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Atomic and electronic structures of the Rb–C(1 0 0) chemisorption system
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Physica B 383 (2006) 219–225 www.elsevier.com/locate/physb
Atomic and electronic structures of the Rb–C(1 0 0) chemisorption system J.L. Niea, H.Y. Xiaoa, X.T. Zua,b,, Fei Gaoc a
Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu, 610054, PR China b International Center for Material Physics, Chinese Academy of Sciences, Shenyang 110015, PR China c Pacific Northwest National Laboratory, MS K8-93, P. O. Box 999, Richland, WA 99352, USA Received 23 January 2006; received in revised form 1 March 2006; accepted 14 March 2006
Abstract First-principles calculations based on DFT–GGA method have been performed on Rb adsorption on C(1 0 0)(2 1) surface. The optimized geometries, adsorption energies have been obtained and the preferred binding sites have been determined for the coverage (Y) of one monolayer and half a monolayer. The calculated results have shown that Rb adsorbate preferred to occupy valley-bridge sites at the coverage of 0.5 ML. At higher coverage of 1 ML, two Rb adsorbates were found to reside in pedestal site and valley-bridge site, respectively. It was also found that when Rb was adsorbed on C(1 0 0)(2 1) surface the work function decreases linearly with increasing coverage and reaches a minimum at Y ¼ 0.5 ML, at higher coverage, the work function is increased again, which may be caused by depolarization effect of the adsorbate. The adsorption behavior was found to be similar to that of Rb on Si(0 0 1) and Ge(0 0 1) surface. r 2006 Elsevier B.V. All rights reserved. Keywords: First-principles calculations; Diamond; Rubidium; Work function
1. Introduction The electronic and structural properties of alkali metal (AM) adsorption on the semiconductor surfaces have been intensively investigated in the last two decades [1–9]. The strong interest in these adsorption systems has been raised in that it plays an important role in electrochemistry and heterogeneous catalysis [10]. On the other hand, since the electronic structures of alkali atoms are very simple, the study on the adsorption of AMs on metal surfaces has been taken as a prototype in chemisorption study. Knowledge of the interaction between AM and surfaces is crucial in understanding fundamental physics and important technological applications. To our best knowledge, great effort has been devoted to AM adsorption on silicon surfaces [1–8,11–14], while Corresponding author. Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu, 610054, PR of China. Tel.: 86 28 83201939; fax: 86 28 83201939. E-mail addresses: [email protected] (H.Y. Xiao), [email protected] (X.T. Zu).
0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.03.015
germanium [15–17] and diamond surfaces [18] have gained much less attention. Diamond films are potential materials for commercial applications such as machine tools, optical coatings, and high-temperature electronics, due to its properties which include extreme hardness, high thermal conductivity, and chemical inertness [19]. From technological point of view, because of its favorable mechanical and thermal properties, diamond has been suggested as a suitable material for a number of applications even in extreme conditions, including its use as a possible replacement for silicon in electronic devices. The growth of diamond films on the (1 0 0) surface has been successfully achieved by the technique of chemical vapor deposition (CVD) [20,21]. In early LEED study performed by Lurie and Wilson it was observed that the reconstruction of the C(1 0 0) surface consisting of a (2 1) pattern at elevated temperature (about 1300 K) [22]. It is well known that the ideal C(1 0 0) surface is characterized by two dangling bonds per surface atom, leading to a variety of bonding possibilities, and a rich and varied surface chemistry. Numerous theoretical and experimental studies have been devoted to investigate
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the bare diamond surface [23–29] and most of the investigations have given supports to the reconstruction of the C(1 0 0) surface with rows of surface symmetric dimers formed. Hydrogen-covered C(1 0 0) surface has been investigated extensively and it was also found that symmetric C–C dimer exists with hydrogen coverage up to 1 ML [30–33]. Despite the importance of the interaction between AM and diamond surfaces, information on this issue is still limited. Recently, Hossain et al. [18] have studied K adsorption on C(1 0 0) surface using EELS and TDS techniques. It was demonstrated that two different chemisorbed states of K on the C(1 0 0) surface exist at higher coverage (above 0.5 ML). They also proposed that at low coverage (below 0.5 ML) K-substrate bond is highly polarized, and charge regain of K adatoms occurs with increasing coverage. To reveal the interaction nature between Na, K and diamond surface, we have performed ab initio studies on the chemisorption of Na and K in our previous work [34]. Some experimental observations were explained and adsorption states were assigned. Recently, Xiao and Zu of our research group found the adsorption behavior of AMs on Ge(0 0 1) surface are size dependent [35]. Since no experimental and theoretical investigation of Rb/C(0 0 1) system has been reported so far, here we performed the calculations of Rb adsorption on C(1 0 0) surface and compared the results with those of Na and K adsorption. This adsorption system was studied by selfconsistent, periodic, density-functional theory (DFT) calculations. The development of electron structure calculations using DFT has been rapid during the last decade and it has now become feasible to obtain quite-high accuracy for a variety of systems [9,36]. The preferred binding sites, detailed adsorption structures and binding energies have been determined. The surface relaxation and work function due to Rb adsorption have also been analyzed. All results have been compared with those of Na and K adsorption on C(1 0 0)(2 1) surface. 