First-Principles Calculations of Atomic and Electronic Properties of Tl and In on Si(111)

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1 Commun. Theor. Phys. (Beijing, China) 54 (2010) pp c Chinese Physical Society and IOP Publishing Ltd Vol. 54, No. 3, September 15, 2010 First-Principles Calculations of Atomic and Electronic Properties of Tl and In on Si(111) DAI Xian-Qi (àđ), 1,2, ZHAO Jian-Hua ( Ù), 1 SUN Yong-Can (ê ), 1 WEI Shu-Yi ( þ), 1 and WEI Guo-Hong ( Á ) 1 1 College of Physics & Information Engineering, Henan Normal University, Xinxiang , China 2 Department of Physics, Zhengzhou Normal University, Zhengzhou , China (Received December 23, 2009; revised manuscript received February 11, 2010) Abstract The atomic and electronic structures of Tl and In on Si(111) surfaces are investigated using the firstprinciples total energy calculations. Total energy optimizations show that the energetically favored structure is 1/3 ML Tl adsorbed at the T 4 sites on Si(111) surfaces. The adsorption energy difference of one Tl adatom between ( 3 3) and (1 1) is less than that of each In adatom. The DOS indicates that Tl 6p and Si 3p electrons play a very important role in the formation of the surface states. It is concluded that the bonding of Tl adatoms on Si(111) surfaces is mainly polar covalent, which is weaker than that of In on Si(111). So Tl atom is more easy to be migrated than In atom in the same external electric field and the structures of Tl on Si(111) is prone to switch between ( 3 3) and (1 1). PACS numbers: Bc, E-, A-, f, Mb Key words: thallium, indium, silicon, charge density, adsorption, first principles 1 Introduction Adsorption of group-iii metals such as aluminum (Al), gallium (Ga), and indium (In) on silicon (Si) surfaces has been the subject of great theoretical and experimental interests due to their fundamental and technological promises. In particular, all three metals have been found to demonstrate a very similar behavior. On the Si(111)- (7 7) surface, they form magic cluster arrays at modest temperatures, [1 5] and a ( 3 3) reconstruction with a 1/3 monolayer (ML) coverage of metal atoms adsorbed on T 4 sites at higher temperatures. [6 7] Recently, the studies on group-iii metals on Si(111) surfaces have been expanded to the heaviest element of this group, thallium (T1), whose behavior differs from those of the lighter group-iii metals (Al, Ga, and In), i.e., Tl has a peculiar behavior in the form of the socalled inert pair effect. [8] Growth of the Tl overlayers on Si(111) and Ge(111) surfaces has been studied in the number of investigations. In the low-energy electron diffraction (LEED) studies, a (1 1) pattern was observed at Tl coverage of 1 ML [9 10] and a ( 3 3) pattern is observed at coverage of 1/3 ML. [11] The (1 1) phase has not been observed by the adsorption of other group-iii metals and where 6s 2 electrons of Tl have been considered inactive as an inert pair in the Tl-Si bonding so as to explain the presence of this phase. Hence, Tl was believed to be chemically more close to the monovalent metals. This feature is in sharp contrast with the trivalent nature found in the ( 3 3) phase observed commonly in all other group-iii elements on Si(111) surfaces. It is found that on the (111) surface T 4 sites is the most stable for Tl on the bulk terminated Si(111) surface. This adsorption sites has also been confirmed by recent LEED I(V) analysis. [12] Sakamoto et al. [13] showed recently that the charge state of the surface Si atoms on Tl/Si(111)-( 3 3) is different from that of the ( 3 3) surfaces induced by the other group-iii metals. In their very recent work, [14] using angle-resolved photoelectron spectroscopy (ARPES), three semiconducting surface states were observed in the gap of the bulk band projection. In addition, Ozkaya et al. [15] have also identified one unoccupied and two occupied surface states by calculating the electronic band structure for the T 4 configuration and determined the origin of these surface states. By means of LEED, Visikovskiy et al. [16] found a reversible structural change between (1 1) and ( 3 3) as thallium (T1) adsorbed on Si(111) surfaces by switching the polarity of applied DC voltage for heating the sample. It is clarified that the structural change is caused by the surface electromigration (SE) of the Tl adatoms. On the other hand, indium in group-iii metals, for example, undergoes SE by forming a surface silicide of (4 1), but it is an irreversible SE. Furthermore, it should be noted that SE would not occur in the case of (1 1)-Tl on the Ge(111) surface. That is to say, the present reversible SE is specific to Tl atoms on Si(111). However, to our best of knowledge there are little theoretical work to study the electronic properties of Tl on Si(111) and compare it with Supported by National Natural Science Foundation of China under Grant No , and Program for Science & Technology Innovation Talents in Universities of Henan Province under Grant No. 2008HASTIT030 xqdai@hotmail.com

