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Theoretical study of hydrogenated 3C–SiC(0 0 1)-(2 × 1) surface
Surface Science 571 (2004) 21–30 www.elsevier.com/locate/susc
Theoretical study of hydrogenated 3C–SiC(0 0 1)-(2 · 1) surface Xiangyang Peng *, Ling Ye, Xun Wang Surface Physics Laboratory, Fudan University, Shanghai 200433, China Received 22 October 2003; accepted for publication 21 June 2004 Available online 2 July 2004
Abstract The atomic structure and electronic states of the hydrogenated 3C–SiC(0 0 1)-(2 · 1) surface are investigated by the first-principles calculations. Two models of the hydrogenated surfaces are studied, i.e., the hydrogenated alternating up and down dimer (AUDD) surface and the missing row asymmetric dimer (MRAD) surface, respectively. It is found that the length of the dimers on monohydrided AUDD surface is significantly reduced after hydrogenation, in sharp contrast to the case of Si(0 0 1)-(2 · 1) surface on which the dimers become longer after hydrogenation. The strengthening of the dimers on monohydrided AUDD surface can explain the strong S-state observed in experiments. In the calculated partial density of states (PDOS) of the adsorbed hydrogen atoms on monohydrided AUDD surface, there is only one sharp peak at the energy of about 2.6 eV below the valence band maximum (VBM), in good agreement with the recent photoemission experiments. This binding energy is considerably lower than that of the hydrogen-induced states on Si(0 0 1) surface. The reduction of the dimer length, the strong S-state, and the low binding energy of the hydrogeninduced states on the monohydrided AUDD surface can be uniformly explained by the smaller lattice constant of SiC and the stronger Coulomb interaction between the adsorbed H atoms. In the PDOS of the hydrogen atoms on dihydrided MRAD surface, there are several large peaks with the main surface resonance peak located at about 4 eV below the VBM. The calculation shows that the position of the calculated hydrogen-induced states of monohydrided AUDD surface agrees with the photoemission experiments. 2004 Elsevier B.V. All rights reserved. Keywords: Density functional calculations; Surface relaxation and reconstruction; Silicon carbide; Hydrogen atom; Adatoms
1. Introduction
*
Corresponding author. Tel.: +86 21 65643418; fax: +86 21 65104949. E-mail address: [email protected] (X. Peng).
Silicon carbide (SiC) is a kind of binary compound existing in solid phase formed by group IV elements. Due to its exceptional properties, such as large band gap, high thermal conductivity and high hardness, SiC is a competitive material in
0039-6028/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2004.06.173
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fabricating novel microelectronic and optoelectronic devices. Many experimental and theoretical studies have been devoted to the investigation of its surface properties. One of the most popularly studied surfaces of the cubic polytype SiC (3C– SiC) is the (0 0 1) surface [1]. Experimentally p(2 · 1) [2] c(4 · 2) [3] and Si-rich (3 · 2) [4], reconstructions on the Si-terminated 3C–SiC(0 0 1) surface have been found. c(4 · 2) is found to be the most stable geometry of the clean stoichiometric Si–SiC(0 0 1) surface, and the (2 · 1) reconstruction occurs in the presence of contamination or defects on the surface [3]. Two atomic structural models have been proposed for the SiC(0 0 1)-c(4 · 2). The first one is a model of alternating up and down symmetric dimers (AUDD) suggested by Soukiassian et al. [3] based on the scanning tunneling microscopy (STM) observation. The temperature-induced reversible phase transition between c(4 · 2) and (2 · 1) reconstructions found by high temperature STM observation [5] further supported the AUDD model. This surface is terminated by 1 monolayer (ML) Si atoms in accord with the coverage measurements [1,6,7]. This AUDD reconstruction has also been reproduced by Catellani et al. [8] in their ab initio calculations with an applied tensile stress. Another model of SiC(0 0 1)-c(4 · 2) is a missing row and asymmetric dimer (MRAD) model suggested by Lu et al. [9]. The coverage of Si was supposed to be 1.5 ML, in consistency with some Si core level experiments [10]. According to LuÕs calculation [9], the MRAD model is found to be more stable than the AUDD model in the whole physical range of Si chemical potential values. Therefore, controversies still remain regarding the most stable geometries of SiC(0 0 1)-c(4 · 2) surface, both experimentally and theoretically. Hydrogen adsorption can be served as a probe to discriminate the surface atomic structures. Recently, it was found experimentally [11] that there is a reversible transition between c(4 · 2) and (2 · 1) patterns induced by hydrogen adsorption and desorption on the Si-terminated SiC(0 0 1) surface. Photoemission experiments [11] have observed a hydrogen induced state at about 2.4 eV below the valence band maximum (VBM). In comparison, the hydrogen induced states on monohydrided Si(0 0 1) surface lie 4.4 and 5.1 eV below the VBM [12]. It re-
mains to be explained why the binding energy of the hydrogen induced states of SiC(0 0 1) is about 2 eV lower than that of Si(0 0 1). The experiments [11] have also found an S-state near the VBM in the photoemission spectrum of hydrogenated Si–SiC(0 0 1) surface, which is assumed to be associated with the r-bond of surface Si–Si dimers. The S-state indicates a strong dimerization, which is not reconciled with the weak dimerization on AUDD surface predicted by the first-principle calculations [8,13]. The analyses of H-induced states in Ref. [11] seem to support the AUDD model, but the S-state does not seem to agree with the weak dimerization on AUDD surface. In this work, we study the atomic and electronic structures of the hydrogenated Si-SiC(0 0 1)-(2 · 1) surfaces by the first principles pseudopotential calculation. The AUDD and MRAD models for SiC(0 0 1)-c(4 · 2) surface are investigated using the hydrogenated surfaces as a probe. The H-induced states on AUDD surface derived by the calculation are in good agreement with the photoemission experiment. The calculation found that it is the short lattice constant of SiC that causes the difference between the H-induced states on the monohydrided SiC(0 0 1) and those on the Si(0 0 1) surfaces. The calculation of the monohydrided AUDD surface also gives the S-state, i.e., the surface resonances near the VBM, which can be explained by the strengthening of the dimer bonds after hydrogenation. The disagreement between the strong S-state [11] and the weak dimerization on monohydrided AUDD surface predicted by previous calculations [8,13] can be solved. On the dihydrided MRAD surface, the calculation shows that the position of the H-induced states is much lower than the experimental results. But there is also a strong state near the valence band maximum where the S-state lies, indicating that the hydrogenated SiC(0 0 1)-c(4 · 2) surface might be a mixture of monohydrided and dihydrided phases. This is corroborated by the LEED experiment [11] and IRAS experiment [14]. 2. Computational models and methods The AUDD and MRAD models for Si– SiC(0 0 1) c(4 · 2) surface are shown in Fig. 1(a)