2. Computational details All calculations presented in this work were carried out utilizing plane-wave pseudopotential method within DFT framework. The C(1 0 0) surface was modeled by an eightlayer slab periodically repeated in a supercell geometry with fifteen equivalent layers of vacuum between any two successive slabs. The interaction between ions and electrons is described using ultrasoft pseudopotentials introduced by Vanderbilt [37] and provided by Kresse and Hafner [38]. The generalized gradient approximation functional proposed by Perdew and Wang, known as PW91, is used [39]. The electronic ground state is calculated with residuumminimization technique. The geometric structure is optimized with conjugated-gradient technique. For the calculation of the fractional occupancies, a broadening approach proposed by Methfessel and Paxton is used with a width of 0.1 eV [40]. All total energies have been extrapolated to KBT ¼ 0 eV. The influence of different K-point sampling
Table 1 Total energy per C atom (eV) as a function of kinetic cutoff energy and k points Kinetic cutoff energy (eV)
300
350
k-point scheme
Total energy per C atom (eV)
441 661 881
8.03 8.01 8.01
7.98 7.96 7.96
400
7.97 7.95 7.95
and plane-wave cutoff energy was explored in a series of test calculations, leading to the calculations being performed with 6 6 1 k-point sampling and a cutoff energy of 350 eV. The results are reported in Table 1. For Rb adsorption on C(1 0 0)(2 1) surface, Rb atoms are adsorbed on one side of the diamond surfaces. The pseudopotential of C atoms has been tested in our previous work [34], where lattice constant of 3.57 A˚ has been obtained, in excellent agreement with the experimental value of 3.57 A˚ [41]. For bulk rubidium, the optimized lattice constant was 5.66 A˚, agreeing well with experimental values of 5.59 A˚. Our calculation gave a cohesive energy of 0.80 eV, corresponding to experimental value of 0.90 eV. The cohesive energy of Rb is defined as the difference between the energy per free Rb atom and the energy per bulk atom. Spin polarized calculation has been performed for isolated Rb atom, which was placed in a box with size of 14 14 14 A˚. 3. Results and discussion 3.1. Energetic properties of the Rb–C(1 0 0) chemisorption system The reconstruction of bare C(1 0 0)(2 1) surface consists of symmetric diamond dimers has been obtained in our previous work [34] which is in good agreement with other works [23,26,27,29]. The bond length of the dimer is determined to be 1.38 A˚, agreeing well with other available calculated results [23,26,27,29]. A buckling in the third substrate layer has been found to be 0.26 A˚ and for the fourth layer it goes with 0.14 A˚, corresponding to the values of 0.26 A˚ and 0.14 A˚ obtained from DFT calculations performed by Kress et al. [27]. All the following chemisorption studies are performed on this reconstructed diamond surface. On the dimerized C(1 0 0)(2 1) surface, the existing four high-symmetric sites named pedestal (HH), valley bridge (T3, on top a third layer Si atom), bridge (HB), and cave (T4, on top a fourth layer Si atom) sites all have been considered, as shown in Fig. 1. The adsorption energy of Rb adsorbate on the C(1 0 0)(2 1) surface is defined as Eads ¼ (ERbC(1 0 0)–EC(1 0 0)–NERb )/N, where ERbC(1 0 0) and EC(1 0 0) are the total energy of the C(1 0 0) system with or without adsorbed atoms, ERb is the total energy of an
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isolated Rb atom, and N is the number of the Rb atoms in the surface unit cell. In the case of Y ¼ 0.5 ML, It is found that Rb adsorbate prefer to occupy T3 site on C(1 0 0) surface. As listed in Table 2, the adsorption energy of 1.35 eV has been obtained for T3 site which is lower than those of other adsorption sites up to 0.80 eV. In our previous paper [34], it has been found that T3 site is also energetically most favorable for Na and K on C(1 0 0) surface. These results suggest that the adsorption of AMs on C(1 0 0)(2 1) surface are consistent in adsorption site. For AMs adsorption on Si(0 0 1)(2 1) surface, most of the experimental and theoretical investigations have also given supports to T3 site adsorption [2,4,5,7,42]. To investigate the nature of interaction between Sb and C at higher coverage, two Sb atoms adsorbed in C(1 0 0)(2 1) unit cell have also been considered in the present work corresponding to the coverage of 1 ML. Six possible combinations of the four high symmetric sites have been considered. Our results indicated that there exist
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two different chemisorbed sites for AM adsorbed on C(1 0 0) surface at Y ¼ 1 ML, in consistent with those experimentally observed for K on C(1 0 0) surface [18]. It turned out that the combinations of HB-HH and T3-T4 are not stable for Sb. The combination of HH-T3 is energetically most favorable with adsorption energy of 0.90 eV per atom. Other three stable adsorption combinations are higher in adsorption energy up to 0.48 eV. For Na and K adsorption on C(1 0 0) surface studied in our previous work, it has also been found that HH-T3 is most favorable [34], suggesting that the energetic property for different AM adsorption on C(1 0 0) surface is similar both at the coverage of 0.5 ML and higher coverage of 1 ML. Numerous investigations of AM/Si(1 0 0) systems have also found the configuration of HH-T3 to be the most stable state at Y ¼ 1 ML [2,5,7]. It is noted that when the coverage was increased from 0.5 to 1 ML, the adsorption energy of Rb is found to increase significantly, implying a weaker adsorbate-substrate interaction. This has been ascribed to the consequence of the significant depolarization effects in our previous work [34]. 3.2. Coverage dependence of the atomic structures of Rb–C(1 0 0) system
Fig. 1. Schematic view of the four high-symmetry sites on dimerized C(1 0 0)(2 1) surface. The dashed rectangle denotes the 2 1 unit cells.
