Si(111) Interfaces: Cluster calculations

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Surface Science 205 (1988) 549-568 North-Holland, Amsterdam

THE COORDINATION OF METAL ATOMS AT CoSi ,/Si(lll) AND Nisi J Si( 111) INTERFACES: CLUSTER CALCULATIONS P.J. VAN DEN HOEK FOM-Institute for Atomic and Molecular Physics, Kraislaan The Netherlam&

W. RAVENEK

407, 1098 SJ Amsterdam,

and E.J. BAERENDS

Free University, Department The Netherlands

of Theoretical Chemistry,

De Boelelaan 1083, 1081 HV Amsterdam,

Received 27 April 1988; accepted for publication 4 July 1988

We have performed local-density-approximation calculations on clusters modeling the CoSi,/Si(lll) and NiSi,/Si(lll) interfaces. On the basis of these calculations, we propose a new structure for the CoSi,/Si(lll) interface, in which the interface metal atom is 8-fold coordinated. In addition, we show that for NiSi,/Si(lll), the structure with ‘I-fold coordination of the interface metal atom is the most stable one. An explanation is given for the difference in interface structure between CoSi,/Si(lll) and NiSi,/Si(lll).

1. Introduction The metallic disilicides CoSi, and Nisi,, which both have the cubic CaF, structure, form epitaxial and atomically abrupt interfaces with a silicon substrate [l]. Therefore, the interfaces of these disilicides with silicon serve as model systems for metal-semiconductor interfaces. Especially, the Schottky barrier height at these interfaces may be directly correlated to the interface chemical bond. Recent experiments have shown that the geometric structures, and therefore the interface chemical bonds, at the CoSi,/Si(lll) and Nisi,/ Si(ll1) interfaces are quite different. Whereas CoSi, binds with its metal atoms to the silicon substrate [2,3], Nisi, binds with its silicon atoms to the silicon substrate [4-61. For disilicide silicon to substrate silicon bonding, the metal atoms closest to the interface are 7-fold coordinated (fig. lc). For disilicide metal to substrate silicon bonding, the interface metal atoms are 5-fold coordinated if one assumes that all Si atoms are 4-fold coordinated (fig. la). If, however, the latter constraint is lifted, there is the possibility of saturating the three interface metal dangling bonds by adding an extra silicon layer (fig. lb). In 0039-6028/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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0 silicon

interfaces

0 metal

MSi2 Si (al

ib)

(cl

Fig. 1. Possible structures for the epitaxial MSi,/Si(lll) (M = Co, Ni) interfaces: 5-fold {a), S-fold (b) and 7-fold (c) coordination of the interface metal atoms. All structures shown are of the “B-type”.

this case the coordination number of the interface metal atoms is, as in bulk disilicide, eight. The extra Si atoms are 3-fold coordinated (fig. lb) if the disilicide overlayer is 180° rotated about the [ill] normal with respect to the Si substrate (“B-type” epitaxy). There is no experimental evidence which favours either the 5-fold or g-fold coordinated interface for metal to substrate silicon bonding. Until now, the 5-fold structure was generally assumed. Recently, however, we showed that the g-fold structure is more stable than the 5-fold structure 171. A subsequent study using bandstructure calculations confirmed our results [8]. In this paper we present results of electronic structure calculations on model clusters representing different geometric structures of the MSi,/Si(lll) interface. For metal to substrate silicon bonding, we discuss the 5-fold and 8-fold structures, and explain why the latter is energetically more favorable. Furthermore, we explain why for NiSiJSi, the 7-fold structure is more stable than the &fold structure, and why this is reverse for CoSiJSi. Throughout this paper we will assume that all interfaces are B-type; we will not address possible differences in chemical bonding between “A-type” (same orientation of overlayer and substrate) and B-type interfaces. In order to get insight into the chemical bonding at the interfaces, we analyzed the calculations using the concept of “frontier orbitals”; a frontier orbital is a candidate orbital for a chemical bond. This has proven to be a powerful concept in the understanding of both molecular [9] and crystal [lo] structures. From a Mulliken orbital population analysis a picture of the interface chemical bond in terms of frontier orbitals is derived. Although quantitative results from cluster calculations should be taken with care, the analysis of such calculations gives a simple description of the interface in terms of local chemical bonds. Trends in calculated interaction energies serve as a check on the correctness of the chemical bond picture. We note that cluster calculations have been quite successful in understanding the interactions between gas particles (atoms, molecules) and metal surfaces [ll].

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The paper is organized as follows. Section 2 gives an outline of the computational details and a description of the model clusters. In section 3, we present and discuss results. First, chemical bonding in the bulk disilicides is discussed (section 3.1). Next, we consider the metal-terminated (section 3.2) and silicon-terminated (section 3.3) disilicide (111) surfaces. Sections 3.4 and 3.5 discuss the 5-fold and 8-fold coordinated interfaces. Finally, we compare in section 3.6 these interfaces with the 7-fold coordinated one. Section 4 summarizes the results.