X. Peng et al. / Surface Science 571 (2004) 21–30
and (b), respectively. To realize the observed H-induced pattern transition from c(4 · 2) to (2 · 1) [11], the AUDD surface needs to be monohydrided [3] with each surface Si atom attached to one H atom, while the MRAD surface has to be dihydrided, involving bond breaking of the surface dimers [9]. In this paper, we denote the monohydrided AUDD surface and dihydrided MRAD surface as AUDD-(2 · 1)-H and MRAD-(2 · 1)-2H, respectively. For comparison, we also calculated the hydrogenated Si(0 0 1) surface. The calculations are performed within the framework of density functional theory (DFT). The generalized-gradient corrected functional (generalized-gradient approximation or GGA) proposed by Perdew and Wang [15] is employed
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for evaluation of the exchange-correlation energy. Vanderbilt-type ultrasoft pseudopotentials [16,17] are used to describe the electron–ion interaction and the wave function is expanded by plane wave basis set with the energy cutoff of about 26 Ry. The surface Brillouin zone is sampled by a Monkhorst mesh of 8 · 4. The partial density of states (PDOS) are calculated with tetrahedron method. The convergence of the PDOS with respect to k points has been tested by employing a more dense Monkhost mesh of 12 · 6, and the PDOS remain almost unchanged with the increase of k points. The details of the calculation methods are described in Ref. [18]. The optimal surface configuration is determined within supercell approach. For the AUDD-(2 · 1)-H surface, we employ a (2 · 1) supercell with seven Si layers and seven C layers and two adsorbed hydrogen atoms atop. The (2 · 1) supercell for MRAD-(2 · 1)-2H surface contains six Si layers, six C layers, and the adsorbed 0.5 ML Si layer and two hydrogen atoms on the top. The bottom of the atomic slabs in the two supercells is a C layer and is saturated with hydrogen atoms. The thickness of the vacuum region in ˚ . The lower both supercells is greater than 15 A four atomic layers are fixed in bulk configuration ˚. with the calculated lattice constant of 4.37 A The remaining layers are allowed to move during the relaxation until all forces vanish within 0.01 ˚. eV/A
3. Results and discussion 3.1. The geometrical structures of AUDD-(2 · 1)-H and MRAD-(2 · 1)-2H surfaces
Fig. 1. Top views of (a) AUDD model, and (b) MRAD model for Si–SiC(0 0 1)-c(4 · 2) reconstruction. The gray big balls are substrate Si atoms, and the dark gray and white big balls are surface Si atoms. The white balls are lower than the dark gray ones. The carbon atoms are denoted by small black balls. The unit cells are shown by the dashed rectangles.
The optimized structure of AUDD-(2 · 1)-H surface is shown in Fig. 2. The bond lengths are labeled near the bonds. After hydrogenation, the dimer is symmetric and the dimer length is 2.38 ˚ , quite close to Si–Si bond length. The atomic A structure of clean SiC(0 0 1)-(2 · 1) surface is also calculated. Being consistent with the recent ab initio calculations [8,13], we obtain a symmetric weak ˚ , quite dimer structure with bond length of 2.73 A different from the results of semi-empirical calculations in which asymmetric and strong dimer
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Fig. 2. Side views of (a) the monohydrided SiC(0 0 1) surface, and (b) the dihydrided SiC(0 0 1) surface, showing the bond ˚ . The length and distance between atoms in the unit of A numbers in parentheses are the corresponding values for monohydrided Si(0 0 1) surface. The black dots represent the hydrogen atoms. The Si and C atoms are denoted by big gray balls and small black balls, respectively.
˚ ) is obtained [19]. One would exstructure (2.329 A pect that the hydrogen adsorption will weaken the dimer and make the dimer longer. But for SiC, the result is quite the opposite. The dimer length is re˚ rather than increased and the duced by 0.35 A bonding within the dimer is greatly strengthened. This contradicts with the semi-empirical calcula-
tion [19] in which the dimer is lengthened by about ˚ after hydrogen adsorption, but is in agree0.15 A ment with the recent ab initio calculation [20]. To study why the length of the Si–Si dimer on the AUDD SiC(0 0 1) surface is greatly reduced after hydrogenation, we also calculated the clean and monohydrided Si(0 0 1)-(2 · 1) surfaces as a comparison. In agreement with the previous calculation [21], we obtained buckled dimers with a ˚ and a height difference of bond length of 2.30 A ˚ on clean Si(0 0 1)-(2 · 1) surface, and sym0.55 A ˚ on metric dimers with a bond length of 2.4 A monohydrided Si(0 0 1)-(2 · 1) surface. The bond ˚ after length of the dimers increases by about 0.1 A hydrogenation. It can be seen that the (0 0 1) surfaces of SiC and Si are quite different in spite of their seeming similarities. Compared with its clean surface, the dimer bonds on monohydrided SiC(0 0 1) surface are significantly strengthened with a decrease of the dimer bond length from ˚ , while the dimer bonds on mono2.73 to 2.38 A hydrided Si(0 0 1) surface are weakened, resulting in an increase of dimer bond length from 2.3 to ˚ . The Si–Si dimer on the clean Si(0 0 1)2.4 A (2 · 1) surface becomes longer after hydrogenation, because hydrogen adsorption breaks the p-like bond between the two sp3 dangling bonds on the same dimer. The dimer length of SiC is also expected to be slightly increased after hydrogen adsorption if the same reason can be applied for SiC. But an important factor should be taken into account. There is repulsive interaction between the two most adjacent hydrogen atoms H2 and H3 in Fig. 2(a) if they are very close [22]. The lattice constant of SiC is about 20% smaller than that of Si. If the length of the dimer on SiC(0 0 1) surface remains unchanged after hydrogen adsorption, i.e., ˚ , the the dimer bond length in Fig. 2(a) is 2.73 A ˚ distance between H2 and H3 is about 2.04 A, while ˚. this distance on Si(0 0 1) surface is about 4.27 A To reduce the repulsive energy, the two hydrogen atoms H1 and H2 in Fig. 2(a) adsorbed on the same dimer of SiC(0 0 1) move toward each other and squeeze the dimer. In Fig. 3, we plot the charge densities of the Si dimers on clean and monohydrided surfaces of Si(0 0 1) and SiC(0 0 1) in gray scale. The plotting plane is perpendicular to the (0 0 1) surface and passes through one Si
X. Peng et al. / Surface Science 571 (2004) 21–30
Fig. 3. (a) and (b) ((c) and (d)) are the gray scale plottings of the charge densities of the Si dimers on SiC(0 0 1) (Si(0 0 1)) surfaces before hydrogenation and after hydrogenation. (a) and (b) ((c) and (d)) have the same gray scale. The gray balls are Si atoms, and the black balls are hydrogen atoms. The plotting plane is perpendicular to the (0 0 1) surface and passes through the dimer.