The structural parameters including Rb–C bond length, the binding height for Rb adsorbates, the C–C bond length and the interlayer buckling in the third and the fourth layers are given in Table 2. Some important parameters such as adsorption energy and AM-C bond length and the binding height for the Rb adsorbates at the favorable site comparing with those of Na and K [34] have been summarized in Table 3. To get a clear picture of the atomic structure of the chemisorption system, we have the side views of the optimized structures with Rb adsorbed
Table 2 Energetic and structural parameters for the C(1 0 0)(2 1) surface with Rb adsorption Site
Eads (eV)
dRbC (A˚)
h (A˚)
Bare surfacea HB HH T3 T4
0.55 0.83 1.35 0.80
3.10 2.96 2.96 2.90
HB–T3
0.42
HB–T4
0.58
HH–T3
0.90
HH–T4
0.41
2.76 2.89 2.86 2.93 2.80 2.95 2.77 2.85
Y ¼ 0.5 ML 3.02 2.58 1.99 2.28 Y ¼ 1.0 ML 2.65 1.93 2.76 2.33 2.38 2.01 2.34 2.26
dCC (A˚)
Dz3 (A˚)
Dz4 (A˚)
1.38
0.26
0.14
1.43 1.46 1.47 1.46
0.25 0.24 0.23 0.23
0.13 0.12 0.12 0.12
1.55
0.20
0.11
1.50
0.22
0.12
1.55
0.21
0.11
1.57
0.20
0.10
Eads is the adsorption energy per atom, h is the shortest binding height with respect to the first layer Z. dRbC is the distance between Rb and the closest C atom. dCC represents the bond length of the C–C dimer. Dz3 and Dz4 are the interlayer buckling of the third layer and fourth layer, respectively. a From Ref. [34].
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Table 3 Comparing of some important features for the most favorable adsorption structures with different AM adsorption on C(1 0 0) (2 1) surface AM
T3
HH-T3
Eads (eV)
dAMC (A˚)
h (A˚)
Eads (eV)
dAMC (A˚)
h (A˚)
Rb
1.35
2.96
1.99
0.90
Ka
1.09
2.83
1.80
0.28
Na
1.32
2.63
1.49
1.00
2.95 2.80 2.77 2.72 2.61 2.48
2.38 2.01 2.35 1.65 2.14 1.25
a
From Ref. [34].
Fig. 3. Side and top view of the optimized structures of the Rb/ C(1 0 0)(2 1) adsorption system at Y ¼ 1 ML. Fig. 2. Side and top view of the optimized structures of Rb/C(1 0 0)(2 1) adsorption system at Y ¼ 0.5 ML.
C(1 0 0)(2 1) surface illustrated in Fig. 2 and Fig. 3. The Rb–C bond length has been calculated to be 2.96 A˚ at Y ¼ 0.5 ML comparing with 2.63 A˚ of Na-C bond length and K-C bond length of 2.83 A˚ [34]. The vertical distance between adsorbed Rb and substrate C is 1.99 A˚. When there’re two Rb atoms adsorbed on C(1 0 0)(2 1) surface
corresponding to Y ¼ 1 ML, it is found that the structural appearance is quite different from that of Y ¼ 0.5 ML. The two adsorbates were found to reside in different distance from the substrate with the bond length between the upper Rb atom and the nearest neighbor C atom being 2.95 A˚ and that of the lower Rb adatom being 2.80 A˚. This indicates that there exists about 0.15 A˚ difference between
ARTICLE IN PRESS J.L. Nie et al. / Physica B 383 (2006) 219–225 Table 4 Relaxation of the C(1 0 0) (2 1) surface with different AM adsorption Site Rb Naa Ka
T3 HH-T3 T3 HH-T3 T3 HH-T3
D12/d0 (%)
D23/d0 (%)
D34/d0 (%)
18.3 13.7 15.0 10.6 17.6 12.0
9.2 8.8 7.7 8.0 8.0 8.6
20.0 18.2 18.6 17.0 19.7 18.0
D12, D23 and D34 represent the interlayer spacing of the four outmost layers of the relaxed surface with AM adsorption. d0 denotes the interlayer spacing of the bulk like surface. a From Ref. [34].
the bond length of the two adsorbates. The first principles studies on the Na and K-C(1 0 0) systems have indicated that the difference between the two adsorbed Na adatoms is 0.13 A˚ and that for K is negligible with the difference being 0.05 A˚ [34]. Similar behavior of the AM adsorbates have also been found on Si(1 0 0) surface as Shi et al. have reported a bond length of 3.18 A˚ for the upper K adatom on Si(1 0 0) surface and 3.38 A˚ for the lower one [7]. The vertical distance between adsorbed Rb and substrate C are 2.38 A˚ and 2.01 A˚ resulting in the vertical distance between two Rb adatoms of 0.37 A˚. Those for Na and K reported in the previous work have also been listed in Table 3. The adsorption of Rb adatoms was found to caused considerable relaxation of the C(1 0 0) surface. The relaxation of the four outmost layers represented by D12, D23 and D34 given as a percentage of the ideal interlayer distance have been summarized in Table 4. At the Rb coverage of 0.5 ML, the substrate surface was found to contract comparing with the bulk like surface with D12/ d0 ¼ 18.3%, D23/d0 ¼ 9.2%and D34/d0 ¼ 20%, where d0 represents the ideal interlayer distance. When the coverage was increased to 1 ML, the relaxation of the C(1 0 0) surface was found to be similar to D12/d0 ¼ 13.7%, D23/ d0 ¼ 8.8%and D34/d0 ¼ 18.2%. For Na adsorption, the calculated results are D12/ d0 ¼ 15%, D23/ d0 ¼ 7.7%, D34/ d0 ¼ 18.6% at Y ¼ 0.5 ML and D12/d0 ¼ 10.6%, D23/ d0 ¼ 8%, D34/d0 ¼ 17% at Y ¼ 1 ML. D12/d0 ¼ 17.6%, D23/d0 ¼ 8%, D34/d0 ¼ 19.7% at Y ¼ 0.5 ML and D12/ d0 ¼ 12%, D23/d0 ¼ 8.6%, D34/d0 ¼ 18% at Y ¼ 1 ML were obtained for K adsorption [34]. It is shown that the relaxation of the C substrate due to different AM adsorption is quite similar. 