Bonding behavior of metal atoms on Si surfaces - Physical Review

PHYSICAL REVIEW B

VOLUME 58, NUMBER 4

15 JULY 1998-II

Bonding behavior of metal atoms on Si surfaces Anna Pomyalov Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76 100, Israel ~Received 28 January 1998! In this paper we suggest a quantitative approach for description of the bonding behavior of the individual metal atoms on Si surfaces. It is proposed to use the relative contribution of electronic and ionic components of the effective polarizability of the metal atom to characterize the type of bond. Individual As, Sb, Na atoms adsorbed on Si(001)231 surface and K atoms adsorbed on both Si(001)231 and Si(111)737 surfaces were studied. It was found that the bonding behavior of the potassium on these two surfaces is completely different. The covalency parameters calculated according to this approach allow one to define the As-Si and Sb-Si bonds as almost pure covalent, Na-Si bond as polarized covalent, K-Si bond in the Si(001)231 surface as largely ionic, while in the Si(111)737 surface it is predominantly covalent. @S0163-1829~98!05928-1#

I. INTRODUCTION

The long-standing scientific interest in metalsemiconductor junctions is dictated by their unique role in microelectronics. The fundamental question of this problem is the adsorption of individual metal atoms on low-index surfaces of silicon. However, the microscopic nature of the interaction of metal atoms with different Si surfaces is still a subject for discussion.1–24 For group-V metals like arsenic or antimony, there is an agreement between the calculated and measured adsorption geometries. Also, the type of the bond these atoms make with the Si~001! surface was unequivocally defined as a covalent one.16–19 The situation is much more complicated for alkali metals ~AM’s! on both Si(001)231 and Si(111)737 surfaces. According to photoemission data,16,20,21 the semiconducting Si(001)231 surface is metallized upon adsorption of a small amount of AM and becomes once more semiconducting with increasing coverage. The metalliclike Si(111)737 surface remains metallic at low K coverage, but the gap opens after about 0.5 ml of K is deposited. These experiments suggest a mixed bonding type with a different degree of covalency for AM/Si(001)231. In K/Si(111)737, a predominantly covalent bond was proposed.22–24 Important information on the local electronic structure around adsorbed AM atoms has been obtained by scanning tunneling microscopy ~STM!.2–4 In filled-state images of AM/Si~001!, the AM atoms are seen as bright spots. The sole reported atomically resolved empty state image of K/Si(001)231 does not show distinct K-related features.3 In contrast, on Si(111)737 the individual K atoms are imaged as missing adatoms ~dark contrast!.2 It was suggested,2 at variance with ultraviolet photoemission spectroscopy ~UPS! data, that the K atoms on this surface are completely ionized, giving rise to the dark contrast in the filled state STM images. Calculations propose various degrees of ionization of K on Si(001)231.5–8,13 For Si~111!, Clotet et al.14,15 argued that the K-Si bond has largely ionic character. However, they considered an unreconstructed surface. It is well known that the Si(111)737 surface has a complicated reconstruction.25 0163-1829/98/58~4!/2038~7!/$15.00

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The configuration of adsorption sites and the local electronic structure in this surface differ significantly from those of the unreconstructed Si~111!. Ishida26 has pointed out that for the adsorption of AM’s on metal surfaces at low coverage the covalent interactions play an important role. It is a common practice to compare results obtained for adsorption of AM atoms on Si~001! surface with the results for the Si~111! surface.2,20,22,27–29 However, it will be shown below that the properties of the same atom adsorbed on two different surfaces of the same crystal may be completely different. The origin of such a wide spread of opinions lays in the complicated nature of the metal-Si bond as well as in the lack of the quantitative measure of the covalency or ionicity of the adsorbate-surface bond. Each experimental or computational method is sensitive to a particular appearance of this phenomenon. To get more insight into the nature of the bond, it is thus instructive to consider the response of the adsorbate-substrate system to some external forcing. A natural choice of such a forcing is an external electric field. The field should be strong enough to affect the polarization state of atoms in question. In the present paper, the results of ab initio calculations of the bonding behavior of individual metal atoms adsorbed on Si(001)231 and Si(111)737 surfaces are reported. The surface response to a strong electric field was used to investigate the nature of the metal-Si bond on these surfaces. We propose to use the relative contribution of electronic and ionic components of the effective polarizability of the adsorbed atom to characterize the type of bond. We have chosen the adsorbates ~i! to test the method on some wellestablished surfaces @e.g., As/Si~001! and Sb/Si~001!#, and ~ii! to show its usefulness in such a disputed case as AM’s on Si~001! and Si~111! surfaces. The covalency parameters calculated according to this approach allow one to define the As-Si and Sb-Si bonds as almost pure covalent, Na-Si bond as polarized covalent, K-Si bond in the Si(001)231 surface as largely ionic, while in the Si(111)737 surface it is predominantly covalent. The differences in the local electronic structure of K/Si(001)231 and K/Si(111)737 surfaces leading to such a different bonding behavior are discussed. The paper is organized as follows. In the next section the 2038