dimer. Fig. 3(a) and (b) (Fig. 3(c) and (d)) are the charge densities of the Si dimers on SiC(0 0 1) (Si(0 0 1)) surfaces before hydrogenation and after hydrogenation. Fig. 3(a) and (b) (Fig. 3(c) and (d)) have the same gray scale. As can be seen in Fig. 3(a) and (b), the charge density in the dimer bond of SiC is greatly increased after hydrogenation. But for Si (see Fig. 3(c) and (d)), the change of the charge density in the dimer bond is not obvious after hydrogenation. The repulsive interaction between adsorbed hydrogen atoms and the strengthening of the dimer bonds on SiC(0 0 1) surface by hydrogen adsorption will affect the electronic states, as will be discussed in Sections 3.2 and 3.3. We also considered another possibility to reduce the repulsion between the H atoms by sideway motion of H atoms, i.e., displacing the H atoms in the direction perpendicular to the Si dimers along the surface. We gave the initial sideway displacement and found that the sideway displacement vanishes and the H atoms return to the zero sideway displacement sites after the ionic relaxation. If the distance between H atoms is the only factor to be considered, sideway motion can increase the distance between H atoms and reduce the Coulomb repulsion. But the sideway motion at the same time distorts the Si–H bonds and the
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Si–Si bonds below, and this costs some energy. The calculations show that the reduction of repulsion energy by sideway motion cannot compensate the increase of distortion energy. Thus the sideway motion is not favorable. To achieve the H-induced (2 · 1) surface structure observed in the experiment [11], the MRAD SiC(0 0 1)-(4 · 2) surface has to be dihydrided, involving the dimer breaking. Similar to the dihydrided Si(0 0 1)-(1 · 1) surface determined by Northrup [22], the canted dihydride structure is also found on the dihydrided MRAD-SiC-(2 · 1)-2H surface in our calculation, as depicted in Fig. 2(b). Such relaxation reduces the repulsive energy of the adjacent dihydrides by 0.7 eV/(1 · 1) as compared with the symmetric dihydride structure. The Si atoms with dangling bonds in the second layer ˚. form dimers with bond length of 2.51 A 3.2. Electronic states of AUDD-(2 · 1)-H and MRAD-(2 · 1)-2H surfaces For the AUDD SiC(0 0 1)-(2 · 1)-H surface, the calculated PDOS of the adsorbed H atoms and the Si atoms in the top layers are shown in Fig. 4. The VBM has been taken as the energy zero. In Fig. 4(a), there is only one sharp peak located at about 2.6 eV below the VBM. The thick solid, thin solid and the dotted curves in Fig. 4(b) represent the PDOS of Si atoms in the first, third and fifth layers (see Fig. 2(a)). There is also a sharp peak at 2.6 eV in the PDOS of Si atoms in the first layer, indicating that this peak is resulted from the Si–H bonds. The magnitudes of the peaks at 2.6 eV of PDOS of Si atoms in the third and fifth layers decrease significantly, suggesting that the peak at 2.6 eV is a surface resonance. In previous work, the only available theoretical study of the electronic states of monohydrided SiC(0 0 1)-(2 · 1) surface is an empirical quantum chemistry calculation [19]. It predicted symmetric dimerization on Si(0 0 1) surface and asymmetric dimerization on Si–SiC(0 0 1) surface, only contrary to the results of ab initio calculations [8,13]. The electronic states calculated by this method are also inconsistent with the experiment. In the local density of states of the adsorbed hydrogen atoms calculated by the empirical method [19],
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(a)
(b) Fig. 4. The PDOS of (a) adsorbed H atoms, and (b) Si atoms in first, third, and fifth layers (see Fig. 2(a)) of AUDD-(2 · 1)-H surface. The H-induced state is located at 2.6 eV below the VBM. The VBM has been taken as energy zero.
there were a lot of peaks distributed over a wide energy range from 2 to 5 eV below the VBM and the largest peak is located about 5 eV below the VBM. These results are hard to be compared with the photoemission experiments [11], in which the H-induced state was determined to be 2.4 eV below the VBM. Our calculation shows that Hinduced state is 2.6 eV below the VBM and is identified as surface resonance, in good agreement with the experiment [11]. Another feature found by the photoemission experiment [11] is a so-called S-state located very close to the VBM, which was supposed to be re-
lated to the r-bond of the Si–Si dimers on the surface. The S-state does not seem to be consistent with the weak dimerization on clean SiC(0 0 1)(2 · 1) surface predicted by previous ab initio calculations [8,13], especially when considering that the dimers were expected to be further weakened by hydrogenation, as occurred on Si(0 0 1) surface. If the S-state is associated with the dimer bond, it would suggest a stronger bond than in the calculation of the clean SiC(0 0 1)-(2 · 1) surface [11]. Our calculation solves the seeming disagreement. In the PDOS of silicon atoms in the top layers shown in Fig. 4(b), there is a sharp strong surface resonance very near the VBM. Its magnitude is large at the Si–Si dimers on the surface and decreases quickly as the Si-layers go deeper into the slab. The strong feature of this state agrees well with the S-state and can be explained by our calculated geometrical structure of AUDD-(2 · 1)-H surface. As discussed in Section 3.1, the expected weakening of the dimer bond on clean SiC(0 0 1) surface by hydrogenation does not occur. On the contrary, our calculation shows that the Si–Si dimers on hydrogenated SiC(0 0 1) surface are much shorter and therefore much stronger than those on the clean SiC(0 0 1) surface. The strong feature of the S-state can be explained by the strong Si–Si dimer bonds on the monohydrided SiC(0 0 1) surface. The electronic states of the MRAD SiC(0 0 1)(2 · 1)-2H surface are also calculated for comparison. The calculated PDOS are shown in Fig. 5. We are only interested in the states above 5 eV (see Fig. 5), since the states below this energy are out of the energy range of experiments [11]. There are several peaks in the PDOS of H1 and H2 (Fig. 2(b)) with the highest peak located at 4.05 eV as shown in Fig. 5(a). Apparently, the states at 4.05 eV are surface resonances since the peaks damp as the Si layers go down (Fig. 5(b)). The second largest peaks of the PDOS of H1 and H2 lie around 3.0 eV. They are not surface resonances since the peaks of Si atoms in different layers at this position do not vary much. The other peaks in PDOS of H1 and H2 are relatively small and above 1.5 eV, far away from 2.4 eV, where the experimentally observed H-induced states are located [11]. The calculated surface states of MRAD-(2 · 1)-2H surface do not agree with the
X. Peng et al. / Surface Science 571 (2004) 21–30
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on the 3C–SiC(100)-c(4 · 2) surface results in dihydride formation. Therefore, on the hydrogenated SiC(0 0 1)-c(4 · 2) surface, dihydride Si atoms can coexist with monohydride Si dimers. 3.3. H-induced states on SiC(0 0 1) and Si(0 0 1)
(a)
On monohydrided SiC(0 0 1)-(2 · 1) surface, recent photoemission experiments [11] and our calculation found that the hydrogen induced surface states are about 2.4 eV below the VBM. In contrast, the H-induced states on monohydrided Si(0 0 1)-H were found by experiments [12] at 4– 5.1 eV below the VBM. For comparison, we also calculated the PDOS of the adsorbed hydrogen atoms on monohydrided Si(0 0 1)-(2 · 1) surface, as shown in Fig. 6. The main peak is located at 4.08 eV below the VBM and is also determined as a surface resonance. This result well agrees with the experiments [12]. The Si–SiC(0 0 1) and Si(0 0 1) surfaces are thought to be similar to each other in many ways, but the calculated H-induced states on SiC(0 0 1) surface are about 1.5 eV closer to the VBM than those on the Si(0 0 1) surface. Why the binding energy of the hydrogen induced states of monohydrided SiC(0 0 1) is much lower than that of monohydrided Si(0 0 1)? There are two possible
(b) Fig. 5. The PDOS of (a) adsorbed H atoms, and (b) Si atoms in first, second, and fourth layers (see Fig. 2(b)) of MRAD-(2 · 1)2H surface. The H-induced state is located at 4.05 eV below the VBM. The VBM has been taken as energy zero.