3.3. The change of the C–C bond due to the AM adsorption When Rb atoms are adsorbed on C(1 0 0)(2 1) surface, the C–C dimer bond length of the C(1 0 0) surface is found to be elongated with the symmetry of the dimer preserved. The dimer bond length is increased by 0.09 A˚ with respect to that of bare C(1 0 0)(2 1) surface. The elongate of the C–C dimer due to the adsorption of Na and K have also
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been reported [34]. This finding is consistent with that obtained by Kobayashi et al. [2] for Na and K-adsorbed Si(0 0 1) surface. The dimer bond length of the asymmetric Si dimer have been determined to be 2.26, 2.42, and 2.38 A˚ for the clean, Na and K covered surface, respectively [2]. For the coverage of 1 ML, the C–C dimer bond length yield a value of 1.55 A˚ which is 0.17 A˚ larger than that of bare C(1 0 0)(2 1) surface. Its shown that when the coverage is increased from 0.5 to 1 ML the dimer bond length was elongated by 0.08 A˚, indicating that the dimer bond becomes weaker with increasing coverage. The elongation of the C–C bond length by 0.5 ML of Na and K has been reported to be 0.14 and 0.1 A˚, respectively. At Y ¼ 1 ML, the elongation was obtained as 0.21 A˚ for Na and 0.16 A˚ for K adsorption, respectively [34]. As analysis in our previous work [34], this dimer-bond elongate may be ascribed to the occupation of antibonding p* bands of carbon dimer dangling bonds by the donation of valence electrons from AM adatoms. The same conclusion has been drawn from our previous investigations of AM adsorption on Si and Ge(0 0 1)(2 1) surface [9,35,43]. All the results suggested that AM adsorption on C(1 0 0)(2 1) surface is AM size and coverage dependent. 3.4. Work function analysis Work function study showed that work function changes significantly due to Rb adsorption. The work function change is defined as Dj ¼ jRbCjC, where jRb–C and jC denotes the work function of the Rb–C(1 0 0) chemisorption system and the bare substrate surface, respectively. The work function value j is defined by the formula j ¼ EvacEF, where Evac is the vacuum energy, and EF is the Fermi energy of the system. The vacuum energy is estimated by averaging the electrostatic potential of the vacuum layers. In the previous work [34], the work function of the bare diamond surface has been calculated to be 5.54 eV, which is in good agreement with the diamond band gap of 5.47 eV [44]. With Rb adsorption, its found that the work function of the chemisorption system is decreased dramatically’, DF being 2.80 eV at Y ¼ 0.5 ML. When Rb coverage was increased to 1 ML, the work function was found to be considerably increased comparing with that at Y ¼ 0.5 ML with DF of 2.4 eV. This is in consistent with that the adsorption of AM on a solid surface remarkably decreases the substrate work function. Hossain et al. [18] have experimentally observed a similar trend of work function change upon K adsorption on C(1 0 0). The current result for Rb adsorption on C(1 0 0) surface is also similar with those of Na and K adsorption [34] as illustrated in Fig. 4. It was showed that the work function decreased sharply for AMs at Y ¼ 0.5 ML and considerably increased at Y ¼ 1 ML. As analysis in the previous paper, the sharp decrease of the work function at Y ¼ 0.5 ML indicate that the adsorbed AM atoms, whose dipoles are oriented perpendicular to the surface, are strongly polarized. The considerable increase of the work
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on C(1 0 0)(2 1) surface the work function decreasing linearly with increasing coverage, up to a minimum, and finally increasing again because of the depolarization of the adsorbate was found to be in excellent agreement with experiments. Acknowledgments This study was supported financially by the Program for New Century Excellent Talents in University (NCET-040899) and the Ph.D. Funding Support Program of Education Ministry of China (20050614013) and by the Sichuan Young Scientists Foundation (03ZQ026-059). References Fig. 4. The coverage dependence of the work-function change due to Rb adsorption with comparison of those of Na and K adsorption. The solid, dotted and dashed line correspond to Rb, Na and K adsorption, respectively.