2. Method

Self-consistent-field linear-combination-of-atomic-orbitals (SCF-LCAO) calculations [12] have been performed in the local-density approximation (LDA). We used the LDA parametrization from Vosko, Wilk and Nusair [13] in combination with a correction proposed by Stoll [14]. A recently developed numerical integration scheme [15] allowed for an accurate and efficient evaluation of the matrix elements appearing in the secular equation. Interaction energies were calculated using a transition state method 1161. We used a standard [17] (triple-zeta) Slater-type-orbital (STO) basis set, together with a 4p polarization function, for the metal atoms. In the calculations, the metal atom cores (including 3s and 3p orbitals) were kept frozen. For a number of clusters, we also performed calculations where the 3s and 3p orbitals were unfrozen, but this had hardly any influence on the results. The Si atom basis set was double-zeta, together with a d-function. Here, all orbitals up to 2p were kept frozen. All clusters were saturated by hydrogen [18,19] or by “pseudo-hydrogen” atoms. For both hydrogen and pseudo-hydrogen we used a double-zeta basis set with a 2p polarization function. Below, we will discuss both the saturation of the clusters and the hydrogen and pseudo-hydrogen basis sets in more detail. 2.2. Clusters We have modeled the bulk disilicides by clusters consisting of one metal atom surrounded by eight silicon atoms. The disilicide silicon interfaces were modeled either by clusters containing one metal atom or by clusters containing three metal atoms. Fig. 2 shows the clusters modeling the interfaces in a projected view along the [liO] direction. The interface bonds are indicated by dashed lines. Next to each metal or Si atom is a number indicating the actual number of cluster metal or Si atoms this atom “represents” in the projected view. The metal and Si atoms in these clusters are saturated by hydrogen and

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ofmetalatoms

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3 metal atoms

(a)

6%

Cc) 0

Metal

l 8

Si

. H D Pr~udo-H~)

Fig. 2. Projected view along the [liO] direction of the clusters modeling the MSi,/Si(lll) interfaces. In the figure, the interface chemical bonds are indicated by dashed lines. The numbers next to each metal or Si atom indicate the actual numbers of metal or Si atoms in the cluster this atom represents in the projected view. The clusters of (a) and (b) model the S-fold or &fold interfaces; in the latter case the shaded Si atoms and pseudo-H atoms are included in the clusters. The clusters of (c) and (d) model the 7-fold coordinated interface.

pseudo-hydrogen atoms in such a way that their coordination numbers are the same as in the infinite systems. The top Si atoms in the interface clusters containing 3 metal atoms (figs. 2b and 2d) only serves to saturate the 3 Si atoms (2 of which are seen in the projected view) in the “layer” below, that is, it merely replaces 3 hydrogen atoms which would have come too close otherwise. Figs. 2a and 2b show the model clusters for the calculations on the 5-fold (without shaded Si and pseudo-H atoms) or 8-fold (with shaded Si and pseudo-H atoms) coordinated interfaces; the model clusters for the 7-fold coordinated interface are shown in figs. 2c and 2d. 2.3. Saturation

of the clusters

2.3.1. Hydrogen (H) and pseudo-hydrogen (H *) The silicon parts of the clusters were, as usual, saturated by hydrogen atoms [18,19]. Since the bonding in the disilicides has a different character than the bonding in silicon, we cannot simply also saturate the disilicide parts of the

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clusters with hydrogen. The reason is that saturation (e.g. by hydrogen) may cause an artificial (and therefore unwanted) shift of the Fermi level in the cluster with respect to that in the bulk material, i.e., bonds which are unoccupied in the crystal may become occupied in the cluster or vice versa. Let us start with considering the saturation of the disilicide Si atoms which are fourfold coordinated in the bulk crystals. These are the eight Si atoms which surround the metal atom in the clusters representing bulk MSi,, and the “filled” (black) Si atoms (see figs. 2a and 2b) in the disilicide parts of the interface clusters. A 4-fold coordinated Si atom has one electron available for each of the four bonds it has with neighbouring atoms. Therefore, if this Si atom is only partially coordinated in a cluster, its remaining (dangling) bonds have to be saturated by hydrogen atoms. The resulting Si-H bonds (with orbital energies far below the Fermi level) are completely filled, and no electron charge can therefore move between these bonds and other parts of the cluster: there is no artificial shift of the Fermi level. This situation applies to the clusters representing bulk MSi,, but also to the clusters representing the metal-terminated disilicide surfaces and the 5-fold coordinated interfaces (figs. 2a and 2b, without the shaded Si atoms). In all these cases the Si atoms to be saturated are 4-fold coordinated in the infinite crystal. Next, we consider the saturation of the disilicide Si atoms which are not 4-fold coordinated in the infinite crystal. This is the case for the surface Si atoms at the silicon-terminated disilicide surface, which are bonded to three (second layer) metal atoms and have one dangling bond. Let us first discuss the filling of the M-Si bonds and the Si dangling bonds with electrons at the infinite disilicide surface; next we will discuss it for the clusters. We consider the silicon-terminated disilicide surface as being built by adding a Si layer to the metal-terminated surface. The reason to do this is that in the latter case we can, using clusters (which we can saturate by hydrogen, see above), calculate how the filling of the bonds will be; by subsequently adding a Si layer we can argue how the filling at the silicon-terminated surface will be. Our calculations of the metal-terminated surface (to be discussed in section 3.2) indicate that a Co atom at this surface has one electron available for the 3 bonds it has to form with the extra layer Si atoms when the Si-terminated surface is made; on average l/3 electron per Co-Si bond. Similarly, Ni at metal-terminated NiSi,(lll) has, on average, 2/3 electron available per Ni-surface Si bond when S&terminated NiSi,(lll) is formed. Now, when we make the Si-terminated surface, the surface Si atoms have, in principle, 4/3 electron available per M-surface Si bond, since they are bonded to 3 metal atoms. Since Co has only l/3 electron available per Co-Si bond, the other electron charge has to be supported by the surface Si atoms. Therefore, the Co-surface Si bonds at the infinite Si-terminated CoSi,(lll) surface contain, on average, l/3 (Co) + 4/3 (Si) = 5/3 electrons, i.e., they are not yet completely filled. In addition, the surface Si dangling bonds are empty, since the Si