experimental results [11]. The energy gap of MRAD-(2 · 1)-2H surface is smaller than that of AUDD-(2 · 1)-H surface because MRAD-(2 · 1)2H surface has non-saturated Si bonds caused by the missing rows, giving rise to the surface states in the gap. From Fig. 5(a), it can be seen that there is a peak near the valence band maximum for H2 atoms, where the S-state is located. This means that if there are dihydrides on the surface, they may also give rise to the S-state. Widstrand et al. [11], found that high H exposure leads to dihydrides. Amy and Chabal [14], have also demonstrated that even low atomic hydrogen exposure
Fig. 6. The PDOS of the adsorbed H atoms of monohydrided Si(0 0 1) surface. The H-induced state is located at 4.08 eV below the VBM. The VBM has been taken as energy zero.
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factors that may cause the energy level shift of the H-induced states. One is due to the different backbonds below the top Si atoms [11]. For SiC(0 0 1), the backbonds for the Si atoms bonded to H atoms are Si–C bonds (Fig. 2(a)), while for Si(0 0 1), are Si–Si bonds. Since carbon atoms are more electro-negative than Si and H atoms, it was assumed that the carbon atoms closest to the Si–H bonds e.g., C1 in Fig. 2(a), may take electrons away from H and Si, thereby leaving less charge for the Si–H bonds and pushing up the energy of the Si–H bonds [11]. Based on this argument, it was supposed that the low binding energy of the H-induced states on SiC(0 0 1) surface indicates 1 ML Si termination [11]. We calculated the charge of each carbon atom in the surfaces before and after hydrogenation, within ˚) various radius, from its covalent radius (0.77 A ˚ ). It was found that to the Si–C bond length (1.88 A the charge of carbon atom C1 (Fig. 2(a)) increased no more than 0.3% after hydrogenation. The charge accepted by C1 from Si–H bonds is so small that it seems to be unlikely that such a small charge transfer alone can lead to an energy shift of the H-induced states as large as 1.5 eV. If there are 2 ML Si atoms at the surface of SiC(0 0 1) in Fig. 2(a), the position of H-induced states of this hypothetical system should be significantly downshifted according to the above argument, since the backbonds of the top Si atoms are Si–Si bonds instead of Si–C bonds. We calculated the PDOS of such hypothetical system and found that the H-induced states almost do not move if we compare the largest peak in Fig. 7(a) with that in Fig. 4(a). Another factor is the short lattice constant of SiC, which is about 20% smaller than that of Si. The distances between H2 and H3 in Fig. 2(a) ˚ on SiC(0 0 1) surface and 4.27 A ˚ on are 2.39 A Si(0 0 1) surface, respectively. Since the charge of H atoms is concentrated in the Si–H bonds, the nucleus of H atoms are poorly screened and are exposed to each other, bringing repulsive interaction between H atoms. The H2 and H3 atoms are much closer to each other on SiC(0 0 1) surface than on Si(0 0 1) surface, and the repulsive interaction is much larger, raising the energy level of H-induced states. The change of the energy level can be roughly estimated by calculating the change of
(a)
(b) Fig. 7. The PDOS of the adsorbed H atoms on monohydrided SiC(0 0 1) surfaces with 2 ML Si termination (a), and with the lattice constant of Si (b). The VBM has been taken as energy zero.
the Coulomb repulsive energy between two naked protons: e2 e2 e2 e2 þ ¼ 2:28 eV; SiC SiC Si 4p0 d 12 4p0 d 23 4p0 d 12 4p0 d Si 23 where d12 (d23) is the distance between H1 and H2 (H2 and H3), and its value is given in Fig. 2(a). If the screening effect is taken into account, the change of the Coulomb repulsive energy should be smaller than 2.28 eV. According to such reasoning, if the distance between the H2 and H3 atoms is increased by expanding the lattice of SiC, the en-
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ergy level of the H-induced states should be shifted downward due to the reduced repulsive interaction between H2 and H3. To study the influence of the lattice constant on the H-induced states, we employ an expanded SiC(0 0 1)-H surface by replacing the bond lengths in Fig. 2(a) with those of the monohydrided Si(0 0 1) surface. This is almost equivalent to letting the SiC take the lattice constant of Si. We calculated the H-induced states of such system and indeed found that the H-induced states were shifted to the position of 3.6 eV below the VBM, as shown in Fig. 7(b), which is close to the H-induced states on Si(0 0 1)-H surface at 4 eV. The small discrepancy might be brought about by the carbon atoms in the substrate. Therefore, the low binding energy of the H-induced states on AUDD-(2 · 1)-H surface is not mainly due to the single Si monolayer termination, but the small lattice constant of SiC and the coulomb repulsive interaction between adjacent H atoms.
rise to much stronger Si dimeriztion and thus the strong S-state. The calculated electronic states of AUDD-(2 · 1)-H surface agree well with the experiment [11]. For the dihydrided MRAD surface, the calculation shows that there are no H-induced states around the position 2.6 eV below the VBM, not in agreement with the experiment. But the dihydrides can also lead to the states at the position where the S-state is located, indicating the monohydrided and the dihydrided phases can coexist on hydrogenated SiC(0 0 1)-c(4 · 2) surface.
4. Conclusions
References
In summary, we have calculated the geometrical structures and the electronic states of the hydrogenated SiC(0 0 1)-(2 · 1) surfaces. For the SiC(0 0 1) AUDD-(2 · 1)-H surface, the calculation shows that the length of the Si–Si dimer is significantly reduced after hydrogenation, while the Si– Si dimers on the corresponding hydrogenated Si(0 0 1)-(2 · 1) surface are enlarged. The H-induced states and the S-state found by photoemission experiments [11] are well explained by our calculation. The sharp peak of the PDOS of the adsorbed hydrogen atom is located at 2.6 eV below VBM, very close to the experimental value of 2.4 eV [11]. The energy level of the H-induced states of SiC(0 0 1) surface is up-shifted compared with the corresponding H-induced states on Si(0 0 1)-H surface. We found the underlying physics of the low binding energy of the hydrogen-induced states, the reduction of the dimer length, and the strong S-state on the monohydrided AUDD surface is the smaller lattice constant of SiC and the stronger Coulomb interaction between the adsorbed H atoms, which will push up the energy level of Si–H states, compress the Si dimers, and give
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Acknowledgments The authors wish to thank Prof. J.G. Che at our laboratory for helpful and fruitful discussions. This work is supported by the National Natural Science Foundation of China under award number NFS-60176005.
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[15] Y. Wang, J.P. Perdew, Phys. Rev. B 44 (1991) 13298. [16] G. Kresse, J. Hafner, J. Phys.: Condensed Matter 6 (1996) 5824. [17] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [18] G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) 14251; G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169; G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15.