function at Y ¼ 1 ML relative to that at Y ¼ 0.5 ML indicates charge regain of the AMs upon adsorption on diamond surface [18]. The trend of work function change due to AM adsorption on diamond surface was found to be somewhat different from that of potassium on silicon surface for which it has been shown that the work function change does not pass through a minimum up to Y ¼ 1 ML [5]. 4. Conclusions Density-functional theory with generalized gradient approximation has been used to study rubidium adsorption on C(1 0 0)(2 1) surface. The atomic and electronic structures of the Rb–C(1 0 0) chemisorption system have been calculated and compared with those for Na and K adsorption studied previously. One and two Rb adatoms adsorbed on the C(1 0 0)(2 1) surface have been considered, corresponding to the coverage of 0.5 and 1 ML. With the adsorption of Rb, the C–C dimer bond length of the C(1 0 0) surface is found to be elongated with the symmetry of the dimer preserved. The substrate surface has shown considerable relaxation due to Rb adsorption. At the coverage of 0.5 ML, in the calculated results it turned out that T3 site is energetically preferred for Rb with adsorption energy of 1.35 eV being lower than that of the less stable site by 0.52 eV. When the Rb coverage was increased to 1 ML, the most stable configuration is determined to be the combination of the HH and T3 sites with the adsorption energy of 0.90 eV per atom. The atomic structures of the Rb–C(1 0 0) system with two Rb adsorbates are found to be quite different from that with one adsorbate. Work-function analysis showed that for Rb adsorption, the work function change decreases to 2.80 eV as the coverage increases to 0.5 ML, then increases to 2.4 eV at the coverage of 1 ML. The fact that upon AM adsorption
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Physica B 383 (2006) 219–225 www.elsevier.com/locate/physb
Atomic and electronic structures of the Rb–C(1 0 0) chemisorption system J.L. Niea, H.Y. Xiaoa, X.T. Zua,b,, Fei Gaoc a
Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu, 610054, PR China b International Center for Material Physics, Chinese Academy of Sciences, Shenyang 110015, PR China c Pacific Northwest National Laboratory, MS K8-93, P. O. Box 999, Richland, WA 99352, USA Received 23 January 2006; received in revised form 1 March 2006; accepted 14 March 2006
Abstract First-principles calculations based on DFT–GGA method have been performed on Rb adsorption on C(1 0 0)(2 1) surface. The optimized geometries, adsorption energies have been obtained and the preferred binding sites have been determined for the coverage (Y) of one monolayer and half a monolayer. The calculated results have shown that Rb adsorbate preferred to occupy valley-bridge sites at the coverage of 0.5 ML. At higher coverage of 1 ML, two Rb adsorbates were found to reside in pedestal site and valley-bridge site, respectively. It was also found that when Rb was adsorbed on C(1 0 0)(2 1) surface the work function decreases linearly with increasing coverage and reaches a minimum at Y ¼ 0.5 ML, at higher coverage, the work function is increased again, which may be caused by depolarization effect of the adsorbate. The adsorption behavior was found to be similar to that of Rb on Si(0 0 1) and Ge(0 0 1) surface. r 2006 Elsevier B.V. All rights reserved. Keywords: First-principles calculations; Diamond; Rubidium; Work function
1. Introduction The electronic and structural properties of alkali metal (AM) adsorption on the semiconductor surfaces have been intensively investigated in the last two decades [1–9]. The strong interest in these adsorption systems has been raised in that it plays an important role in electrochemistry and heterogeneous catalysis [10]. On the other hand, since the electronic structures of alkali atoms are very simple, the study on the adsorption of AMs on metal surfaces has been taken as a prototype in chemisorption study. Knowledge of the interaction between AM and surfaces is crucial in understanding fundamental physics and important technological applications. To our best knowledge, great effort has been devoted to AM adsorption on silicon surfaces [1–8,11–14], while Corresponding author. Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu, 610054, PR of China. Tel.: 86 28 83201939; fax: 86 28 83201939. E-mail addresses: [email protected] (H.Y. Xiao), [email protected] (X.T. Zu).
0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.03.015
germanium [15–17] and diamond surfaces [18] have gained much less attention. Diamond films are potential materials for commercial applications such as machine tools, optical coatings, and high-temperature electronics, due to its properties which include extreme hardness, high thermal conductivity, and chemical inertness [19]. From technological point of view, because of its favorable mechanical and thermal properties, diamond has been suggested as a suitable material for a number of applications even in extreme conditions, including its use as a possible replacement for silicon in electronic devices. The growth of diamond films on the (1 0 0) surface has been successfully achieved by the technique of chemical vapor deposition (CVD) [20,21]. In early LEED study performed by Lurie and Wilson it was observed that the reconstruction of the C(1 0 0) surface consisting of a (2 1) pattern at elevated temperature (about 1300 K) [22]. It is well known that the ideal C(1 0 0) surface is characterized by two dangling bonds per surface atom, leading to a variety of bonding possibilities, and a rich and varied surface chemistry. Numerous theoretical and experimental studies have been devoted to investigate
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the bare diamond surface [23–29] and most of the investigations have given supports to the reconstruction of the C(1 0 0) surface with rows of surface symmetric dimers formed. Hydrogen-covered C(1 0 0) surface has been investigated extensively and it was also found that symmetric C–C dimer exists with hydrogen coverage up to 1 ML [30–33]. Despite the importance of the interaction between AM and diamond surfaces, information on this issue is still limited. Recently, Hossain et al. [18] have studied K adsorption on C(1 0 0) surface using EELS and TDS techniques. It was demonstrated that two different chemisorbed states of K on the C(1 0 0) surface exist at higher coverage (above 0.5 ML). They also proposed that at low coverage (below 0.5 ML) K-substrate bond is highly polarized, and charge regain of K adatoms occurs with increasing coverage. To reveal the interaction nature between Na, K and diamond surface, we have performed ab initio studies on the chemisorption of Na and K in our previous work [34]. Some experimental observations were explained and adsorption states were assigned. Recently, Xiao and Zu of our research group found the adsorption behavior of AMs on Ge(0 0 1) surface are size dependent [35]. Since no experimental and theoretical investigation of Rb/C(0 0 1) system has been reported so far, here we performed the calculations of Rb adsorption on C(1 0 0) surface and compared the results with those of Na and K adsorption. This adsorption system was studied by selfconsistent, periodic, density-functional theory (DFT) calculations. The development of electron structure calculations using DFT has been rapid during the last decade and it has now become feasible to obtain quite-high accuracy for a variety of systems [9,36]. The preferred binding sites, detailed adsorption structures and binding energies have been determined. The surface relaxation and work function due to Rb adsorption have also been analyzed. All results have been compared with those of Na and K adsorption on C(1 0 0)(2 1) surface. 