. ˚ vacuum region, was used to model A slab, separated by a 20 A the Ru(0 0 0 1) substrate to ensure that the interaction through the vacuum is negligible. Adatoms are adsorbed on one side of the substrate. The lattice parameters are set to the values calculated for HCP bulk Ru crystal, a = 2.723, a/c = 1.582. The k-space integration was made by summing over different Monkhorst–Pack special points [20] in the surface Brillouin zone (SBZ) for different surface unit cell. To accelerate electronic relaxation, we apply the Fermi-level smearing approach of Methfessel–Paxton [21] with a width of 0.2 eV. Energy convergence is reached when the forces on the relaxed ˚. atoms are less than 0.03 eV/A The coverage dependence of relative stability for the Ge/ Ru(0 0 0 1) system was approached with ordered superstructures at Ge sub-monolayer coverage. It has been proved that the HCP site is the most favorable adsorption site of germanium [22]. However, in the present case, both the HCP and FCC sites for Ge adsorption on Ru(0 0 0 1) were examined. A 2 2 supercell with a five layers of Ru slab (to model the substrate) was selected for Ge coverages of 1/2 ML (monolayer) and 1/4 ML, while a 3 3 supercell was selected for Ge coverage of 1/9 ML. Especially, as the optimized pffiffiffiffiffi adsorption structure in Fig. 2, a 21 pffiffiffiffiffi pffiffiffiffiffi shown pffiffiffiffiffi 21 ðRuð0 0 0 1Þ- 21 21-3GeÞ supercell was chosen for Ge coverage of 1/7 ML. We used 9 9 1 k-point grid of SBZ sampling for the 2 2 supercell, 7 7 1 k-point grid for 3 3 supercell, and 3 3 1 k-point grid after pffiffiffiffiffithe convergence test at the number of k points for the 21 p ffiffiffiffiffi 21 supercell. In energy minimization, we allow all the atoms in the slab to be fully relaxed, except for the atoms at the bottom two layers, which are fixed at their respective bulk positions. Adsorption energy Ead was calculated by Eq. (1): Ead ¼
EGe=Ru ERuð0 0 0 1Þ NEGe N
(1)
by means of the wavefunction cnk and the dispersion enk of the nth band with the wavenumber k. Therefore, the tunnel current with the bias voltage V is given as Z
EF
IðV; RÞ1
dErðE; RÞ
(4)
EF þeV
Since these simplified relations for STM/STS spectra are obtained under the assumption that the influence of the tip electronic structures can be ignored, they sometimes fail [24,25], but they would be utilized as a first step [26,27]. 3. Results and discussion The coverage-dependent adsorption energy of germanium on Ru(0 0 0 1) for Ge adatoms adsorbed at the HCP site is summarized in Fig. 1. The adsorption energy of germanium for Ge adsorbed at the FCC site is also included in Fig. 1, in comparison with that for Ge adsorbed at the HCP sites. Apparently, at the lower coverage limit, the HCP site is the more stable adsorption site, and the Ge-phase is dominated by the laterally repulsive interaction, in agreement with the recent experimental measurements and the previous theoretical calculations [13,22]. The germanium bulk cohesive energy is much lower than the Ge adsorption energy on Ru(0 0 0 1) at low Ge coverages, and the Ge–Ge interaction is weaker than that of Ge–Ru. Therefore, Ge adatoms prefer to separately forming wetting layer on Ru(0 0 0 1) [13], in order to maximize Ge–Ru bonds and lower the system energy. pffiffiffiffiffiHowever, pffiffiffiffiffi this trend is broken at a Ge coverage of 1/7 ML ð 21 21-3GeÞ. The adsorption energy, which is evaluated to be 4.94 eV, 15 meV lower than that for Ge overlayer at a coverage 1/9 monolayer, showed as a local minimum. pffiffiffiffiffi pffiffiffiffiffi The optimized structure of Ruð0 0 0 1Þ- 21 21-3Ge ˚, was shown in Fig. 2. The nearest Ge–Ru distance is 2.476 A ˚ and the Ge–Ru interlayer space is 1.83 A. The rumpling of ˚ . The nearest Ge–Ge distance surface atoms is within 0.02 A ˚ , about 0.05 A ˚ (indicated as dGe1–Ge2 in Fig. 2) is 5.494 A
where EGe/Ru is the energy of the whole adsorption system, ERu(0 0 0 1) the energy of the Ru(0 0 0 1) substrate, EGe the energy of a single Ge atom, and N is the number of Ge adatoms. By neglecting the effect of the atomic and electronic structures of the STM tip, in STM/STS measurements, a simple extension of the Tersoff–Hamann formula [23] can be used to determine the tunnel conductance I(V; R) at a bias voltage of V in terms R of surface LDOS (local density of states), E IðV; RÞ1 EFFþeV dErðE; RÞrðE; RÞ at the point R and the energy E, where r(E, R) is the LDOS of the sample, and as the following, the STS spectra is proportional to the LDOS: dIðV; RÞ 1rðEF þ eV; RÞ dV
(2)
where rðE; RÞ ¼
X n;k
jcnk ðRÞj2 dðE enk Þ
(3)
Fig. 1. The coverage-dependent adsorption energy for Ge overlayer on Ru(0 0 0 1) with Ge adsorbed at the HCP site (filled triangle), the adsorption energy for Ge adsorbed at the FCC site (filled circle) is also included, and the pffiffiffiffiffi pffiffiffiffiffi adsorption energy of 1/7 ML Ge ðRuð0 0 0 1Þ- 21 21-3GeÞ for Ge adsorbed at the HCP site is indicated by the square.