[19] B.I. Craig, P.V. Smith, Physica B 170 (1991) 518; B.I. Craig, P.V. Smith, Surf. Sci. 233 (1990) 255. [20] A. Catellani, L. Pizzagalli, G. Galli, Mater. Sci. Eng. B 96 (2002) 132. [21] P. Kratzer, B. Hammer, J.K. Norskov, Phys. Rev. B 51 (1995) 13432. [22] J.E. Northrup, Phys. Rev. B 44 (1991) 1419.
Theoretical study of hydrogenated 3C–SiC(0 0 1)-(2 · 1) surface Xiangyang Peng *, Ling Ye, Xun Wang Surface Physics Laboratory, Fudan University, Shanghai 200433, China Received 22 October 2003; accepted for publication 21 June 2004 Available online 2 July 2004
Abstract The atomic structure and electronic states of the hydrogenated 3C–SiC(0 0 1)-(2 · 1) surface are investigated by the first-principles calculations. Two models of the hydrogenated surfaces are studied, i.e., the hydrogenated alternating up and down dimer (AUDD) surface and the missing row asymmetric dimer (MRAD) surface, respectively. It is found that the length of the dimers on monohydrided AUDD surface is significantly reduced after hydrogenation, in sharp contrast to the case of Si(0 0 1)-(2 · 1) surface on which the dimers become longer after hydrogenation. The strengthening of the dimers on monohydrided AUDD surface can explain the strong S-state observed in experiments. In the calculated partial density of states (PDOS) of the adsorbed hydrogen atoms on monohydrided AUDD surface, there is only one sharp peak at the energy of about 2.6 eV below the valence band maximum (VBM), in good agreement with the recent photoemission experiments. This binding energy is considerably lower than that of the hydrogen-induced states on Si(0 0 1) surface. The reduction of the dimer length, the strong S-state, and the low binding energy of the hydrogeninduced states on the monohydrided AUDD surface can be uniformly explained by the smaller lattice constant of SiC and the stronger Coulomb interaction between the adsorbed H atoms. In the PDOS of the hydrogen atoms on dihydrided MRAD surface, there are several large peaks with the main surface resonance peak located at about 4 eV below the VBM. The calculation shows that the position of the calculated hydrogen-induced states of monohydrided AUDD surface agrees with the photoemission experiments. 2004 Elsevier B.V. All rights reserved. Keywords: Density functional calculations; Surface relaxation and reconstruction; Silicon carbide; Hydrogen atom; Adatoms
1. Introduction
*
Corresponding author. Tel.: +86 21 65643418; fax: +86 21 65104949. E-mail address: [email protected] (X. Peng).
Silicon carbide (SiC) is a kind of binary compound existing in solid phase formed by group IV elements. Due to its exceptional properties, such as large band gap, high thermal conductivity and high hardness, SiC is a competitive material in
0039-6028/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2004.06.173
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fabricating novel microelectronic and optoelectronic devices. Many experimental and theoretical studies have been devoted to the investigation of its surface properties. One of the most popularly studied surfaces of the cubic polytype SiC (3C– SiC) is the (0 0 1) surface [1]. Experimentally p(2 · 1) [2] c(4 · 2) [3] and Si-rich (3 · 2) [4], reconstructions on the Si-terminated 3C–SiC(0 0 1) surface have been found. c(4 · 2) is found to be the most stable geometry of the clean stoichiometric Si–SiC(0 0 1) surface, and the (2 · 1) reconstruction occurs in the presence of contamination or defects on the surface [3]. Two atomic structural models have been proposed for the SiC(0 0 1)-c(4 · 2). The first one is a model of alternating up and down symmetric dimers (AUDD) suggested by Soukiassian et al. [3] based on the scanning tunneling microscopy (STM) observation. The temperature-induced reversible phase transition between c(4 · 2) and (2 · 1) reconstructions found by high temperature STM observation [5] further supported the AUDD model. This surface is terminated by 1 monolayer (ML) Si atoms in accord with the coverage measurements [1,6,7]. This AUDD reconstruction has also been reproduced by Catellani et al. [8] in their ab initio calculations with an applied tensile stress. Another model of SiC(0 0 1)-c(4 · 2) is a missing row and asymmetric dimer (MRAD) model suggested by Lu et al. [9]. The coverage of Si was supposed to be 1.5 ML, in consistency with some Si core level experiments [10]. According to LuÕs calculation [9], the MRAD model is found to be more stable than the AUDD model in the whole physical range of Si chemical potential values. Therefore, controversies still remain regarding the most stable geometries of SiC(0 0 1)-c(4 · 2) surface, both experimentally and theoretically. Hydrogen adsorption can be served as a probe to discriminate the surface atomic structures. Recently, it was found experimentally [11] that there is a reversible transition between c(4 · 2) and (2 · 1) patterns induced by hydrogen adsorption and desorption on the Si-terminated SiC(0 0 1) surface. Photoemission experiments [11] have observed a hydrogen induced state at about 2.4 eV below the valence band maximum (VBM). In comparison, the hydrogen induced states on monohydrided Si(0 0 1) surface lie 4.4 and 5.1 eV below the VBM [12]. It re-
mains to be explained why the binding energy of the hydrogen induced states of SiC(0 0 1) is about 2 eV lower than that of Si(0 0 1). The experiments [11] have also found an S-state near the VBM in the photoemission spectrum of hydrogenated Si–SiC(0 0 1) surface, which is assumed to be associated with the r-bond of surface Si–Si dimers. The S-state indicates a strong dimerization, which is not reconciled with the weak dimerization on AUDD surface predicted by the first-principle calculations [8,13]. The analyses of H-induced states in Ref. [11] seem to support the AUDD model, but the S-state does not seem to agree with the weak dimerization on AUDD surface. In this work, we study the atomic and electronic structures of the hydrogenated Si-SiC(0 0 1)-(2 · 1) surfaces by the first principles pseudopotential calculation. The AUDD and MRAD models for SiC(0 0 1)-c(4 · 2) surface are investigated using the hydrogenated surfaces as a probe. The H-induced states on AUDD surface derived by the calculation are in good agreement with the photoemission experiment. The calculation found that it is the short lattice constant of SiC that causes the difference between the H-induced states on the monohydrided SiC(0 0 1) and those on the Si(0 0 1) surfaces. The calculation of the monohydrided AUDD surface also gives the S-state, i.e., the surface resonances near the VBM, which can be explained by the strengthening of the dimer bonds after hydrogenation. The disagreement between the strong S-state [11] and the weak dimerization on monohydrided AUDD surface predicted by previous calculations [8,13] can be solved. On the dihydrided MRAD surface, the calculation shows that the position of the H-induced states is much lower than the experimental results. But there is also a strong state near the valence band maximum where the S-state lies, indicating that the hydrogenated SiC(0 0 1)-c(4 · 2) surface might be a mixture of monohydrided and dihydrided phases. This is corroborated by the LEED experiment [11] and IRAS experiment [14]. 2. Computational models and methods The AUDD and MRAD models for Si– SiC(0 0 1) c(4 · 2) surface are shown in Fig. 1(a)