2. Computational details All calculations presented in this work were carried out utilizing plane-wave pseudopotential method within DFT framework. The C(1 0 0) surface was modeled by an eightlayer slab periodically repeated in a supercell geometry with fifteen equivalent layers of vacuum between any two successive slabs. The interaction between ions and electrons is described using ultrasoft pseudopotentials introduced by Vanderbilt [37] and provided by Kresse and Hafner [38]. The generalized gradient approximation functional proposed by Perdew and Wang, known as PW91, is used [39]. The electronic ground state is calculated with residuumminimization technique. The geometric structure is optimized with conjugated-gradient technique. For the calculation of the fractional occupancies, a broadening approach proposed by Methfessel and Paxton is used with a width of 0.1 eV [40]. All total energies have been extrapolated to KBT ¼ 0 eV. The influence of different K-point sampling
Table 1 Total energy per C atom (eV) as a function of kinetic cutoff energy and k points Kinetic cutoff energy (eV)
300
350
k-point scheme
Total energy per C atom (eV)
441 661 881
8.03 8.01 8.01
7.98 7.96 7.96
400
7.97 7.95 7.95
and plane-wave cutoff energy was explored in a series of test calculations, leading to the calculations being performed with 6 6 1 k-point sampling and a cutoff energy of 350 eV. The results are reported in Table 1. For Rb adsorption on C(1 0 0)(2 1) surface, Rb atoms are adsorbed on one side of the diamond surfaces. The pseudopotential of C atoms has been tested in our previous work [34], where lattice constant of 3.57 A˚ has been obtained, in excellent agreement with the experimental value of 3.57 A˚ [41]. For bulk rubidium, the optimized lattice constant was 5.66 A˚, agreeing well with experimental values of 5.59 A˚. Our calculation gave a cohesive energy of 0.80 eV, corresponding to experimental value of 0.90 eV. The cohesive energy of Rb is defined as the difference between the energy per free Rb atom and the energy per bulk atom. Spin polarized calculation has been performed for isolated Rb atom, which was placed in a box with size of 14 14 14 A˚. 3. Results and discussion 3.1. Energetic properties of the Rb–C(1 0 0) chemisorption system The reconstruction of bare C(1 0 0)(2 1) surface consists of symmetric diamond dimers has been obtained in our previous work [34] which is in good agreement with other works [23,26,27,29]. The bond length of the dimer is determined to be 1.38 A˚, agreeing well with other available calculated results [23,26,27,29]. A buckling in the third substrate layer has been found to be 0.26 A˚ and for the fourth layer it goes with 0.14 A˚, corresponding to the values of 0.26 A˚ and 0.14 A˚ obtained from DFT calculations performed by Kress et al. [27]. All the following chemisorption studies are performed on this reconstructed diamond surface. On the dimerized C(1 0 0)(2 1) surface, the existing four high-symmetric sites named pedestal (HH), valley bridge (T3, on top a third layer Si atom), bridge (HB), and cave (T4, on top a fourth layer Si atom) sites all have been considered, as shown in Fig. 1. The adsorption energy of Rb adsorbate on the C(1 0 0)(2 1) surface is defined as Eads ¼ (ERbC(1 0 0)–EC(1 0 0)–NERb )/N, where ERbC(1 0 0) and EC(1 0 0) are the total energy of the C(1 0 0) system with or without adsorbed atoms, ERb is the total energy of an
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isolated Rb atom, and N is the number of the Rb atoms in the surface unit cell. In the case of Y ¼ 0.5 ML, It is found that Rb adsorbate prefer to occupy T3 site on C(1 0 0) surface. As listed in Table 2, the adsorption energy of 1.35 eV has been obtained for T3 site which is lower than those of other adsorption sites up to 0.80 eV. In our previous paper [34], it has been found that T3 site is also energetically most favorable for Na and K on C(1 0 0) surface. These results suggest that the adsorption of AMs on C(1 0 0)(2 1) surface are consistent in adsorption site. For AMs adsorption on Si(0 0 1)(2 1) surface, most of the experimental and theoretical investigations have also given supports to T3 site adsorption [2,4,5,7,42]. To investigate the nature of interaction between Sb and C at higher coverage, two Sb atoms adsorbed in C(1 0 0)(2 1) unit cell have also been considered in the present work corresponding to the coverage of 1 ML. Six possible combinations of the four high symmetric sites have been considered. Our results indicated that there exist
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two different chemisorbed sites for AM adsorbed on C(1 0 0) surface at Y ¼ 1 ML, in consistent with those experimentally observed for K on C(1 0 0) surface [18]. It turned out that the combinations of HB-HH and T3-T4 are not stable for Sb. The combination of HH-T3 is energetically most favorable with adsorption energy of 0.90 eV per atom. Other three stable adsorption combinations are higher in adsorption energy up to 0.48 eV. For Na and K adsorption on C(1 0 0) surface studied in our previous work, it has also been found that HH-T3 is most favorable [34], suggesting that the energetic property for different AM adsorption on C(1 0 0) surface is similar both at the coverage of 0.5 ML and higher coverage of 1 ML. Numerous investigations of AM/Si(1 0 0) systems have also found the configuration of HH-T3 to be the most stable state at Y ¼ 1 ML [2,5,7]. It is noted that when the coverage was increased from 0.5 to 1 ML, the adsorption energy of Rb is found to increase significantly, implying a weaker adsorbate-substrate interaction. This has been ascribed to the consequence of the significant depolarization effects in our previous work [34]. 3.2. Coverage dependence of the atomic structures of Rb–C(1 0 0) system
Fig. 1. Schematic view of the four high-symmetry sites on dimerized C(1 0 0)(2 1) surface. The dashed rectangle denotes the 2 1 unit cells.