Y.H. Lu et al. / Applied Surface Science 254 (2007) 431–435
pffiffiffiffiffi Fig. p ffiffiffiffiffi 2. (a) Schematic top view of an area of four times the Ruð0 0 0 1Þ- 21 21-3Ge cell, Ge (small balls), the first layer Ru (blue balls) and the second layer Ru (yellow balls) atoms, and also optimized parameters (distances between atoms) are indicated. All the parameters included are in an unit of ˚ . (For interpretation of the references to colour in this figure legend, the reader A is referred to the web version of the article.)
˚ ) in non-relaxed (nonlarger than the original set value (5.446 A reconstructed) structure. The distortion of the substrate is obvious. Because of the strong interaction between Ge adatoms and the substrate, the three Ru atoms nearest to Ge adatoms (shown as Ru1, Ru2 and Ru3 in Fig. 2) in the first Ru layer were ˚ , about 0.2 A ˚ larger than expanded up to a dRu1–Ru2 of 2.922 A ˚ that of the clean Ru(0 0 0 1) surface (2.723 A), while the distance between the other three Ru (labeled as Ru7, Ru8 and Ru9 in Fig. 2) atoms within the small germanium triangular ˚ , which can be attributed area decreases from 2.723 to 2.580 A to the competition between the Ge–Ru and the Ge–Ge interaction. These strong interactions result in high densities of electrons in these triangular areas. On the other hand, the Ge– Ru bonding or the Ge–Ge bonding would attract electrons from
433
other areas of the surface, and new empty states may occur. The changes of the distances between Ru4, Ru5 and Ru6, and between Ru10, Ru11 and Ru12 were lesser than 0.8%, in comparison with that of the clean Ru(0 0 0 1) surface. Therefore, even some states are depleted (which will be discussed below), the distortions of those Ru atoms are little. The coverage dependent adsorption energy shown inpFig. ffiffiffiffiffi 1 indicates that there may be exist an ordered Ruð0 0 0 1Þ21 pffiffiffiffiffi 21-3Ge superstructure for Ge overlayer on Ru(0 0 0 1) in the monolayer regime. Actually in the STM for the pffiffiffiffiffimeasurements pffiffiffiffiffi 21 21 phase was Ge/Ru(0 0 0 1) growth system, a pffiffiffiffiffi observed [13]. In order to understand the Ruð0 0 0 1Þ21 pffiffiffiffiffi 21-3Ge superstructure deeply and compare with the experimental STM image, we carried out the simulations pffiffiffiffiffi pffiffiffiffiffi of STM/STS image based on the Ruð0 0 0 1Þ- 21 p ffiffiffiffiffi 21-3Ge pffiffiffiffiffi structure shown in Fig. 2. An area of four times the 21 21 cell is used to show the results of the simulated STM images by means of Eq. (4) within energy window relevant to EF. For the LDOS calculation, the distance between the STM tip ˚ [27], is and the substrate surface, typical one in a range of 3–7 A ˚ taken to be 5 A above the Ru(0 0 0 1) surface. Fig. 3a shows a map of the tunnel currents at the bias voltage of 0.5 V. It can be clearly seen that the three nearest bright spots correspond to the bridge sites between the three Ru atoms (shown as Ru7, Ru8 and Ru9 in Fig. 2) within the small Ge triangular area, indicating somewhat Ge–Ge bondings mediated by the Ru substrate were formed. The higher LDOS in these Ge triangular areas, i.e., the three nearest bright spots, can be recognized as the occupied electronic states since the bias (sample) voltage is negative, and is in well agreement with the geometry distortions discussed above. These bright spots should be disappeared if the bias voltage is reversed, which will result in a map of the empty states. Fig. 3b shows a map of the tunnel currents at the
pffiffiffiffiffi pffiffiffiffiffi ˚ Fig. 3. Simulated map of the tunnel currents for Ruð0 0 0 1Þ- 21 21-3Ge at biasp voltages ffiffiffiffiffi pof ffiffiffiffiffi(a) 0.5 V, (b) +1.0 V, and (c) +2.1 V, with a STM tip of 5 A above ˚ above the the first layer of Ru(0 0 0 1), and (d) simulated dI/dV (LDOS) map of the Ruð0 0 0 1Þ- 21 21-3Ge superstructure at EF + 2.1 eV with a STM tip of 5 A first layer of Ru(0 0 0 1).