2 546 DAI Xian-Qi, ZHAO Jian-Hua, SUN Yong-Can, WEI Shu-Yi, and WEI Guo-Hong Vol. 54 that of other group-iii metals such as In on same silicon surface. In our previous work, [17] the atomic structures of In atoms on Si(100)-(2 1) surface have been investigated using first-principles total energy calculations. In this study, using a similar approach, we carry out theoretical studies of the atomic and electronic structures of Tl and In on Si(111) surfaces and investigated the difference of adsorption behaviors between Tl on Si(111) and In on Si(111) by analyzing the density of states and the electron density of two stable configurations. 2 Models and Methods The calculations are performed within the framework of the generalized-gradient approximation (GGA), as implemented within the Vienna Ab-initio Simulation Package (VASP), [18 19] employing non-norm conserving ultrasoft Vanderbilt pseudopotentials (US-PP). The Kohn Sham orbitals are expanded in plane wave with a relatively high energy cutoff of 400 ev. We do not find any significant changes in structural parameters when the energy cutoff is increased from 400 ev to 450 ev. The Tl 5d (In 4d) states must be treated as valence electrons in the pseudopotentials because of hybridization between Tl 5d (In 4d) and Si 3s3p electrons. [20 21] Silicon lattice constant Å, obtained by US-PP calculations and are used in our calculations, is in very good agreement with experimental results of Å. [22] The Si (111) surface is modeled in repeated slab geometry. Each slab consists of ten layers of Si atoms and neighboring slabs are separated by a vacuum layer of 15 Å. [17] Bottom four layers are frozen into their bulk positions, and each Si atom at the back surface is saturated with one hydrogen atoms. All the remaining substrate atoms, the adsorbate atoms and the saturating H atoms are allowed to relax into their minimum energy positions. Self-consistent solutions are obtained by employing the (4 4 1) and (7 7 1) Monkhorst Pack grid of k- points for the integration over the Brillouin zone for the (2 2) and ( 3 3)R30 surface unit cell (Fig. 1(a)), respectively. A test has shown that further increasing the number of K points only leads to an energy change of less than 0.5 mev per atom. In our calculation, three high symmetry adsorption sites the on-top site, the fcc and hcp hollow sites (labeled as Top, H 3, and T 4, respectively, in Fig. 1(a) are considered. Calculations for these sites are done at four different coverage, Θ = 1/3, 1/2, 3/4, and 1 ML, with use of the unit cells of (2 2) and ( 3 3)R30 structures. The adsorption energy of each one of adatoms is defined by E ads = (E tot E slab n X µ X )/n X. In the above equation, E tot is the total energy of structure resulting from the optimization of the structure with respect to atomic positions. E slab is the energy of the silicon substrate saturating with hydrogen atoms. n X and µ X represent the number and chemical potential of X adatoms (X denotes Tl or In), respectively. In addition, the chemical potential of X atom is obtained by calculating the energy of per X atom in bulk X. Fig. 1 Top view (a) and side view (b) of Si(111) surface. Examples of the T 4, H 3, and Top sites are labeled, while the unit cells of (2 2), ( 3 3)R30 structures are marked by solid and dashed lines, respectively. 3 Results and Discussions 3.1 Atomic Structure of Tl and In on Si(111) We focus on the adsorption energy of Tl and In adsorbed on Si(111). Figure 2 shows the adsorption energy of the surface structures induced by adsorption of Tl and In at the H 3, T 4, and Top sites of the surface at different coverage, respectively. It can be found that the adsorption energy increases basically with increasing Tl (or In) coverage for H 3 and T 4 sites, but it is reverse for Top site. Energy optimizations show that, at full monolayer (ML) coverage, Tl atoms preferentially adsorb at the T 4 sites with the adsorption energies (0.537) ev/atom lower than that when they adsorbed at the H 3 (Top) sites. At the lower coverage of 3/4 and 1/2 ML, Tl atoms occupy some of the T 4 sites, giving rise to the (2 2) surface structures, their adsorption energies are shown to be reduced by (0.682) ev/atom and (0.881) ev/atom than the similar structures caused by Tl adsorption at the H 3 (Top) sites, respectively. However, Tl atoms preferentially adsorb at the H 3 sites at lower coverage of 1/4 ML. As we know that H 3 and T 4 sites are energetically more favorable than Top sites for the group-iii metals (Al, Ga, In). [6,23] The results show that this rule is also applicable to the case of Tl atoms adsorb on Si(111) surfaces. Moreover, it is also found that 1/3 ML Tl adsorbed at T 4 sites on Si(111)-( 3 3)R30 is more stable structure than 1/3