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and (b), respectively. To realize the observed H-induced pattern transition from c(4 · 2) to (2 · 1) [11], the AUDD surface needs to be monohydrided [3] with each surface Si atom attached to one H atom, while the MRAD surface has to be dihydrided, involving bond breaking of the surface dimers [9]. In this paper, we denote the monohydrided AUDD surface and dihydrided MRAD surface as AUDD-(2 · 1)-H and MRAD-(2 · 1)-2H, respectively. For comparison, we also calculated the hydrogenated Si(0 0 1) surface. The calculations are performed within the framework of density functional theory (DFT). The generalized-gradient corrected functional (generalized-gradient approximation or GGA) proposed by Perdew and Wang [15] is employed
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for evaluation of the exchange-correlation energy. Vanderbilt-type ultrasoft pseudopotentials [16,17] are used to describe the electron–ion interaction and the wave function is expanded by plane wave basis set with the energy cutoff of about 26 Ry. The surface Brillouin zone is sampled by a Monkhorst mesh of 8 · 4. The partial density of states (PDOS) are calculated with tetrahedron method. The convergence of the PDOS with respect to k points has been tested by employing a more dense Monkhost mesh of 12 · 6, and the PDOS remain almost unchanged with the increase of k points. The details of the calculation methods are described in Ref. [18]. The optimal surface configuration is determined within supercell approach. For the AUDD-(2 · 1)-H surface, we employ a (2 · 1) supercell with seven Si layers and seven C layers and two adsorbed hydrogen atoms atop. The (2 · 1) supercell for MRAD-(2 · 1)-2H surface contains six Si layers, six C layers, and the adsorbed 0.5 ML Si layer and two hydrogen atoms on the top. The bottom of the atomic slabs in the two supercells is a C layer and is saturated with hydrogen atoms. The thickness of the vacuum region in ˚ . The lower both supercells is greater than 15 A four atomic layers are fixed in bulk configuration ˚. with the calculated lattice constant of 4.37 A The remaining layers are allowed to move during the relaxation until all forces vanish within 0.01 ˚. eV/A
3. Results and discussion 3.1. The geometrical structures of AUDD-(2 · 1)-H and MRAD-(2 · 1)-2H surfaces
Fig. 1. Top views of (a) AUDD model, and (b) MRAD model for Si–SiC(0 0 1)-c(4 · 2) reconstruction. The gray big balls are substrate Si atoms, and the dark gray and white big balls are surface Si atoms. The white balls are lower than the dark gray ones. The carbon atoms are denoted by small black balls. The unit cells are shown by the dashed rectangles.
The optimized structure of AUDD-(2 · 1)-H surface is shown in Fig. 2. The bond lengths are labeled near the bonds. After hydrogenation, the dimer is symmetric and the dimer length is 2.38 ˚ , quite close to Si–Si bond length. The atomic A structure of clean SiC(0 0 1)-(2 · 1) surface is also calculated. Being consistent with the recent ab initio calculations [8,13], we obtain a symmetric weak ˚ , quite dimer structure with bond length of 2.73 A different from the results of semi-empirical calculations in which asymmetric and strong dimer
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Fig. 2. Side views of (a) the monohydrided SiC(0 0 1) surface, and (b) the dihydrided SiC(0 0 1) surface, showing the bond ˚ . The length and distance between atoms in the unit of A numbers in parentheses are the corresponding values for monohydrided Si(0 0 1) surface. The black dots represent the hydrogen atoms. The Si and C atoms are denoted by big gray balls and small black balls, respectively.
˚ ) is obtained [19]. One would exstructure (2.329 A pect that the hydrogen adsorption will weaken the dimer and make the dimer longer. But for SiC, the result is quite the opposite. The dimer length is re˚ rather than increased and the duced by 0.35 A bonding within the dimer is greatly strengthened. This contradicts with the semi-empirical calcula-
tion [19] in which the dimer is lengthened by about ˚ after hydrogen adsorption, but is in agree0.15 A ment with the recent ab initio calculation [20]. To study why the length of the Si–Si dimer on the AUDD SiC(0 0 1) surface is greatly reduced after hydrogenation, we also calculated the clean and monohydrided Si(0 0 1)-(2 · 1) surfaces as a comparison. In agreement with the previous calculation [21], we obtained buckled dimers with a ˚ and a height difference of bond length of 2.30 A ˚ on clean Si(0 0 1)-(2 · 1) surface, and sym0.55 A ˚ on metric dimers with a bond length of 2.4 A monohydrided Si(0 0 1)-(2 · 1) surface. The bond ˚ after length of the dimers increases by about 0.1 A hydrogenation. It can be seen that the (0 0 1) surfaces of SiC and Si are quite different in spite of their seeming similarities. Compared with its clean surface, the dimer bonds on monohydrided SiC(0 0 1) surface are significantly strengthened with a decrease of the dimer bond length from ˚ , while the dimer bonds on mono2.73 to 2.38 A hydrided Si(0 0 1) surface are weakened, resulting in an increase of dimer bond length from 2.3 to ˚ . The Si–Si dimer on the clean Si(0 0 1)2.4 A (2 · 1) surface becomes longer after hydrogenation, because hydrogen adsorption breaks the p-like bond between the two sp3 dangling bonds on the same dimer. The dimer length of SiC is also expected to be slightly increased after hydrogen adsorption if the same reason can be applied for SiC. But an important factor should be taken into account. There is repulsive interaction between the two most adjacent hydrogen atoms H2 and H3 in Fig. 2(a) if they are very close [22]. The lattice constant of SiC is about 20% smaller than that of Si. If the length of the dimer on SiC(0 0 1) surface remains unchanged after hydrogen adsorption, i.e., ˚ , the the dimer bond length in Fig. 2(a) is 2.73 A ˚ distance between H2 and H3 is about 2.04 A, while ˚. this distance on Si(0 0 1) surface is about 4.27 A To reduce the repulsive energy, the two hydrogen atoms H1 and H2 in Fig. 2(a) adsorbed on the same dimer of SiC(0 0 1) move toward each other and squeeze the dimer. In Fig. 3, we plot the charge densities of the Si dimers on clean and monohydrided surfaces of Si(0 0 1) and SiC(0 0 1) in gray scale. The plotting plane is perpendicular to the (0 0 1) surface and passes through one Si
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Fig. 3. (a) and (b) ((c) and (d)) are the gray scale plottings of the charge densities of the Si dimers on SiC(0 0 1) (Si(0 0 1)) surfaces before hydrogenation and after hydrogenation. (a) and (b) ((c) and (d)) have the same gray scale. The gray balls are Si atoms, and the black balls are hydrogen atoms. The plotting plane is perpendicular to the (0 0 1) surface and passes through the dimer.