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bias voltage of 1.0 V. Apparently, the bright spots, corresponding to the empty states, are now localized at the three Ge adatoms labeled by Ge3, Ge5 and Ge6 in Fig. 2, where nearly no reconstruction of the substrate Ru atoms happened, and the spots alignments are same as that of Ge adatoms shown in Fig.p2. ffiffiffiffiffiWith pthe ffiffiffiffiffi symmetry of the spots distribution, the unit cell of 21 21 can be reproduced with the basic vector 10.98 off the [0 0 0 1] direction of the substrate. By changing the bias voltage, for example, up to 2.1 V, the STM image is correspondingly changed. The distance between pthe ffiffiffiffiffi nearest pffiffiffiffiffi strongest spots is nearly one-half of the unit cell of 21 21 (Fig. 3c), but the image symmetries are the same. It should be noted that the STM image of a superstructure, determined by the slight change in the characters of the wavefunctions which contribute to the LDOS at a given energy, is very sensitive to the bias voltage. To clarify this physical mechanism, we also pffiffiffiffiffi simulated the dI/dV map (Fig. 3d) of Ruð0 0 0 1Þ21 pffiffiffiffiffi 21-3Ge at a bias voltage of 2.1 V based on Eq. p (2). All the ffiffiffiffiffi pffiffiffiffiffi bright spots in Fig. 3d are along the basis of the p21 ffiffiffiffiffi p21 ffiffiffiffiffi unit cell, and the spots distributions show the 21 21 symmetry. The difference of the dI/dV map (STS image) from the STM image of the integrated tunneling conductances shown in Fig. 3a–c is also obvious, since the dI/dV map represents the local density of states near EF. Fig. 4 shows a typical STM image taken for Ge wetting layer on Ru(0 0 0 1) at a sub-monolayer coverage (Vs = 2.1 V, It = 0.15 nA at room temperature) [13]. The measured period ˚ or 4.6a0, where a0 is the of the ordered structure is 12.4 A length of basis pffiffiffiffiffi pffiffiffiffiffion Ru(0 0 0 1). This superstructure is assigned as ð 21 21ÞR10:9 [13]. The simulated result (Fig. 3c), appearing as an equilateral triangle with three bright spots at the apexes, is consistent well with the STM measurements. At present, by the theoretical calculations, together pffiffiffiffiffiwith pthe ffiffiffiffiffi STM measurements, the superstructure of the Ge 21 21pphase ffiffiffiffiffi on Ru(0 0 0 1) can be clearly determined as Ruð0 0 0 1Þ- 21 pffiffiffiffiffi 21-3Ge as shown in Fig. 2. However, from the STM image,
pffiffiffiffiffi pffiffiffiffiffi Fig. 4. STM image (21 nm 21 nm) of ð 21 p21 ffiffiffiffiffiÞR10:9 pffiffiffiffiffi superstructure of Ge wetting layer on Ru(0 0 0 1) with unit cell of ð 21 21ÞR10:9 indicated taken at the condition Vs = 2.1 V and It = 0.15 nA.
pffiffiffiffiffi pffiffiffiffiffi we can see the ordering of the Ge 21 21 phase is fairly well, and we actually had difficulty to get this superstructure clear in the STM measurements [13]. The ordering of a superstructure depends on how stale it is, and as discussed pffiffiffiffiffi above, pffiffiffiffiffi even the adsorption energy of the Ruð0 0 0 1Þ- 21 21-3Ge superstructure showed as a minimum in the coveragedependent adsorption energy, but it is only 15 meV lower than that of the 3 3 superstructure. 