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needs all its four electrons for the Co-Si bonds. At Si-te~nat~ NiSi,(lll), the situation is similar in that the snrface Si dangling bonds are also empty; the Ni-Si bonds contain 2/3 (Ni) + 4/3 (Si) = 2 electrons, i.e., they are completely filled. In section 3.3 we will, in a completely different way, arrive at the same result for the filling of the bonds at the silicon-terminated disilicide (111) surfaces. Let us now examine the situation for the disilicide parts of the one-metalatom clusters (see fig. 2a). Here, the surface Si atom (shaded in fig. 2a) is bonded to a metal atom only on one side; therefore it has to be saturated on the two remaining sides. What happens when we do this by hydrogen? In that case, the surface Si needs 2 of its 4 electrons for the SGH bonds, and the rern~~g 2 electrons can be used for the M-Si bond. We have seen, however, that in the case of the infinite crystal, the surface Si atom has only 4/3 electron available for a M-Si bond; if we saturate in the cluster this Si atom with hydrogen, it has, as a result, 2 electrons available for one M-Si bond, that is, 2/3 too many. This causes, of course, an artificial upward shift of the Fermi level in the cluster. We can circumvent this error by saturating the surface Si atoms by “pseudo-hydrogen” (H*) atoms which have a number of electrons (and, consequently, nuclear charge) not equal to one. If the pseudohydrogens have 2/3 electron each, the surface Si needs 4/3 electron per Si-H* bond; consequently it has only 4/3 electron left for the M-Si bond, which is exactly the situation in the infinite crystal. Finally, we have to consider the saturation of the metal atoms on the disilicide parts of the tab-metal-atom clusters (see fig. 2b). In this case, the saturating atoms replace surface Si atoms. Since the surface Si atoms have 4/3 electron available for a M-Si bond, the saturating atoms in this case have to be pseudo-hydrogen atoms with nuclear charge 4/3. 2.3.2. The H and H * basis sets; distances within the clusters A number of authors [18,19] has stressed the importance of choosing the right basis set for the saturating hydrogen atoms. The reason is that in a cluster representing bulk Si, the Si-Si bond covalency can be disturbed due to the H being more electronegative than the Si. We have calculated the M&ken charges on all atoms in a Si(SiH,), cluster (one Si atom tetrahedrally surrounded by hydrogen-satiated Si atoms) as a function of the Si-H distance d,_, (d,i_si was kept fixed at the bulk Si value of 2.35 A), and found that for 1.48 I d,i_n I 2.35 A the maximum charge was always I 0.15 e, if we used for the H atoms a basis consisting of two Is STO’s and one 2p STO. Using this basis, we also calculated the equilibrium d,i_a and dsi_, in Si(SiH,), and found 2.35 and 1.52 A, respectively; the latter number is close to the silane value of 1.48 A. Therefore, in our cluster calculations, we put dSi_H = 1.52 A. Furthermore, we fixed all nearest-neighbour Si-Si and M-Si distances within the clusters at the bulk Si value of 2.35 A: no relaxation effects were taken

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into account. This is reasonable when we realize that in the bulk systems, the relaxations accross the interface (which are the only relaxations) are of the order of a few percent [2,6]. For the different pseudohydrogens, we used the same basis set as for the hydrogens; in all cases numerically (Hermann-Skillmann) calculated one-electron energies could be well reproduced using this basis.

3. Results and discussion 3.1. The bulk disilicides We have performed calculations on clusters modeling the bulk disilicides in order to gain full insight into the nature of the MSi,/Si(lll) frontier orbitals. In bulk MM,, each metal atom is 8-fold coordinated. It can therefore be viewed as being in the centre of a cube with eight Si atoms at the corners (fig. 3a); the Si sp3 hybridized orbitals point to the centre of the cube. We now consider the metal-silicon bonding within this cube. This is divided in two steps: the mutual interaction between the sp3 orbitals (step I), and next, the interaction of the resulting orbitals with the metal atom (step II). Fig. 3b gives an interaction diagram for both step I and step II; this diagram is based on a Mulliken orbital population analysis of the calculations. First, we consider step I. Due to a large mutual overlap, the Sisp3 orbitals interact strongly, resulting in bonding (Alg, T,,) and antibonding (T,,, AZ”) levels. The labels A,,, T,,, . . . indicate the irreducible representations of the cubic point group. Next, we consider step II. Due to symmetry, the metal 4s can only interact with the A,, orbital. Three of the five metal d orbitals (xy, xz, yz) have Tzp symmetry and can therefore interact with the sp3-based Tzg orbital; the other two (3z2 - 9, x2 - y2) have E, symmetry and remain nonbonding. It is important to note that for both Co and Ni, the 3d orbital energy is lower than the sp3 orbital energy. From the diagram in fig. 3b, we can see that a “gap” separates metal-silicon (step II) nonbonding and antibonding states. Now, if we fill up the energy levels with the electrons available within the cube (one electron per sp3 orbital, and the metal electrons), we see that for Nisi, all metal-silicon bonding and nonbonding levels are filled, whereas for CoSi, there is still place for one electron in the highest (metal-silicon nonbonding) level (in fig. 3b, the extra Ni electron is put between brackets). This also explains why the difference in cohesive energy between CoSi, and Nisi, is only small (experimental: about 0.02 eV per M-Si bond [20]): the extra Ni electron per unit cell goes into a metal-silicon nonbonding orbital. The energy-level diagram of fig. 3b is qualitatively in agreement with density-ofstates (DOS) pictures from photoemission experiments [21] and band structure calculations [21-251 on bulk CoSi, and Nisi,. As an example, consider fig. 3c,