The structural parameters including Rb–C bond length, the binding height for Rb adsorbates, the C–C bond length and the interlayer buckling in the third and the fourth layers are given in Table 2. Some important parameters such as adsorption energy and AM-C bond length and the binding height for the Rb adsorbates at the favorable site comparing with those of Na and K [34] have been summarized in Table 3. To get a clear picture of the atomic structure of the chemisorption system, we have the side views of the optimized structures with Rb adsorbed
Table 2 Energetic and structural parameters for the C(1 0 0)(2 1) surface with Rb adsorption Site
Eads (eV)
dRbC (A˚)
h (A˚)
Bare surfacea HB HH T3 T4
0.55 0.83 1.35 0.80
3.10 2.96 2.96 2.90
HB–T3
0.42
HB–T4
0.58
HH–T3
0.90
HH–T4
0.41
2.76 2.89 2.86 2.93 2.80 2.95 2.77 2.85
Y ¼ 0.5 ML 3.02 2.58 1.99 2.28 Y ¼ 1.0 ML 2.65 1.93 2.76 2.33 2.38 2.01 2.34 2.26
dCC (A˚)
Dz3 (A˚)
Dz4 (A˚)
1.38
0.26
0.14
1.43 1.46 1.47 1.46
0.25 0.24 0.23 0.23
0.13 0.12 0.12 0.12
1.55
0.20
0.11
1.50
0.22
0.12
1.55
0.21
0.11
1.57
0.20
0.10
Eads is the adsorption energy per atom, h is the shortest binding height with respect to the first layer Z. dRbC is the distance between Rb and the closest C atom. dCC represents the bond length of the C–C dimer. Dz3 and Dz4 are the interlayer buckling of the third layer and fourth layer, respectively. a From Ref. [34].
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Table 3 Comparing of some important features for the most favorable adsorption structures with different AM adsorption on C(1 0 0) (2 1) surface AM
T3
HH-T3
Eads (eV)
dAMC (A˚)
h (A˚)
Eads (eV)
dAMC (A˚)
h (A˚)
Rb
1.35
2.96
1.99
0.90
Ka
1.09
2.83
1.80
0.28
Na
1.32
2.63
1.49
1.00
2.95 2.80 2.77 2.72 2.61 2.48
2.38 2.01 2.35 1.65 2.14 1.25
a
From Ref. [34].
Fig. 3. Side and top view of the optimized structures of the Rb/ C(1 0 0)(2 1) adsorption system at Y ¼ 1 ML. Fig. 2. Side and top view of the optimized structures of Rb/C(1 0 0)(2 1) adsorption system at Y ¼ 0.5 ML.
C(1 0 0)(2 1) surface illustrated in Fig. 2 and Fig. 3. The Rb–C bond length has been calculated to be 2.96 A˚ at Y ¼ 0.5 ML comparing with 2.63 A˚ of Na-C bond length and K-C bond length of 2.83 A˚ [34]. The vertical distance between adsorbed Rb and substrate C is 1.99 A˚. When there’re two Rb atoms adsorbed on C(1 0 0)(2 1) surface
corresponding to Y ¼ 1 ML, it is found that the structural appearance is quite different from that of Y ¼ 0.5 ML. The two adsorbates were found to reside in different distance from the substrate with the bond length between the upper Rb atom and the nearest neighbor C atom being 2.95 A˚ and that of the lower Rb adatom being 2.80 A˚. This indicates that there exists about 0.15 A˚ difference between
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T3 HH-T3 T3 HH-T3 T3 HH-T3
D12/d0 (%)
D23/d0 (%)
D34/d0 (%)
18.3 13.7 15.0 10.6 17.6 12.0
9.2 8.8 7.7 8.0 8.0 8.6
20.0 18.2 18.6 17.0 19.7 18.0
D12, D23 and D34 represent the interlayer spacing of the four outmost layers of the relaxed surface with AM adsorption. d0 denotes the interlayer spacing of the bulk like surface. a From Ref. [34].
the bond length of the two adsorbates. The first principles studies on the Na and K-C(1 0 0) systems have indicated that the difference between the two adsorbed Na adatoms is 0.13 A˚ and that for K is negligible with the difference being 0.05 A˚ [34]. Similar behavior of the AM adsorbates have also been found on Si(1 0 0) surface as Shi et al. have reported a bond length of 3.18 A˚ for the upper K adatom on Si(1 0 0) surface and 3.38 A˚ for the lower one [7]. The vertical distance between adsorbed Rb and substrate C are 2.38 A˚ and 2.01 A˚ resulting in the vertical distance between two Rb adatoms of 0.37 A˚. Those for Na and K reported in the previous work have also been listed in Table 3. The adsorption of Rb adatoms was found to caused considerable relaxation of the C(1 0 0) surface. The relaxation of the four outmost layers represented by D12, D23 and D34 given as a percentage of the ideal interlayer distance have been summarized in Table 4. At the Rb coverage of 0.5 ML, the substrate surface was found to contract comparing with the bulk like surface with D12/ d0 ¼ 18.3%, D23/d0 ¼ 9.2%and D34/d0 ¼ 20%, where d0 represents the ideal interlayer distance. When the coverage was increased to 1 ML, the relaxation of the C(1 0 0) surface was found to be similar to D12/d0 ¼ 13.7%, D23/ d0 ¼ 8.8%and D34/d0 ¼ 18.2%. For Na adsorption, the calculated results are D12/ d0 ¼ 15%, D23/ d0 ¼ 7.7%, D34/ d0 ¼ 18.6% at Y ¼ 0.5 ML and D12/d0 ¼ 10.6%, D23/ d0 ¼ 8%, D34/d0 ¼ 17% at Y ¼ 1 ML. D12/d0 ¼ 17.6%, D23/d0 ¼ 8%, D34/d0 ¼ 19.7% at Y ¼ 0.5 ML and D12/ d0 ¼ 12%, D23/d0 ¼ 8.6%, D34/d0 ¼ 18% at Y ¼ 1 ML were obtained for K adsorption [34]. It is shown that the relaxation of the C substrate due to different AM adsorption is quite similar. 3.3. The change of the C–C bond due to the AM adsorption When Rb atoms are adsorbed on C(1 0 0)(2 1) surface, the C–C dimer bond length of the C(1 0 0) surface is found to be elongated with the symmetry of the dimer preserved. The dimer bond length is increased by 0.09 A˚ with respect to that of bare C(1 0 0)(2 1) surface. The elongate of the C–C dimer due to the adsorption of Na and K have also