4. Conclusions By using the state-of-the art DFT method we investigated the coverage-dependent adsorption energy for the Ge/Ru(0 0 0 1) growth system in the monolayer regime. The results showed mainly a repulsive interaction between Ge adatoms. A stable superstructure at a Ge coverage of 1/7 monolayer, as a local minimum in the coverage-dependent pffiffiffiffiffi pffiffiffiffiffi adsorption energy, is found to have a Ruð0 0 0 1Þ- 21 21-3Ge pffiffiffiffiffisymmetry. pffiffiffiffiffi Based on the optimized structure of Ruð0 0 0 1Þ- 21 21-3Ge, the STM/STS images were simulated with a simple extension of the Tersoff–Hamann formula. The simulated results can pffiffiffiffiffi be comparable well with the STM measurements on the Ge 21 pffiffiffiffiffi 21 phase for the Ge/Ru(0 0 0 1) system in the monolayer regime, i.e., together pffiffiffiffiffi with pffiffiffiffiffithe STM measurements, the atomic structure of the 21 21 phase Ge/Ru(0 0 0 1) system is pffiffiffiffiffi in p ffiffiffiffiffi determined to be Ruð0 0 0 1Þ- 21 21-3Ge. Acknowledgements This work has been supported by the National Natural Science Foundation of China under Grant Nos. 10574108 and 60506019, and the National Important Project on Science and Technology of China under Grant No. 2006CB92500. References [1] H. von Kaenel, Mater. Sci. Rep. 8 (1992) 193. [2] L. Floreano, D. Cvetko, F. Bruno, G. Bavdek, A. Cassaro, R. Gotter, A. Verdini, A. Morgante, Prog. Surf. Sci. 72 (2003) 135. [3] M. Hammar, M. Goethelid, U.O. Karlsson, S.A. Flodstreom, Phys. Rev. B 47 (1993) 15669. [4] C. Collazo-Davila, D. Grozea, L.D. Marks, R. Feidenhans’l, M. Nielsen, L. Seehofer, L. Lottermoser, G. Falkenberg, R.L. Johnson, M. Goethelid, U. Karsson, Surf. Sci. 418 (1998) 395. [5] R. Dudde, H. Bernhoff, B. Reil, Phys. Rev. B 41 (1990) 12029. [6] J.A. Martı´n-Gago, R. Fasel, J. Hayoz, R.G. Agostino, D. Naumoviæ, P. Aebi, L. Schlapbach, Phys. Rev. B 55 (1997) 12896; C. Polop, J.L. Sacedo´n, J.A. Martı´n-Gago, Surf. Sci. 402 (1998) 245. [7] H. Oughaddou, S. Sawaya, J. Goniakowski, B. Aufray, G. Le Lay, J.M. Gay, G. Tre´glia, J.P. Bibe´rian, N. Barrett, C. Guillot, A. Mayne, G. Dujardin, Phys. Rev. B 62 (2000) 16653. [8] H. Oughaddou, J.M. Gay, B. Aufray, L. Lepena, G. Le Lay, O. Bunk, G. Falkenberg, J.H. Zeysing, R.L. Johnson, Phys. Rev. B 61 (2000) 5692. [9] K. Fukutani, Y. Murata, J. Brillo, H. Kuhlenbek, H.J. Frund, M. Taguchi, Surf. Sci. 464 (2000) 48. [10] M. Batzill, T. Matsumoto, C.-S. Ho, B.E. Koel, Phys. Rev. B 69 (2004) 113401. [11] K. Fukutani, T.T. Magekoev, Y. Murata, K. Terakura, Surf. Sci. 363 (1996) 185. [12] T. Komatsu, M. Mesuda, T. Yashima, Appl. Catal. A 194 (2000) 333.
Y.H. Lu et al. / Applied Surface Science 254 (2007) 431–435 [13] H.J. Zhang, B. Lu, X.S. Wang, F. Hu, H.Y. Li, S.N. Bao, P. He, Phys. Rev. B 70 (2004) 235415. [14] J. Peter, Feibelman, Science 295 (2002) 99. [15] K. Honkala, A. Hellman, I.N. Remediakis, A. Logadottir, A. Carlsson, S. Dahl, C.H. Christensen, J.K. Nørskov, Science 307 (2005) 555. [16] K. Pohl, M.C. Bartelt, J. de la Figuera, N.C. Bartelt, J. Hrbek, R.Q. Hwang, Nature 397 (1999) 238. [17] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) R558; G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) 14251; G. Kresse, J. Furthmu¨ller, Comput. Mater. Sci. 6 (1996) 15; G. Kresse, J. Furthmu¨ller, Phys. Rev. B 54 (1996) 11169. [18] J.P. Perdew, K. Burke, K. Ernzerhof, Phys. Rev. Lett. 77 (18) (1996) 3865.
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[19] P. Blo¨chl, Phys. Rev. B 50 (1994) 17953; G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [20] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [21] M. Methfessel, A.T. Paxton, Phys. Rev. B 40 (1989) 3616. [22] Unpublished. [23] J. Tersoff, D.R. Hamann, Phys. Rev. B 31 (1985) 805. [24] M. Tsukada, N. Shlma, J. Phys. Soc. Jpn. 56 (1987) 2875. [25] M. Tsukada, K. Kobayashl, N. Isshikl, S. Watanabe, H. Kageshlma, T. Schlmlzu, Scanning Tunneling Microscopy III, Springer, Berlin, 1993. [26] A. Kikuchi, Surf. Sci. 397 (1998) 288. [27] Q. Li, J.L. Yang, J. Zhao, J.G. Hou, Q.S. Zhu, Prog. Phys. 3 (2000) 234.