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P.J. uan den Hoek et al. / Coordination of metal atoms at disilicide-silicon

interfaces

.._. . l2P-O metal

(4

II

I

Ah

(b)

Fig. 3. (a) Chemical bonding within the bulk disilicides. (b) Energy-level diagrams for steps I and II (see text); the extra Ni electron is indicated between brackets. (c) DOS-curves for bulk Co%, and Nisi, based on band structure calculations. This figure is taken from ref. (201.

which is a DOS picture based on band structure calculations [22]. Clearly, the main features are consistent with fig. 3b: the d-level contribution to the DOS splits into a metal-silicon bonding (T,,) and nonbonding (Es) part, a “quasigap” separates metal-silicon nonbonding and antibonding states, and the extra Nisi, electron per unit cell goes into (mainly) nonbonding states. In the DOS, no T,, peak is seen, since in an extended structure the sp3-based bands are expected to broaden much more than the d-band. We have calculated with the model clusters for both bulk CoSi, and bulk Nisi, a cohesive energy of 2.3 eV per M-Si bond; this energy has been

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calculated with respect to the d ’ s 24F g round state for Co and with respect to the d9s’ ‘D state for Ni (the latter is the Ni ground state if one averages over the multiplet level energies for different J-values [26]). Clearly, the fact that we calculate the same cohesive energy for both disilicides supports the idea that the extra Nisi, electron per unit cell goes into a metal-silicon nonbonding orbital. Furthermore, the value of 2.3 eV is reasonably in agreement with the value calculated by Bylander et al. [24], who calculated a cohesive energy of 1.96 eV per M-Si bond for bulk Nisi 2, and with the values calculated by Lambrecht et al. [25], who calculated cohesive energies of 2.37 and 2.33 eV per M-B bond for bulk CoSi, and Nisi,, respectively. 3.2. The metal-terminated

disilicide surface

In this case, each surface metal atom interacts with four neighbouring Si atoms, which have their sp3 orbitals pointing towards the metal atom (fig. 4a). As in section 3.1, we divide the bonding into two steps: the mutual interaction between the four sp3 orbitals (step I) and the interaction of the metal atom with the resulting orbitals (step II). Fig. 4b gives a schematical energy level diagram for both steps. This diagram follows from a Mulliken orbital population analysis of calculations on the disilicide parts of the clusters depicted in figs. 2a and 2b (without the shaded Si and the H* atoms). First, we consider step I. The mutual interaction between the sp3 orbitals leads to a bonding and an antibonding A, orbital, and a (weakly antibonding) E orbital; the labels A, and E indicate the irreducible representations of the C,, point group. Next, we consider step II. The metal s orbital interacts with both bonding and antibonding A, levels. The A, component of the d orbitals (3~’ - r*, or d=z) has almost no overlap with the bonding A, orbital, but it does have overlap with the antibonding A, orbital. The reason for this difference is depicted in fig. 4c: the overlaps of the positive and negative lobes of the dr2 orbital with the bonding A, orbital almost cancel, whereas these overlaps with the antibonding A, orbital reinforce each other. Therefore, the d,z orbital interacts only with the antibonding A, orbital, as is indicated in fig. 4b. Finally, the E components of the d orbitals (XJJ, xz, yz, x2 - y2) rehybridize, and a part of these rehybridized d orbitals interacts with the sp3-based E orbitals, whereas the other part remains nonbonding. In fig. 4b, the levels are filled with the electrons available; the extra Ni electron is put between brackets. All completely filled orbitals (corresponding to the 4 lowest energy levels in fig. 4b) are deep-lying orbitals and will therefore hardly participate in the chemical bonding when the Si-terminated disilicide surface is formed by adding an extra silicon layer (see section 3.3) or the 5-fold coordinated interface is formed by bonding to substrate silicon (see section 3.4). We will show this in more detail in section 3.4 for the 5-fold coordinated interface. Therefore, the only frontier orbitals at the metal-terminated disilicide surface correspond to

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(a>

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I

ti

A

metal

II

03

Fig. 4. (a, b) Same as figs. 3a and 3b for the metal-terminated disilicide (111) frontier orbitals for the formation of the silicon-terminated surface or of the interface are indicated. (c) Spatial overlap between the bonding Sisp3-based metal d12 orbital (left), and between the antibonding sp3-based A, orbital orbital (right).

the two highest energy for M = Co (Ni). 3.3. The silicon-terminated

levels in fig. 4b. These orbitals

contain

surface. In (b) the S-fold coordinated A, orbital and the and the metal d;2

1 (2) electrons

disilicide surface

In section 3.2, we have shown on the basis of calculations on clusters modeling the metal-terminated disilicide (111) surfaces, that each Co (Ni) atom at this surface has 1 (2) electrons available for its dangling bonds.