3 No. 3 First-Principles Calculations of Atomic and Electronic Properties of Tl and In on Si(111) 547 ML In adsorbed at T 4 sites on the same surface because of the latter s minimum adsorption energies. Fig. 2 The calculated adsorption energies of Si(111) with 1/3, 1/2, 3/4, and 1 ML of Tl (dash triangle), In (solid circle) being adsorbed at the H 3(dashed line), T 4 (solid line), and Top (dot line) sites of the Si(111) surface, respectively. Moreover, it is concluded that, in the same condition, the structures of Tl on Si(111) are easy to switch between ( 3 3) and (1 1) than that of In on Si(111), because that the difference of adsorption energy of one Tl adatom from ( 3 3) to (1 1) is 0.52 ev, which is less than that of each In adatom by about 0.24 ev. The adatom positions are identified by the values of d 01 and d 02 (as shown in Fig. 1(b)). The X-Si bond length d 01 is the distance between adatom and the first layer Si atom which is the nearest from adatom. Adsorption height d 02 represents the perpendicular distance from adatom to the plane determined by the second layer Si atoms. Table 1 lists the values of d 01 and d 02 at different coverage for Tl and In on Si(111). In general, it is found that d 01 and d 02 became larger with increasing of coverage for two species adatoms. We noted that Tl-Si bond length d 01 and adsorption height d 02 are respective about 2.90 Å and 2.79 Å, which is agree with the existing theoretical studies. [15] In addition The bond length of In-Si is shorter than that of Tl-Si by about 0.17 Å. The results indicate that the In adatoms are situated 1.63 Å above the Si(111) surface, and it is in good agreement with experimental data of 1.5 ± 0.2 Å measured by STM. [24] Table 1 Calculated Tl (In)-Si bond length d 01 and adsorbate height d 02 for Tl and In adsorbed on Si(111) at T 4 site at 1/3, 1/2, 3/4, and 1ML coverage, respectively. Coverage/ML 1/3 1/2 3/4 1 Tl/Si(111) In/Si(111) d 01 /Å d 02 /Å d 01 /Å d 02 /Å It can be concluded from the comparisons and analysis above that the In-Si bond may be stronger than the Tl-Si one. So the structure of In on Si(111) is possibly more stable than that of Tl on Si(111) at the same condition such as external electric field. This may be one of the reasons to explain the experiment result that the electromigration of Tl on the Si(111) is a reversible SE, while that of In on the Si(111) surface is an irreversible one. [16] 3.2 Electronic structures of Tl and In on Si (111) Density of States The total density of states (TDOS) and partial density of states (PDOS) of the simulated structures are calculated and the results are partially shown in Fig. 3, Fermienergy is defined as the zero point of energy (as indicated by the vertical dot lines in Fig. 3). The results show that the adsorbate-substrate interaction obviously affects the density of states. With the increasing of Tl coverage, the peaks of the surface states weaken gradually. From the DOS shown in Figs. 3(a) and 3(f), we have found that there exist three surface state peaks labeled S 1 (unoccupied), S 2 and S 3 (occupied) at the around of fundamental band gap region for Tl on Si(111). For In on Si(111), there are mainly three surface state peaks labeled S 4 (unoccupied), S 5 (through the Fermi level), and S 6 (occupied). These are consistent with the experimental results from angle-resolved photoelectron spectroscopy (ARPES) [14] and theoretic results from other calculations. [15,25 27] PDOS gives a qualitative treatment on the nature of electron hybridization in the system. The PDOSs of Tl 6s, 6p, and 5d electrons are shown in Fig. 3(e), which illustrate that the 6p electrons of Tl atoms play an important role in the formation of two occupied surface states. The sharp peak in the Si gap is mainly occupied by 5d electrons of Tl atoms. If the 5d electrons are taken as core electrons, the remarkable peak of unoccupied surface state S 1 cannot be obtained. This is the reason why Tl 5d must be considered as valence electrons in the calculations. By analyzing the characteristics of these peaks, it is found that the empty state S 1 contains contributions mainly from 6s and 5d electrons of Tl adatoms. S 3 is mainly from 6p electrons of Tl adatoms and 3s electrons of the second Si atom. The sharp peaks represent the formation of strong covalent bond between 6p electrons of Tl adatom and 3s electrons of the second Si atom. S 2 are weaker and overlap significantly with S 3 states. It is from 3p electrons of Si 1 and Si 3 atoms. In a word, 6p electrons of Tl adatoms and 3p electrons of Si atoms play a very important role in the forming of two occupied states S 2 and S 3. Similarly, In 5p-Si 3p hybridization is very strong and In 5p and Si 3p electrons react on the formation of the surface states S 5 and S 6.