Adsorption structure of germanium on the Ru(0 0 0 1) surface Y.H. Lu a, Y. Jia b, H.J. Zhang a, B. Song a, H.Y. Li a, S.N. Bao a, P. He a,* b
a Department of Physics, Zhejiang University, Hangzhou 310027, China School of Physics and Engineering, Zhengzhou University, Zhengzhou 450052, China
Received 31 March 2007; received in revised form 25 May 2007; accepted 27 May 2007 Available online 17 June 2007
Abstract Coverage-dependent adsorption energy of the Ge/Ru(0 0 0 1) growth system and the geometrical distortions of the most stable adsorption structure are investigated through first-principles calculations density functional theory. A local minimum in adsorption energy is found to pffiffiffiffiffiwithin pffiffiffiffiffi be at a Ge coverage of 1/7 monolayer with a Ru(0 0 0 1)- 21 21-3Ge symmetry. Based on this stale superstructure, the scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) p images are ffiffiffiffiffi p ffiffiffiffiffisimulated by means of surface local-density of states (LDOS). The results are consistent well with the STM measurements on the 21 21 phase for Ge overlayer on Ru(0 0 0 1). From this stimulation, the relations between the STM images and the lattice distortion are also clarified. # 2007 Published by Elsevier B.V. PACS : 71.15.Mb; 68.37.Ef; 68.03.Hj Keywords: Ge/Ru growth system; Adsorption structure; Ab initio DFT calculation; Scanning tunneling microscopy
1. Introduction Film growth and interface behavior of metals on semiconductor surfaces have been intensively explored in the past [1–4], whereas there are only a few studies on the reverse systems, i.e. semiconductors on metal surfaces, especially on the transition metal substrate [5–10]. Such systems also involve fundamental issues, such as adsorption structures, growth mechanism, novel surface electronic structures, and formation of surface alloy/compound. Understanding of the adsorption geometries and growth mechanism is helpful to the applications of these systems in catalysis and possibly electronics in the future [11,12]. Germanium, as a typical semiconductor, shows very interesting behaviors on closed packed substrate of transition metal. On the (1 1 1) surfaces of noble metals (Cu and Ag) [5,7], a sub-monolayer of Ge deposited at room temperature forms surface alloy pffiffiffi layers pffiffiffi through replacement reaction, while on Pt(1 1 1), a 5 5 dilute surface alloy is formed after two monolayer (ML) Ge deposition followed with a 1300 K
annealing [9]. Ruthenium is a very important transition metal in the catalysis industry, and the close packed Ru(0 0 0 1) surface have some special electronic structure [14–16]. Ge growth on Ru(0 0 0 1) can be considered as a model system for well understanding growth behavior of semiconductors on close packed surface of transition metal. Recently scanning tunneling microscopy (STM) investigations of germanium growth on the Ru(0 pffiffiffiffiffi 0 0p1)ffiffiffiffiffisurface was reported, and the results showed a ð 21 21ÞR10:9 superstructure in the sub-monolayer regime [13]. In this paper, we report on coverage-dependent adsorption energy of germanium on the Ru(0 0 0 1) surface by using the state-of-the art DFT calculation method, pffiffiffiffiffi andpwith ffiffiffiffiffi a relatively stable model structure of Ruð0 0 0 1Þ-ð 21 21ÞR10:9 -3Ge, The scanning tunneling microscopy (STM) images and the scanning tunneling spectra (STS) images are well simulated, pffiffiffiffiffi consisting well with the STM measurements on the ð 21 pffiffiffiffiffi 21ÞR10:9 superstructure of Ge/Ru(0 0 0 1) system in the monolayer regime [13]. 2. Calculational details
* Corresponding author. Tel.: +86 571 87953256; fax: +86 571 87951328. E-mail address: [email protected] (P. He). 0169-4332/$ – see front matter # 2007 Published by Elsevier B.V. doi:10.1016/j.apsusc.2007.05.084
The first-principle density-functional-theory (DFT) calculations for the Ge/Ru(0 0 0 1) system were performed by using
432
Y.H. Lu et al. / Applied Surface Science 254 (2007) 431–435
the Vienna ab initio simulation package (VASP) [17]. The generalized gradient approximation (PBE) [18] is used for exchange-correlation energy functional. We used PAW [19] potential and plane-waves basis with a cutoff energy of 400 eV. ˚ vacuum region, was used to model A slab, separated by a 20 A the Ru(0 0 0 1) substrate to ensure that the interaction through the vacuum is negligible. Adatoms are adsorbed on one side of the substrate. The lattice parameters are set to the values calculated for HCP bulk Ru crystal, a = 2.723, a/c = 1.582. The k-space integration was made by summing over different Monkhorst–Pack special points [20] in the surface Brillouin zone (SBZ) for different surface unit cell. To accelerate electronic relaxation, we apply the Fermi-level smearing approach of Methfessel–Paxton [21] with a width of 0.2 eV. Energy convergence is reached