dimer. Fig. 3(a) and (b) (Fig. 3(c) and (d)) are the charge densities of the Si dimers on SiC(0 0 1) (Si(0 0 1)) surfaces before hydrogenation and after hydrogenation. Fig. 3(a) and (b) (Fig. 3(c) and (d)) have the same gray scale. As can be seen in Fig. 3(a) and (b), the charge density in the dimer bond of SiC is greatly increased after hydrogenation. But for Si (see Fig. 3(c) and (d)), the change of the charge density in the dimer bond is not obvious after hydrogenation. The repulsive interaction between adsorbed hydrogen atoms and the strengthening of the dimer bonds on SiC(0 0 1) surface by hydrogen adsorption will affect the electronic states, as will be discussed in Sections 3.2 and 3.3. We also considered another possibility to reduce the repulsion between the H atoms by sideway motion of H atoms, i.e., displacing the H atoms in the direction perpendicular to the Si dimers along the surface. We gave the initial sideway displacement and found that the sideway displacement vanishes and the H atoms return to the zero sideway displacement sites after the ionic relaxation. If the distance between H atoms is the only factor to be considered, sideway motion can increase the distance between H atoms and reduce the Coulomb repulsion. But the sideway motion at the same time distorts the Si–H bonds and the
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Si–Si bonds below, and this costs some energy. The calculations show that the reduction of repulsion energy by sideway motion cannot compensate the increase of distortion energy. Thus the sideway motion is not favorable. To achieve the H-induced (2 · 1) surface structure observed in the experiment [11], the MRAD SiC(0 0 1)-(4 · 2) surface has to be dihydrided, involving the dimer breaking. Similar to the dihydrided Si(0 0 1)-(1 · 1) surface determined by Northrup [22], the canted dihydride structure is also found on the dihydrided MRAD-SiC-(2 · 1)-2H surface in our calculation, as depicted in Fig. 2(b). Such relaxation reduces the repulsive energy of the adjacent dihydrides by 0.7 eV/(1 · 1) as compared with the symmetric dihydride structure. The Si atoms with dangling bonds in the second layer ˚. form dimers with bond length of 2.51 A 3.2. Electronic states of AUDD-(2 · 1)-H and MRAD-(2 · 1)-2H surfaces For the AUDD SiC(0 0 1)-(2 · 1)-H surface, the calculated PDOS of the adsorbed H atoms and the Si atoms in the top layers are shown in Fig. 4. The VBM has been taken as the energy zero. In Fig. 4(a), there is only one sharp peak located at about 2.6 eV below the VBM. The thick solid, thin solid and the dotted curves in Fig. 4(b) represent the PDOS of Si atoms in the first, third and fifth layers (see Fig. 2(a)). There is also a sharp peak at 2.6 eV in the PDOS of Si atoms in the first layer, indicating that this peak is resulted from the Si–H bonds. The magnitudes of the peaks at 2.6 eV of PDOS of Si atoms in the third and fifth layers decrease significantly, suggesting that the peak at 2.6 eV is a surface resonance. In previous work, the only available theoretical study of the electronic states of monohydrided SiC(0 0 1)-(2 · 1) surface is an empirical quantum chemistry calculation [19]. It predicted symmetric dimerization on Si(0 0 1) surface and asymmetric dimerization on Si–SiC(0 0 1) surface, only contrary to the results of ab initio calculations [8,13]. The electronic states calculated by this method are also inconsistent with the experiment. In the local density of states of the adsorbed hydrogen atoms calculated by the empirical method [19],
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(a)
(b) Fig. 4. The PDOS of (a) adsorbed H atoms, and (b) Si atoms in first, third, and fifth layers (see Fig. 2(a)) of AUDD-(2 · 1)-H surface. The H-induced state is located at 2.6 eV below the VBM. The VBM has been taken as energy zero.
there were a lot of peaks distributed over a wide energy range from 2 to 5 eV below the VBM and the largest peak is located about 5 eV below the VBM. These results are hard to be compared with the photoemission experiments [11], in which the H-induced state was determined to be 2.4 eV below the VBM. Our calculation shows that Hinduced state is 2.6 eV below the VBM and is identified as surface resonance, in good agreement with the experiment [11]. Another feature found by the photoemission experiment [11] is a so-called S-state located very close to the VBM, which was supposed to be re-
lated to the r-bond of the Si–Si dimers on the surface. The S-state does not seem to be consistent with the weak dimerization on clean SiC(0 0 1)(2 · 1) surface predicted by previous ab initio calculations [8,13], especially when considering that the dimers were expected to be further weakened by hydrogenation, as occurred on Si(0 0 1) surface. If the S-state is associated with the dimer bond, it would suggest a stronger bond than in the calculation of the clean SiC(0 0 1)-(2 · 1) surface [11]. Our calculation solves the seeming disagreement. In the PDOS of silicon atoms in the top layers shown in Fig. 4(b), there is a sharp strong surface resonance very near the VBM. Its magnitude is large at the Si–Si dimers on the surface and decreases quickly as the Si-layers go deeper into the slab. The strong feature of this state agrees well with the S-state and can be explained by our calculated geometrical structure of AUDD-(2 · 1)-H surface. As discussed in Section 3.1, the expected weakening of the dimer bond on clean SiC(0 0 1) surface by hydrogenation does not occur. On the contrary, our calculation shows that the Si–Si dimers on hydrogenated SiC(0 0 1) surface are much shorter and therefore much stronger than those on the clean SiC(0 0 1) surface. The strong feature of the S-state can be explained by the strong Si–Si dimer bonds on the monohydrided SiC(0 0 1) surface. The electronic states of the MRAD SiC(0 0 1)(2 · 1)-2H surface are also calculated for comparison. The calculated PDOS are shown in Fig. 5. We are only interested in the states above 5 eV (see Fig. 5), since the states below this energy are out of the energy range of experiments [11]. There are several peaks in the PDOS of H1 and H2 (Fig. 2(b)) with the highest peak located at 4.05 eV as shown in Fig. 5(a). Apparently, the states at 4.05 eV are surface resonances since the peaks damp as the Si layers go down (Fig. 5(b)). The second largest peaks of the PDOS of H1 and H2 lie around 3.0 eV. They are not surface resonances since the peaks of Si atoms in different layers at this position do not vary much. The other peaks in PDOS of H1 and H2 are relatively small and above 1.5 eV, far away from 2.4 eV, where the experimentally observed H-induced states are located [11]. The calculated surface states of MRAD-(2 · 1)-2H surface do not agree with the
X. Peng et al. / Surface Science 571 (2004) 21–30
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on the 3C–SiC(100)-c(4 · 2) surface results in dihydride formation. Therefore, on the hydrogenated SiC(0 0 1)-c(4 · 2) surface, dihydride Si atoms can coexist with monohydride Si dimers. 3.3. H-induced states on SiC(0 0 1) and Si(0 0 1)
(a)
On monohydrided SiC(0 0 1)-(2 · 1) surface, recent photoemission experiments [11] and our calculation found that the hydrogen induced surface states are about 2.4 eV below the VBM. In contrast, the H-induced states on monohydrided Si(0 0 1)-H were found by experiments [12] at 4– 5.1 eV below the VBM. For comparison, we also calculated the PDOS of the adsorbed hydrogen atoms on monohydrided Si(0 0 1)-(2 · 1) surface, as shown in Fig. 6. The main peak is located at 4.08 eV below the VBM and is also determined as a surface resonance. This result well agrees with the experiments [12]. The Si–SiC(0 0 1) and Si(0 0 1) surfaces are thought to be similar to each other in many ways, but the calculated H-induced states on SiC(0 0 1) surface are about 1.5 eV closer to the VBM than those on the Si(0 0 1) surface. Why the binding energy of the hydrogen induced states of monohydrided SiC(0 0 1) is much lower than that of monohydrided Si(0 0 1)? There are two possible
(b) Fig. 5. The PDOS of (a) adsorbed H atoms, and (b) Si atoms in first, second, and fourth layers (see Fig. 2(b)) of MRAD-(2 · 1)2H surface. The H-induced state is located at 4.05 eV below the VBM. The VBM has been taken as energy zero.