4 548 DAI Xian-Qi, ZHAO Jian-Hua, SUN Yong-Can, WEI Shu-Yi, and WEI Guo-Hong Vol. 54 Fig. 3 Density of states (DOS) of Tl (a) (e) and In (f) (j) on Si(111) plots. The TDOS for the clear Si(111) substrate (dot line) and the Tl or In on Si(111) (solid line) (a, f). The PDOS for one of the 3 rd (b, j), the 2 nd (c, h), the 1 st (d, i) layer Si substrate atoms, Tl adatom after 1/3 ML Tl adsorbed on Si(111)(e). In adatom after 1/3 ML In adsorbed on Si(111)(j). The signs such as Si 1, Si 2, and Si 3 represent the outmost, second, and third layer Si atoms, respectively. The vertical dot lines indicate the Fermi level and S 1-S 6 denote surface states Charge Density To analyze the issues of adatom-si bonding, we calculated the total valence charge density and difference charge density (as shown in Fig. 4) of the two stable structures. Thinking of the three-fold symmetry, the contour plots depict the (10 1) plane perpendicular to the (111) surface passing through the center of the adatoms. In Figs. 4(a) and 4(b), it is shown that the surface charge densities are extensively overlapping, resulting in the increase of electron cloud, which demonstrated that adatoms forms strong adatom-si polar covalent bonds with Si atoms of Si(111) surface. For the difference charge density maps as shown in Figs. 4(c) and 4(d), it is obtained by subtracting the sum of the charge densities of the isolated adatom layer and the Si substrate from that of the adatoms on Si(111) surface. The solid (dashed) line denotes regions of charge accumulation (depletion) and contour lines are drawn at about e/å 3 intervals in Figs. 4(c) and 4(d). It is noted that the charges are partially transferred from the adatoms to the surface of silicon, which saturates the dangling bonds of on-top Si, and the charge transfer lead to a change that the surface turn from metal properties to semiconductor s. The results are in good agreement with our previous DOS calculation (Fig. 3). By comparing the difference charge density maps of the two structures, It is noticed that Tl adatom takes more net charge than that In adatom and the maximum transferred charge between In and Si is 0.07 e/å 3, which is higher than that between Tl and Si by about 0.02 e/å 3. That is to say, In-Si bond is stronger than Tl- Si bond in Si(111) surface, and also Tl atom is easier to be migrated than In atom in the same external electric field. The results may help explain why the electromigration of Tl on the Si(111) is a reversible SE, while that of In on the Si(111) surface is an irreversible one. [16]

5 No. 3 First-Principles Calculations of Atomic and Electronic Properties of Tl and In on Si(111) 549 Fig. 4 Total valence charge density plots (a, b) and difference electron density plots (c, d) for 1/3 ML Tl(a, c) and In(b, d) adsorbed at T 4 sites on Si(111)-( 3 3)R30. The contour plots depict the (101) plane perpendicular to the (111) surface passing through the center of the adatoms. The solid (dot) line denotes regions of charge accumulation (depletion) in plots (c) and (d). Contour lines in plots (a, b) and plots (c, d) are drawn at about 0.1 e/å 3 and e/å 3 intervals, respectively. 4 Conclusions The first-principles plane wave pseudopotential method is performed to study the atomic and electronic properties of Tl and In on Si(111) surface. By comparing the adsorption energy of various investigated structural models, it is found that 1/3 ML Tl adsorbed on Si(111) at T 4 sites is the most stable structure for Tl on Si(111). Electronic structures show that 6p electrons of Tl adatoms and 3p electrons of Si atoms play a very important role in the forming of the occupied surface states. In addition, we calculated the total valence charge density and difference charge density of the two stable structures. The results indicate that the polar covalent bond is formed between Tl (or In) atom and surface Si atom. The electron cloud is redistributed while Tl (or In) adatoms absorbed on Si(111) surface. Difference charge density shows that In-Si bond is stronger than Tl-Si bond in Si(111) surface. So Tl atom is easier to be migrated than In atom in the same external electric field. From adsorption energy and electronic structures, it is concluded that the configuration of In adsorbed on Si(111) is more stable than that of Tl adsorbed on the same surface. The results are consistent with the experimental results. [16] References [1] M.Y. Lai and Y.L. Wang, Phys. Rev. B 64 (2001) [2] J. Jia, J.Z. Wang, X. Liu, Q.K. Xue, Z.Q. Li, Y. Kawazoe, and S.B. Zhang, Appl. Phys. Lett. 80 (2002) [3] J.L. Li, J.F. Jia, X.J. Liang, X. Liu, J.Z. Wang, Q.K. Xue, Z.Q. Li, J.S. Tse, Z.Y. Zhang, and S.B. Zhang, Phys. Rev. Lett. 88 (2002) [4] V.G. Kotlyar, A.V. Zotov, A.A. Saranin, T.V. Kasyanova, M.A. Cherevik, I.V. Pisarenko, and V.G. Lifshits, Phys.

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