when the forces on the relaxed ˚. atoms are less than 0.03 eV/A The coverage dependence of relative stability for the Ge/ Ru(0 0 0 1) system was approached with ordered superstructures at Ge sub-monolayer coverage. It has been proved that the HCP site is the most favorable adsorption site of germanium [22]. However, in the present case, both the HCP and FCC sites for Ge adsorption on Ru(0 0 0 1) were examined. A 2 2 supercell with a five layers of Ru slab (to model the substrate) was selected for Ge coverages of 1/2 ML (monolayer) and 1/4 ML, while a 3 3 supercell was selected for Ge coverage of 1/9 ML. Especially, as the optimized pffiffiffiffiffi adsorption structure in Fig. 2, a 21 pffiffiffiffiffi pffiffiffiffiffi shown pffiffiffiffiffi 21 ðRuð0 0 0 1Þ- 21 21-3GeÞ supercell was chosen for Ge coverage of 1/7 ML. We used 9 9 1 k-point grid of SBZ sampling for the 2 2 supercell, 7 7 1 k-point grid for 3 3 supercell, and 3 3 1 k-point grid after pffiffiffiffiffithe convergence test at the number of k points for the 21 p ffiffiffiffiffi 21 supercell. In energy minimization, we allow all the atoms in the slab to be fully relaxed, except for the atoms at the bottom two layers, which are fixed at their respective bulk positions. Adsorption energy Ead was calculated by Eq. (1): Ead ¼
EGe=Ru ERuð0 0 0 1Þ NEGe N
(1)
by means of the wavefunction cnk and the dispersion enk of the nth band with the wavenumber k. Therefore, the tunnel current with the bias voltage V is given as Z
EF
IðV; RÞ1
dErðE; RÞ
(4)
EF þeV
Since these simplified relations for STM/STS spectra are obtained under the assumption that the influence of the tip electronic structures can be ignored, they sometimes fail [24,25], but they would be utilized as a first step [26,27]. 3. Results and discussion The coverage-dependent adsorption energy of germanium on Ru(0 0 0 1) for Ge adatoms adsorbed at the HCP site is summarized in Fig. 1. The adsorption energy of germanium for Ge adsorbed at the FCC site is also included in Fig. 1, in comparison with that for Ge adsorbed at the HCP sites. Apparently, at the lower coverage limit, the HCP site is the more stable adsorption site, and the Ge-phase is dominated by the laterally repulsive interaction, in agreement with the recent experimental measurements and the previous theoretical calculations [13,22]. The germanium bulk cohesive energy is much lower than the Ge adsorption energy on Ru(0 0 0 1) at low Ge coverages, and the Ge–Ge interaction is weaker than that of Ge–Ru. Therefore, Ge adatoms prefer to separately forming wetting layer on Ru(0 0 0 1) [13], in order to maximize Ge–Ru bonds and lower the system energy. pffiffiffiffiffiHowever, pffiffiffiffiffi this trend is broken at a Ge coverage of 1/7 ML ð 21 21-3GeÞ. The adsorption energy, which is evaluated to be 4.94 eV, 15 meV lower than that for Ge overlayer at a coverage 1/9 monolayer, showed as a local minimum. pffiffiffiffiffi pffiffiffiffiffi The optimized structure of Ruð0 0 0 1Þ- 21 21-3Ge ˚, was shown in Fig. 2. The nearest Ge–Ru distance is 2.476 A ˚ and the Ge–Ru interlayer space is 1.83 A. The rumpling of ˚ . The nearest Ge–Ge distance surface atoms is within 0.02 A ˚ , about 0.05 A ˚ (indicated as dGe1–Ge2 in Fig. 2) is 5.494 A
where EGe/Ru is the energy of the whole adsorption system, ERu(0 0 0 1) the energy of the Ru(0 0 0 1) substrate, EGe the energy of a single Ge atom, and N is the number of Ge adatoms. By neglecting the effect of the atomic and electronic structures of the STM tip, in STM/STS measurements, a simple extension of the Tersoff–Hamann formula [23] can be used to determine the tunnel conductance I(V; R) at a bias voltage of V in terms R of surface LDOS (local density of states), E IðV; RÞ1 EFFþeV dErðE; RÞrðE; RÞ at the point R and the energy E, where r(E, R) is the LDOS of the sample, and as the following, the STS spectra is proportional to the LDOS: dIðV; RÞ 1rðEF þ eV; RÞ dV
(2)
where rðE; RÞ ¼
X n;k
jcnk ðRÞj2 dðE enk Þ
(3)
Fig. 1. The coverage-dependent adsorption energy for Ge overlayer on Ru(0 0 0 1) with Ge adsorbed at the HCP site (filled triangle), the adsorption energy for Ge adsorbed at the FCC site (filled circle) is also included, and the pffiffiffiffiffi pffiffiffiffiffi adsorption energy of 1/7 ML Ge ðRuð0 0 0 1Þ- 21 21-3GeÞ for Ge adsorbed at the HCP site is indicated by the square.
Y.H. Lu et al. / Applied Surface Science 254 (2007) 431–435
pffiffiffiffiffi Fig. p ffiffiffiffiffi 2. (a) Schematic top view of an area of four times the Ruð0 0 0 1Þ- 21 21-3Ge cell, Ge (small balls), the first layer Ru (blue balls) and the second layer Ru (yellow balls) atoms, and also optimized parameters (distances between atoms) are indicated. All the parameters included are in an unit of ˚ . (For interpretation of the references to colour in this figure legend, the reader A is referred to the web version of the article.)