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Therefore, if we add an extra silicon layer to make the disilicide surface Si-terminated, each surface Si atom will need all its four valence electrons to make the three bonds with the second layer metal atoms. Consequently, the surface Si dangling bonds are empty, and at CoSi,(lll), every Co-surface Si bond contains, on average, 5,/3 electrons, i.e., is not completely filled; at NiSi,(lll) the 3 Ni-surface Si bonds are completely filled. This is an important feature of the silicon-terminated disilicide (111) surfaces, which we already discussed in connection with the saturation of the interface clusters (see section 2.3). Sofar, we have only considered the formation of the silicon-terminated surface by adding a Si layer to the metal-terminated surface. Another way of forming the (111) surface is by simply cutting bulk disilicide along the (111) plane. In this section we show that if we do this in such a way that the surface is silicon-terminated, we obtain the same description for the Si-terminated surface as given above, i.e. the frontier orbitals at this surface are filled the same way with electrons as described above. We start with the results presented in section 3.1 for the bulk disilicides. Cutting the bulk MSi, along the (111) plane means for the “unit cubes” of fig. 3 closest to the surface that

g-fold

7-fold

(a)

(cl

&

4

Fig. 5. (a) Bonding arrangements and frontier orbitals at the 7-fold (left) and I-fold (right) coordinated disilicide-silicon (111) interfaces. Nos. 1 and 3 indicate disilicide and substrate silicon dangling bonds, respectively; No. 2 indicates a metal-centered low-lying orbital and No. 4 a bonding orbital between a first and second layer substrate Si atom. (b, c) energy level diagrams for the interface chemical bonds for ‘I-fold (left) and 8-fold (right) coordinated interface metal atoms. CoSi,/Si(lll) (b) and NiSi,/Si(lll) (c) are compared.

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one Si corner atom is removed. The three Si atoms sitting next to this atom become surface Si atoms, each with a dangling sp3 orbital pointing in the [ill] direction. The removal of one si corner atom will, of course, change the interaction diagram of fig. 3b (for example, there will be some mixing between T,, and Es orbitals), but we do not expect considerable changes. Therefore, the most important effect of removing one Si corner atom is that one electron is “taken away” from the cube. The level energies of the surface Si sp3 dangling bonds, however, are higher than those of (mixtures of) the (metalTherefore, the electrons in the surface Si centered) T,, and Es orbitals. dangling bonds will prefer these lower-lying orbitals. Since there is one surface Si dangling bond per metal atom, the electron from this dangling bond just replaces the electron removed with the corner Si atom. Consequently, the Si atoms of the MSi,(lll) surface have empty dangling bonds, and the orbitals within the cube will be filled the same way as in the bulk disilicide. The latter means that in the case of Nisi,, all metal-centered low-lying orbitals within the cube are filled with electrons, whereas in the case of CoSi,, there is still place for one electron in these orbitals. In other words, there is one “electron vacancy” per three Co-surface Si bonds, whereas there is no such vacancy for NiSi,(lll). Fig. 5a shows the frontier orbitals at the MSi,(lll) surface: the MSi, surface Si dangling bond (No. 1) and the highest (in the case of CoSi, partially filled) metal-centered orbital (No. 2). In addition, the Si substrate dangling bond (No. 3) is shown; No. 4 indicates a bonding orbital between first and second layer substrate Si atoms. 3.4. The 5-fold coordinated

interface

In the case of disilicide metal to substrate silicon bonding, there are two possible interface structures: the 5-fold coordinated interface (fig. la) and the &fold coordinated interface (fig. lb). In this section we discuss the 5-fold coordinated interface; in the next section we will compare this with the s-fold coordinated interface. The 5-fold coordinated interface was modeled using the clusters of fig. 2a and 2b without the shaded Si and pseudo-hydrogen atoms. The interaction diagram that follows from the calculations on this interface is quite simple (fig. 6). The A, frontier orbital of the disilicide surface (corresponding to the highest level in fig. 4b) interacts with the Si substrate dangling bond. The resulting bonding orbital is completely filled. In addition, for NiSi,/Si, the nonbonding E level contains one electron (indicated between brackets in fig. 6). The calculations show that the disilicide orbitals corresponding to the four lowest levels in fig. 4b hardly interact with the Si substrate. Table 1 shows the calculated interaction energies per interface bond. Clearly, the difference between Co and Ni is small, as is to be expected from the fact that the extra Ni electron goes into a nonbonding orbital, while in both cases the energy gain

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Fig. 6. Schematic interaction diagram of disilicide metal to substrate silicon bonding in the case of a 5-fold coordinated interface.