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been reported [34]. This finding is consistent with that obtained by Kobayashi et al. [2] for Na and K-adsorbed Si(0 0 1) surface. The dimer bond length of the asymmetric Si dimer have been determined to be 2.26, 2.42, and 2.38 A˚ for the clean, Na and K covered surface, respectively [2]. For the coverage of 1 ML, the C–C dimer bond length yield a value of 1.55 A˚ which is 0.17 A˚ larger than that of bare C(1 0 0)(2 1) surface. Its shown that when the coverage is increased from 0.5 to 1 ML the dimer bond length was elongated by 0.08 A˚, indicating that the dimer bond becomes weaker with increasing coverage. The elongation of the C–C bond length by 0.5 ML of Na and K has been reported to be 0.14 and 0.1 A˚, respectively. At Y ¼ 1 ML, the elongation was obtained as 0.21 A˚ for Na and 0.16 A˚ for K adsorption, respectively [34]. As analysis in our previous work [34], this dimer-bond elongate may be ascribed to the occupation of antibonding p* bands of carbon dimer dangling bonds by the donation of valence electrons from AM adatoms. The same conclusion has been drawn from our previous investigations of AM adsorption on Si and Ge(0 0 1)(2 1) surface [9,35,43]. All the results suggested that AM adsorption on C(1 0 0)(2 1) surface is AM size and coverage dependent. 3.4. Work function analysis Work function study showed that work function changes significantly due to Rb adsorption. The work function change is defined as Dj ¼ jRbCjC, where jRb–C and jC denotes the work function of the Rb–C(1 0 0) chemisorption system and the bare substrate surface, respectively. The work function value j is defined by the formula j ¼ EvacEF, where Evac is the vacuum energy, and EF is the Fermi energy of the system. The vacuum energy is estimated by averaging the electrostatic potential of the vacuum layers. In the previous work [34], the work function of the bare diamond surface has been calculated to be 5.54 eV, which is in good agreement with the diamond band gap of 5.47 eV [44]. With Rb adsorption, its found that the work function of the chemisorption system is decreased dramatically’, DF being 2.80 eV at Y ¼ 0.5 ML. When Rb coverage was increased to 1 ML, the work function was found to be considerably increased comparing with that at Y ¼ 0.5 ML with DF of 2.4 eV. This is in consistent with that the adsorption of AM on a solid surface remarkably decreases the substrate work function. Hossain et al. [18] have experimentally observed a similar trend of work function change upon K adsorption on C(1 0 0). The current result for Rb adsorption on C(1 0 0) surface is also similar with those of Na and K adsorption [34] as illustrated in Fig. 4. It was showed that the work function decreased sharply for AMs at Y ¼ 0.5 ML and considerably increased at Y ¼ 1 ML. As analysis in the previous paper, the sharp decrease of the work function at Y ¼ 0.5 ML indicate that the adsorbed AM atoms, whose dipoles are oriented perpendicular to the surface, are strongly polarized. The considerable increase of the work
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on C(1 0 0)(2 1) surface the work function decreasing linearly with increasing coverage, up to a minimum, and finally increasing again because of the depolarization of the adsorbate was found to be in excellent agreement with experiments. Acknowledgments This study was supported financially by the Program for New Century Excellent Talents in University (NCET-040899) and the Ph.D. Funding Support Program of Education Ministry of China (20050614013) and by the Sichuan Young Scientists Foundation (03ZQ026-059). References Fig. 4. The coverage dependence of the work-function change due to Rb adsorption with comparison of those of Na and K adsorption. The solid, dotted and dashed line correspond to Rb, Na and K adsorption, respectively.
function at Y ¼ 1 ML relative to that at Y ¼ 0.5 ML indicates charge regain of the AMs upon adsorption on diamond surface [18]. The trend of work function change due to AM adsorption on diamond surface was found to be somewhat different from that of potassium on silicon surface for which it has been shown that the work function change does not pass through a minimum up to Y ¼ 1 ML [5]. 4. Conclusions Density-functional theory with generalized gradient approximation has been used to study rubidium adsorption on C(1 0 0)(2 1) surface. The atomic and electronic structures of the Rb–C(1 0 0) chemisorption system have been calculated and compared with those for Na and K adsorption studied previously. One and two Rb adatoms adsorbed on the C(1 0 0)(2 1) surface have been considered, corresponding to the coverage of 0.5 and 1 ML. With the adsorption of Rb, the C–C dimer bond length of the C(1 0 0) surface is found to be elongated with the symmetry of the dimer preserved. The substrate surface has shown considerable relaxation due to Rb adsorption. At the coverage of 0.5 ML, in the calculated results it turned out that T3 site is energetically preferred for Rb with adsorption energy of 1.35 eV being lower than that of the less stable site by 0.52 eV. When the Rb coverage was increased to 1 ML, the most stable configuration is determined to be the combination of the HH and T3 sites with the adsorption energy of 0.90 eV per atom. The atomic structures of the Rb–C(1 0 0) system with two Rb adsorbates are found to be quite different from that with one adsorbate. Work-function analysis showed that for Rb adsorption, the work function change decreases to 2.80 eV as the coverage increases to 0.5 ML, then increases to 2.4 eV at the coverage of 1 ML. The fact that upon AM adsorption
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