˚ ) in non-relaxed (nonlarger than the original set value (5.446 A reconstructed) structure. The distortion of the substrate is obvious. Because of the strong interaction between Ge adatoms and the substrate, the three Ru atoms nearest to Ge adatoms (shown as Ru1, Ru2 and Ru3 in Fig. 2) in the first Ru layer were ˚ , about 0.2 A ˚ larger than expanded up to a dRu1–Ru2 of 2.922 A ˚ that of the clean Ru(0 0 0 1) surface (2.723 A), while the distance between the other three Ru (labeled as Ru7, Ru8 and Ru9 in Fig. 2) atoms within the small germanium triangular ˚ , which can be attributed area decreases from 2.723 to 2.580 A to the competition between the Ge–Ru and the Ge–Ge interaction. These strong interactions result in high densities of electrons in these triangular areas. On the other hand, the Ge– Ru bonding or the Ge–Ge bonding would attract electrons from
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other areas of the surface, and new empty states may occur. The changes of the distances between Ru4, Ru5 and Ru6, and between Ru10, Ru11 and Ru12 were lesser than 0.8%, in comparison with that of the clean Ru(0 0 0 1) surface. Therefore, even some states are depleted (which will be discussed below), the distortions of those Ru atoms are little. The coverage dependent adsorption energy shown inpFig. ffiffiffiffiffi 1 indicates that there may be exist an ordered Ruð0 0 0 1Þ21 pffiffiffiffiffi 21-3Ge superstructure for Ge overlayer on Ru(0 0 0 1) in the monolayer regime. Actually in the STM for the pffiffiffiffiffimeasurements pffiffiffiffiffi 21 21 phase was Ge/Ru(0 0 0 1) growth system, a pffiffiffiffiffi observed [13]. In order to understand the Ruð0 0 0 1Þ21 pffiffiffiffiffi 21-3Ge superstructure deeply and compare with the experimental STM image, we carried out the simulations pffiffiffiffiffi pffiffiffiffiffi of STM/STS image based on the Ruð0 0 0 1Þ- 21 p ffiffiffiffiffi 21-3Ge pffiffiffiffiffi structure shown in Fig. 2. An area of four times the 21 21 cell is used to show the results of the simulated STM images by means of Eq. (4) within energy window relevant to EF. For the LDOS calculation, the distance between the STM tip ˚ [27], is and the substrate surface, typical one in a range of 3–7 A ˚ taken to be 5 A above the Ru(0 0 0 1) surface. Fig. 3a shows a map of the tunnel currents at the bias voltage of 0.5 V. It can be clearly seen that the three nearest bright spots correspond to the bridge sites between the three Ru atoms (shown as Ru7, Ru8 and Ru9 in Fig. 2) within the small Ge triangular area, indicating somewhat Ge–Ge bondings mediated by the Ru substrate were formed. The higher LDOS in these Ge triangular areas, i.e., the three nearest bright spots, can be recognized as the occupied electronic states since the bias (sample) voltage is negative, and is in well agreement with the geometry distortions discussed above. These bright spots should be disappeared if the bias voltage is reversed, which will result in a map of the empty states. Fig. 3b shows a map of the tunnel currents at the
pffiffiffiffiffi pffiffiffiffiffi ˚ Fig. 3. Simulated map of the tunnel currents for Ruð0 0 0 1Þ- 21 21-3Ge at biasp voltages ffiffiffiffiffi pof ffiffiffiffiffi(a) 0.5 V, (b) +1.0 V, and (c) +2.1 V, with a STM tip of 5 A above ˚ above the the first layer of Ru(0 0 0 1), and (d) simulated dI/dV (LDOS) map of the Ruð0 0 0 1Þ- 21 21-3Ge superstructure at EF + 2.1 eV with a STM tip of 5 A first layer of Ru(0 0 0 1).
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Y.H. Lu et al. / Applied Surface Science 254 (2007) 431–435
bias voltage of 1.0 V. Apparently, the bright spots, corresponding to the empty states, are now localized at the three Ge adatoms labeled by Ge3, Ge5 and Ge6 in Fig. 2, where nearly no reconstruction of the substrate Ru atoms happened, and the spots alignments are same as that of Ge adatoms shown in Fig.p2. ffiffiffiffiffiWith pthe ffiffiffiffiffi symmetry of the spots distribution, the unit cell of 21 21 can be reproduced with the basic vector 10.98 off the [0 0 0 1] direction of the substrate. By changing the bias voltage, for example, up to 2.1 V, the STM image is correspondingly changed. The distance between pthe ffiffiffiffiffi nearest pffiffiffiffiffi strongest spots is nearly one-half of the unit cell of 21 21 (Fig. 3c), but the image symmetries are the same. It should be noted that the STM image of a superstructure, determined by the slight change in the characters of the wavefunctions which contribute to the LDOS at a given energy, is very sensitive to the bias voltage. To clarify this physical mechanism, we also pffiffiffiffiffi simulated the dI/dV map (Fig. 3d) of Ruð0 0 0 1Þ21 pffiffiffiffiffi 21-3Ge at a bias voltage of 2.1 V based on Eq. p (2). All the ffiffiffiffiffi pffiffiffiffiffi bright spots in Fig. 3d are along the basis of the p21 ffiffiffiffiffi p21 ffiffiffiffiffi unit cell, and the spots distributions show the 21 21 symmetry. The difference of the dI/dV map (STS image) from the STM image of the integrated tunneling conductances shown in Fig. 3a–c is also obvious, since the dI/dV map represents the local density of states near EF. Fig. 4 shows a typical STM image taken for Ge wetting layer on Ru(0 0 0 1) at a sub-monolayer coverage (Vs = 2.1 V, It = 0.15 nA at room temperature) [13]. The measured period ˚ or 4.6a0, where a0 is the of the ordered structure is 12.4 A length of basis pffiffiffiffiffi pffiffiffiffiffion Ru(0 0 0 1). This superstructure is assigned as ð 21 21ÞR10:9 [13]. The simulated result (Fig. 3c), appearing as an equilateral triangle with three bright spots at the apexes, is consistent well with the STM measurements. At present, by the theoretical calculations, together pffiffiffiffiffiwith pthe ffiffiffiffiffi STM measurements, the superstructure of the Ge 21 21pphase ffiffiffiffiffi on Ru(0 0 0 1) can be clearly determined as Ruð0 0 0 1Þ- 21 pffiffiffiffiffi 21-3Ge as shown in Fig. 2. However, from the STM image,
pffiffiffiffiffi pffiffiffiffiffi Fig. 4. STM image (21 nm 21 nm) of ð 21 p21 ffiffiffiffiffiÞR10:9 pffiffiffiffiffi superstructure of Ge wetting layer on Ru(0 0 0 1) with unit cell of ð 21 21ÞR10:9 indicated taken at the condition Vs = 2.1 V and It = 0.15 nA.