experimental results [11]. The energy gap of MRAD-(2 · 1)-2H surface is smaller than that of AUDD-(2 · 1)-H surface because MRAD-(2 · 1)2H surface has non-saturated Si bonds caused by the missing rows, giving rise to the surface states in the gap. From Fig. 5(a), it can be seen that there is a peak near the valence band maximum for H2 atoms, where the S-state is located. This means that if there are dihydrides on the surface, they may also give rise to the S-state. Widstrand et al. [11], found that high H exposure leads to dihydrides. Amy and Chabal [14], have also demonstrated that even low atomic hydrogen exposure
Fig. 6. The PDOS of the adsorbed H atoms of monohydrided Si(0 0 1) surface. The H-induced state is located at 4.08 eV below the VBM. The VBM has been taken as energy zero.
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factors that may cause the energy level shift of the H-induced states. One is due to the different backbonds below the top Si atoms [11]. For SiC(0 0 1), the backbonds for the Si atoms bonded to H atoms are Si–C bonds (Fig. 2(a)), while for Si(0 0 1), are Si–Si bonds. Since carbon atoms are more electro-negative than Si and H atoms, it was assumed that the carbon atoms closest to the Si–H bonds e.g., C1 in Fig. 2(a), may take electrons away from H and Si, thereby leaving less charge for the Si–H bonds and pushing up the energy of the Si–H bonds [11]. Based on this argument, it was supposed that the low binding energy of the H-induced states on SiC(0 0 1) surface indicates 1 ML Si termination [11]. We calculated the charge of each carbon atom in the surfaces before and after hydrogenation, within ˚) various radius, from its covalent radius (0.77 A ˚ ). It was found that to the Si–C bond length (1.88 A the charge of carbon atom C1 (Fig. 2(a)) increased no more than 0.3% after hydrogenation. The charge accepted by C1 from Si–H bonds is so small that it seems to be unlikely that such a small charge transfer alone can lead to an energy shift of the H-induced states as large as 1.5 eV. If there are 2 ML Si atoms at the surface of SiC(0 0 1) in Fig. 2(a), the position of H-induced states of this hypothetical system should be significantly downshifted according to the above argument, since the backbonds of the top Si atoms are Si–Si bonds instead of Si–C bonds. We calculated the PDOS of such hypothetical system and found that the H-induced states almost do not move if we compare the largest peak in Fig. 7(a) with that in Fig. 4(a). Another factor is the short lattice constant of SiC, which is about 20% smaller than that of Si. The distances between H2 and H3 in Fig. 2(a) ˚ on SiC(0 0 1) surface and 4.27 A ˚ on are 2.39 A Si(0 0 1) surface, respectively. Since the charge of H atoms is concentrated in the Si–H bonds, the nucleus of H atoms are poorly screened and are exposed to each other, bringing repulsive interaction between H atoms. The H2 and H3 atoms are much closer to each other on SiC(0 0 1) surface than on Si(0 0 1) surface, and the repulsive interaction is much larger, raising the energy level of H-induced states. The change of the energy level can be roughly estimated by calculating the change of
(a)
(b) Fig. 7. The PDOS of the adsorbed H atoms on monohydrided SiC(0 0 1) surfaces with 2 ML Si termination (a), and with the lattice constant of Si (b). The VBM has been taken as energy zero.
the Coulomb repulsive energy between two naked protons: e2 e2 e2 e2 þ ¼ 2:28 eV; SiC SiC Si 4p0 d 12 4p0 d 23 4p0 d 12 4p0 d Si 23 where d12 (d23) is the distance between H1 and H2 (H2 and H3), and its value is given in Fig. 2(a). If the screening effect is taken into account, the change of the Coulomb repulsive energy should be smaller than 2.28 eV. According to such reasoning, if the distance between the H2 and H3 atoms is increased by expanding the lattice of SiC, the en-
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ergy level of the H-induced states should be shifted downward due to the reduced repulsive interaction between H2 and H3. To study the influence of the lattice constant on the H-induced states, we employ an expanded SiC(0 0 1)-H surface by replacing the bond lengths in Fig. 2(a) with those of the monohydrided Si(0 0 1) surface. This is almost equivalent to letting the SiC take the lattice constant of Si. We calculated the H-induced states of such system and indeed found that the H-induced states were shifted to the position of 3.6 eV below the VBM, as shown in Fig. 7(b), which is close to the H-induced states on Si(0 0 1)-H surface at 4 eV. The small discrepancy might be brought about by the carbon atoms in the substrate. Therefore, the low binding energy of the H-induced states on AUDD-(2 · 1)-H surface is not mainly due to the single Si monolayer termination, but the small lattice constant of SiC and the coulomb repulsive interaction between adjacent H atoms.
rise to much stronger Si dimeriztion and thus the strong S-state. The calculated electronic states of AUDD-(2 · 1)-H surface agree well with the experiment [11]. For the dihydrided MRAD surface, the calculation shows that there are no H-induced states around the position 2.6 eV below the VBM, not in agreement with the experiment. But the dihydrides can also lead to the states at the position where the S-state is located, indicating the monohydrided and the dihydrided phases can coexist on hydrogenated SiC(0 0 1)-c(4 · 2) surface.
4. Conclusions
References
In summary, we have calculated the geometrical structures and the electronic states of the hydrogenated SiC(0 0 1)-(2 · 1) surfaces. For the SiC(0 0 1) AUDD-(2 · 1)-H surface, the calculation shows that the length of the Si–Si dimer is significantly reduced after hydrogenation, while the Si– Si dimers on the corresponding hydrogenated Si(0 0 1)-(2 · 1) surface are enlarged. The H-induced states and the S-state found by photoemission experiments [11] are well explained by our calculation. The sharp peak of the PDOS of the adsorbed hydrogen atom is located at 2.6 eV below VBM, very close to the experimental value of 2.4 eV [11]. The energy level of the H-induced states of SiC(0 0 1) surface is up-shifted compared with the corresponding H-induced states on Si(0 0 1)-H surface. We found the underlying physics of the low binding energy of the hydrogen-induced states, the reduction of the dimer length, and the strong S-state on the monohydrided AUDD surface is the smaller lattice constant of SiC and the stronger Coulomb interaction between the adsorbed H atoms, which will push up the energy level of Si–H states, compress the Si dimers, and give
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Acknowledgments The authors wish to thank Prof. J.G. Che at our laboratory for helpful and fruitful discussions. This work is supported by the National Natural Science Foundation of China under award number NFS-60176005.
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