of the two electrons going into the bonding orbital is (about) the same. Furthermore, we see from this table that there are no large variations of the bond energies with cluster size. 3.5. The j-fold verse

the &fold coordinated

interface

If we saturate the three metal dangling bonds at the 5-fold coordinated interface by Si atoms, we obtain the &fold coordinated interface. The g-fold coordinated interface will be more stable than the 5-fold coordinated interface if the energy of the three M-Si bonds is larger than the repulsive energy the extra layer Si atom experiences from the Si substrate; this is, in fact, for both CoSiJSi and NiSiJSi the case, according to our calculations. Table 1 shows the calculated total energy lowerings per added Si atom (i.e., per three metal-surface Si bonds) when going from the 5-fold to the 8-fold structure. Also, the calculated energy lowerings per Si atom when adding a Si layer to the metal-terminated disilicide surface are shown. From this table, we can see that if we add a Si layer to the 5-fold coordinated CoSi,/Si(lll) interface, the energy is lowered even more than if we add a Si layer to the metal-terminated Table 1 Calculated interaction energies (in eV) per interface bond for the 5-fold coordinated interface (first row) and calculated energy lowerings per added Si atom if a Si layer is added to the metal-terminated disilicide surface, thus making the silicon-terminated surface (second row), or to the S-fold coordinated interface, thus making the I-fold coordinated interface (third row) (all energies have been calculated with clusters containing one (left) and three (right) metal atoms) 1 metal atom

3 metal atoms

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8.2 8.5

8.2 7.6

9.8 10.3

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4.00

Fig. 7. PDOS curves (solid line) of the pz orbital of the disilicide first layer atoms at the &fold coordinated interface, and COOP curves (dashed line) of the interaction between this p, orbital and the substrate (first layer) Sip, and pVorbitals. The z-axis is defined perpendicular to the (111) interface plane. The zero of the energy scale is at the Fermi level. The curves are based on the calculations with the three-metal-atom clusters.

CoSi,(lll) surface; for M = Ni it is just the other way around. This difference between Co and Ni suggests that it is especially the antibonding interaction between the dangling bonds of the extra Si atoms and the filled Si substrate orbitals which raises the total energy of the 8-fold structure (see figs. 5b and 5c, right); for, as we will argue in the next section, these dangling bonds are empty at the 8-fold coordinated CoSi,/Si interface, but get partially filled at the g-fold coordinated Nisi */Si interface. This point is illustrated in more detail in fig. 7. This figure shows for both S-fold CoSi /Si and Nisi JSi partial-density-of-states (PDOS) curves of the disilicide extra Sip, orbital and crystal-orbital-overlap-population (COOP) curves of the interaction between the extra Sip, orbital and the first layer substrate Sip, and pJ orbitals; the z-axis is defined perpendicular to the (111) interface plane. The COOP, introduced by Hoffmann and coworkers [9], is a

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measure of the bonding/antibonding character of the states in the (P)DOS: a positive COOP indicates bonding states, and a negative COOP antibonding states. The COOP curves of fig. 7 give the bonding and antibonding regions between the extra Sip, orbital and the first layer substrate Sip, and p.” orbitals. We note, that the extra Si dangling bonds are largely of pZ character and that the filled first layer substrate Si orbitals are largely of p, and pv character. Now, if we consider the p, PDOS at B-fold CoSiJSi, we see two main structures: the low-energy structure indicates bonding between the p, and substrate Sip, and p, orbitals, as we can see from the COOP curves, and the high-energy structure (just above the Fermi level) indicates antibonding between these orbitals. The antibonding is relatively weak; although there is a considerable PDOS above the Fermi level, the antibonding COOP is relatively small. So in fact, the PDOS structure above the Fermi level largely indicates the dangling bonds of the extra Si layer atoms. Now, if we go to Nisi,/%, we see that the high-energy (weakly antibonding) structure is below the Fermi level. The fact that (weakly) antibonding levels become partially occupied at the interface can explain why for M = Ni adding an extra Si layer is energetically more favorable at the bare MSi,(lll) surface than at the 5-fold coordinated MSi,/Si(lll) interface, whereas this is not the case for M = Co. In summary, we have seen that the formation of M-Si bonds in the disilicide lowers the total energy of the B-fold coordinated interface with respect to the 5-fold interface; the antibonding interaction between the extra layer Si dangling bonds and filled substrate Si orbitals can raise this energy if the dangling bonds are (partially) filled, as is the case for NiSi,/Si. However, for both Co and Ni, the M-Si bond formation is the strongest effect; consequently, for both metals the B-fold interface is more stable than the 5-fold interface.

3.6. The g-fold versus the 7-fold coordinated

interface

Having shown that for both CoSi,/Si and NiSiJSi the B-fold coordinated interface is more stable than the 5-fold coordinated interface, we can compare disilicide silicon to substrate silicon bonding with disilicide metal to substrate silicon bonding using the 7-fold and B-fold (instead of 5-fold) structures, respectively. Fig. 5 gives a schematic picture of the chemical bonding at the 7-fold and B-fold coordinated CoSi,/Si(lll) and NiSi,/Si(lll) interfaces. At the 7-fold coordinated interface, the frontier orbitals 1 and 3 interact, forming a chemical bond, whereas at the B-fold coordinated interface, there is chemical bonding between Nos. 2 and 3. In addition, at the B-fold interface, the disilicide dangling bond (No. 1) is a little destabilized due to a weak antibonding interaction with filled substrate Si-Si bonds (No. 4); we discussed this already in the previous section.