pffiffiffiffiffi pffiffiffiffiffi we can see the ordering of the Ge 21 21 phase is fairly well, and we actually had difficulty to get this superstructure clear in the STM measurements [13]. The ordering of a superstructure depends on how stale it is, and as discussed pffiffiffiffiffi above, pffiffiffiffiffi even the adsorption energy of the Ruð0 0 0 1Þ- 21 21-3Ge superstructure showed as a minimum in the coveragedependent adsorption energy, but it is only 15 meV lower than that of the 3 3 superstructure. 4. Conclusions By using the state-of-the art DFT method we investigated the coverage-dependent adsorption energy for the Ge/Ru(0 0 0 1) growth system in the monolayer regime. The results showed mainly a repulsive interaction between Ge adatoms. A stable superstructure at a Ge coverage of 1/7 monolayer, as a local minimum in the coverage-dependent pffiffiffiffiffi pffiffiffiffiffi adsorption energy, is found to have a Ruð0 0 0 1Þ- 21 21-3Ge pffiffiffiffiffisymmetry. pffiffiffiffiffi Based on the optimized structure of Ruð0 0 0 1Þ- 21 21-3Ge, the STM/STS images were simulated with a simple extension of the Tersoff–Hamann formula. The simulated results can pffiffiffiffiffi be comparable well with the STM measurements on the Ge 21 pffiffiffiffiffi 21 phase for the Ge/Ru(0 0 0 1) system in the monolayer regime, i.e., together pffiffiffiffiffi with pffiffiffiffiffithe STM measurements, the atomic structure of the 21 21 phase Ge/Ru(0 0 0 1) system is pffiffiffiffiffi in p ffiffiffiffiffi determined to be Ruð0 0 0 1Þ- 21 21-3Ge. Acknowledgements This work has been supported by the National Natural Science Foundation of China under Grant Nos. 10574108 and 60506019, and the National Important Project on Science and Technology of China under Grant No. 2006CB92500. References [1] H. von Kaenel, Mater. Sci. Rep. 8 (1992) 193. [2] L. Floreano, D. Cvetko, F. Bruno, G. Bavdek, A. Cassaro, R. Gotter, A. Verdini, A. Morgante, Prog. Surf. Sci. 72 (2003) 135. [3] M. Hammar, M. Goethelid, U.O. Karlsson, S.A. Flodstreom, Phys. Rev. B 47 (1993) 15669. [4] C. Collazo-Davila, D. Grozea, L.D. Marks, R. Feidenhans’l, M. Nielsen, L. Seehofer, L. Lottermoser, G. Falkenberg, R.L. Johnson, M. Goethelid, U. Karsson, Surf. Sci. 418 (1998) 395. [5] R. Dudde, H. Bernhoff, B. Reil, Phys. Rev. B 41 (1990) 12029. [6] J.A. Martı´n-Gago, R. Fasel, J. Hayoz, R.G. Agostino, D. Naumoviæ, P. Aebi, L. Schlapbach, Phys. Rev. B 55 (1997) 12896; C. Polop, J.L. Sacedo´n, J.A. Martı´n-Gago, Surf. Sci. 402 (1998) 245. [7] H. Oughaddou, S. Sawaya, J. Goniakowski, B. Aufray, G. Le Lay, J.M. Gay, G. Tre´glia, J.P. Bibe´rian, N. Barrett, C. Guillot, A. Mayne, G. Dujardin, Phys. Rev. B 62 (2000) 16653. [8] H. Oughaddou, J.M. Gay, B. Aufray, L. Lepena, G. Le Lay, O. Bunk, G. Falkenberg, J.H. Zeysing, R.L. Johnson, Phys. Rev. B 61 (2000) 5692. [9] K. Fukutani, Y. Murata, J. Brillo, H. Kuhlenbek, H.J. Frund, M. Taguchi, Surf. Sci. 464 (2000) 48. [10] M. Batzill, T. Matsumoto, C.-S. Ho, B.E. Koel, Phys. Rev. B 69 (2004) 113401. [11] K. Fukutani, T.T. Magekoev, Y. Murata, K. Terakura, Surf. Sci. 363 (1996) 185. [12] T. Komatsu, M. Mesuda, T. Yashima, Appl. Catal. A 194 (2000) 333.
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