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Figs. 5b and 5c show schematical interaction diagrams for CoSi,/Si and Nisi,/% respectively. Due to more spatial overlap and less orbital energy difference, the interaction between Nos. 1 and 3 will be stronger than that between Nos. 2 and 3. According to our calculations, the orbital energies of No. 2 and of the bonding combination between Nos. 1 and 3 are about the same. We will show this in more detail below. Now, in a real system, we have no discrete levels but broadened (band)structures. Therefore, we expect both the broadened level 2 structure and the broadened l-3 bonding structure to be partially filled with electrons, since they have the same energy. We have indicated this in figs. 5b and 5c by drawing the “electron arrows” through both levels. Now, at the g-fold coordinated CoSi,/Si(lll) interface, the two electrons available for the interface chemical bond will go into the bonding combination between Nos. 2 and 3 (fig. 5b, right), which has a lower orbital energy than orbital No. 2 and the l-3 bonding combination of the 7-fold coordinated interface (fig. 5b, left). Therefore, g-fold coordinated CoSi,/Si will be more stable than 7-fold coordinated CoSi,/Si. Although for NiSi,/Si the interaction diagrams are roughly the same, the extra Ni electron changes the picture. At g-fold Nisi,/& two electrons lower their energy by going into the 2-3 bonding orbital (fig. 5c, right); the third electron goes into the (slightly destabilized) disilicide dangling bond No. 1. At 7-fold Nisi,/%, however, although the energy of the first 2 electrons is not lowered, the energy of the third electron is lowered considerably by going into orbital No. 2 and the bonding combination between Nos. 1 and 3 (fig. 5c, left). The latter configuration (considerable energy lowering of third electron) turns out to be more stable than the first one (smaller energy lowerings of first two electrons), although the energy difference between both configurations (corresponding to the 7-fold and g-fold structures) will be smaller here than for CoSi,/Si(lll). So far, we have given a very schematic description of the disilicide-silicon interface chemical bond. In the following, we discuss this in more detail, using the previously (section 3.5) defined PDOS and COOP curves. Fig. 8 shows for 7- and g-fold CoSi,/Si(lll) (fig. 8a) and NiSi,/Si(lll) (fig. 8b) the PDOS curves of the disilicide surface Sip, and metal d,z orbitals and of the substrate Sip, orbitals. Also COOP curves of the interactions between these orbitals are shown. Clearly we can see from the COOP pictures that at the 7-fold coordinated interfaces, there is much more interaction between the frontier orbitals 1 and 3 (which are largely of p, character) than between the frontier orbitals 2 (largely of dZ2 character) and 3, whereas it is the other way around at the g-fold coordinated interfaces (although in the latter case there is some interaction between substrate and disilicide Sip, orbitals leading to states above the Fermi level). At the 7-fold coordinated NiSiJSi interface, we see that the Sip,-Sip, bonding structure is at about the same energy as the nonbonding d_J structure; for 7-fold CoSi,/Si it is a little lower. For g-fold

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-16.00

-*2.00

-8.00

EIGENVRLUESIEVI I

-1.00

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EIGENVRLUESIEVI

CoSi,/Si

SUBSTR PZ S”8STR PZ

SlLC PZ ------S.liC n ozz -

‘0

;: 4 &fold

n

ii

Fig. 8. PDOS curves and COOP curves of the interactions between some relevant orbitals at the ‘I-fold and S-fold coordinated CoSi,/Si(lll) (a) and NiSi,/Si(lll) (b) interfaces. Shown are the PDOS of the disilicide first layer (solid line) and substrate (dashed line) Si atom pz orbitals, and of the metal d,z orbital (dot-dashed line). The z-direction is defined perpendicular to the (111) interface plane. COOP curves are drawn of the interactions between the substrate Sip, and disilicide metal d,z orbitals (solid line), and between the substrate and first layer disilicide Sip, orbitals (dashed line). The zero of the energy scale is at the Fermi level. The curves are based on the calculations with the three-metal-atom clusters.

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Table 2 Calculated interaction energies (in eV) per interface bond for the 7-fold and I-fold coordinated interfaces (all energies have been calculated with clusters containing one (left) and three (right) metal atoms) 1 metal atom

7-fold 8-fold

3 metal atoms

co

Ni

co

Ni

2.3 3.2

2.2 2.1

1.9 2.9

1.9 1.4

Co!%&, the disilicide Sip, PDOS has a large peak (corresponding to the dangling bond orbital No. 1) above the Fermi level, whereas for &fold NiSi,/Si it is (completely) below the Fermi level; we saw this already in the previous section (fig. 7). On the basis of fig. 5, however, we expect the dangling bond orbital No. 1 to be only partially filled for NiSi,/Si. The reason that it gets completely filled is that in the three-metal-atom clusters there is only one disilicide surface Si atom with a dangling bond whereas there are three substrate Si dangling bonds (see fig. 2b), so in this case one Si dangling bond has to accomodate 3 (instead of 1) extra electrons. This is clearly a cluster artefact. However, this does not change our interpretational picture, since we also calculate for the one-metal-atom clusters that 8-fold Nisi /Si is less stable than 7-fold Nisi JSi, and in the one-metal-atom custers the situation is just the other way around: 3 silicon dangling bonds have to accomodate 1 (instead of 3) extra electrons. Table 2 shows the interaction energies per interface bond calculated with the clusters containing one and containing three metal atoms. Although there are differences between the clusters, we see that the trends in calculated binding energies support our interpretation very well: for CoSiJSi the 8-fold structure is energetically more favorable, whereas for NiSi,/Si the 7-fold structure is. Moreover, for NiSiJSi the energy difference between both structures is smaller than for CoSiJSi, as expected. Quantitatively, the binding energies of the one- and three-metal-atom clusters are reasonably close ( - 0.3 eV) except for the g-fold NiSiJSi structure (0.7 eV difference). This is due to the cluster artefact described above. Consequently, for NiSiJSi the calculated difference in bond energy between 7-fold and 8-fold structures is larger for the three-metal-atom clusters than for the one-metal-atom clusters.

4. Conclusions Our LDA-LCAO calculations on clusters modeling the 5-fold, 7-fold and S-fold coordinated CoSi J Si(ll1) and Nisi J Si(ll1) interfaces show that for

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both CoSi,/Si and NiSi,/Si the &fold coordinated interface is more stable than the 5-fold coordinated interface, and that for Nisi,/%, contrary to CoSi,/Si, the 7-fold coordinated interface is more stable than the 8-fold coordinated interface. Making the 8-fold structure from the 5-fold structure by adding an extra silicon layer lowers the total energy of the system, because the repulsive (antibonding) interaction between the dangling bonds of the extra Si layer atoms and filled substrate Si orbitals is smaller than the bonding interaction between the extra Si and the metal dangling bonds at the 5-fold coordinated interface. 8-fold CoSi,/Si is more stable than 7-fold CoSi,/Si since at the Si-terminated CoSi,(lll) surface, there is a deep-lying metalcentered orbital which is not completely filled and is therefore an ideal candidate for a (partially filled) substrate Si dangling bond to interact with. At NiSi,(lll), all metal-centered orbitals are filled, and therefore the only disilicide candidate for an interface chemical bond with substrate Si is its Si dangling bond. This picture is consistent with the band structures of bulk MSi,, where al deep-lying metal-centered orbitals are not completely filled for M = Co, whereas they are for M = Ni.

Acknowledgements The authors thank J.F. van der Veen for his critical reading of the manuscript. Financial support from the Netherlands Committee for the Use of Supercomputers is greatfully acknowledged. This work is part of the research program of the Netherlands Foundation for Fundamental Research on Matter (Stichting voor Fundamenteel Onderzoek der Materie) and is financially supported by the Netherlands Organization for Scientific Research (Nederlandse Organisatie voor Wetenschappelijk Onderzoek).

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[9] T.A. Albright, J.K. Burdett and M.H. Whangbo, Orbital Interactions in Chemistry (Wiley, New York, 1985). [lo] R. Hoffmann and Chong Zheng, in: Proc. NATO Advanced Research Workshop and 40th Intern. Meeting of the Societe du Chimie Physique, Strasbourg, France, September 1985, Ed. A. Veillard (Reidel, Dordrecht, Holland, 1986) p. 425. [ll] See, for example, D. Post and E.J. Baerends, J. Chem. Phys. 78 (1983) 5663; P.J. van den Hoek, A.D. Tenner, A.W. Kleyn and E.J. Baerends, Phys. Rev. B 34 (1986) 5030. [12] E.J. Baerends, D.E. Ellis and P. Ros, Chem. Phys. 2 (1973) 41. [13] S.H. Vosko, L. Wilk and M. Nusair, Can. J. Phys. 58 (1980) 1200. 1141 H. Stall, C.M.E. Pavlidou and H. PreuB, Theoret. Chim. Acta 49 (1978) 143. [15] P.M. Boerrigter, G. te Velde and E.J. Baerends, Intern. J. Quantum Chem. 33 (1988) 87. [16] T. Ziegler and A. Rauk, Theoret. Chim. Acta 46 (1977) 1. [17] J.G. Snijders, P. Vemooijs and E.J. Baerends, At. Data Nucl. Data Tables 26 (1981) 483; Internal report, Free University, Amsterdam, 1981, unpublished. [18] A. Redondo, W.A. Goddard III, C.A. &arts and T.C. McGill, J. Vacuum Sci. Technol. 19 (1981) 498. [19] P.A. Schultz and R.P. Messmer, Phys. Rev. B 34 (1986) 2532. [20] S.P. Murarka, Silicides for VLSI Applications (Academic Press, Orlando, FL, 1983) p. 73: K.A. Gschneider, in: Solid State Physics, Vol. 16, Eds. F. Seitz and 0. Turnbull (Academic Press, New York, 1964) p. 344. [21] C. Calandra, 0. Bisi and G. Ottaviani, Surface Sci. Rept. 4 (1985) 271, and references therein. [22] J. Tersoff and D.R. Hamann, Phys. Rev. B 28 (1983) 1168. [23] E. van Leuken, On the Electronic Structure of Transition Metal Disilicides, Graduate Thesis, University of Nijmegen, The Netherlands, 1986, unpublished. [24] D.M. Bylander, L. Kleinman, K. Mednick and W.R. Grise, Phys. Rev. B 26 (1982) 6379. [25] W.R.L. Lambrecht, N.E. Christensen and P. Blochl, Phys. Rev. B 36 (1987) 2493. [26] C.E. Moore, National Bureau of Standards, Circ. No. 467. Vol. II (US GPO, Washington, DC, 1958).