© 1998 The American Physical Society

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BONDING BEHAVIOR OF METAL ATOMS ON Si SURFACES

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FIG. 2. Ball-and-stick models for the clusters representing the covered Si~001! surface. ~a! The Si15H20As2~Sb2! cluster representing the As/Si~001! and Sb/Si~001! surfaces, ~b! the Si31H32Na~K! cluster representing the cave adsorption site in Na/Si~001! and K/ Si~001! surfaces. FIG. 1. Ball-and-stick models for the clusters representing the clean Si~001! surface. ~a! The one-dimer Si17H20, ~b! the doubledimer Si31H32, and ~c! the four-dimer Si53H44.

surface model and the details of the computational procedure are specified. In Sec. III the method to characterize the type of metal-Si bond is described. In Sec. IV the method was applied to As, Sb, Na, and K atoms adsorbed on Si(001)2 31 surface and to K atom adsorbed on Si(111)737. In Sec. V we discuss the differences in the local electronic structure of K/Si(001)231 and K/Si(111)737 surfaces, which are likely the origin of different bonding behavior of K on these two surfaces. In Sec. VI the findings are summarized. II. MODEL A. Surface model

To define the appropriate cluster size the structure of the clean Si surface was calculated. The clean Si(001)231 surface was represented by clusters containing one dimer (Si17H20), two dimers from parallel rows (Si31H34), and four dimers (Si53H44), shown in Fig. 1. All calculated atomic structures are in reasonable agreement with other calculations.9,30–32 The parameters of the optimized cluster geometry were reported in Ref. 33. This allows me to use these clusters as a substrate and to proceed with a covered surface. Arsenic and antimony atoms at low coverage are thought to be adsorbed on Si~001! as dimers sitting on top of the Si dimer rows and oriented perpendicularly to the underlying Si dimers.10,11,16,17,34,35 To simulate these surfaces, we have used Si15H20As2~Sb2! @Fig. 2~a!# clusters with alternatively buckled asymmetric Si dimers. After optimization, the buckling of the dimers disappeared completely. In the underlying Si layer the unreconstructed geometry was almost restored, although the Si dimer atoms remained closer to each other than in the ideal surface

~3.6 Å instead of 3.8 Å!. The calculated As and Sb dimer bond lengths are slightly larger than the experimental one. Nevertheless, the obtained geometry33 reasonably agrees with the experimental results.11,34,35 Our study of the relative stability of cave and valley bridge sites showed that the cave site for adsorption of Na and K is the most stable one.33 To represent Na/Si~001! and K/Si~001! surfaces the Si31H32Na~K! clusters were used @Fig. 2~b!#. The large size of the Si(111)737 unit cell makes a direct ab initio calculation for this surface computationally intractable, unless a network of parallel computers is available. On the other hand, it was shown that the local interaction of the adsorbed atoms with the corresponding surface adsorption site can be studied with relatively small clusters.36,37 The local nature of K-Si interactions on this surface ~as follows from STM and UPS data! allows us to use this approach to study changes in the local electronic structure upon K adsorption. It was suggested that the individual AM atoms are directly bonded to adatoms.2 The center adatoms are more reactive, with almost no difference between the faulted and unfaulted halves of the unit cell. To represent this adsorption site we used a Si6H9 cluster composed of the six atoms surrounding the center adatom in the faulted half, as defined in Refs. 38 and 39 @Fig. 3~a!#. All unsaturated bonds, except the adatom dangling bond, were saturated with hydrogen atoms. To simulate the covered surface, a K atom was bonded to the adatom @Fig. 3~b!#. The geometry of the cluster was then optimized, with H atoms fixed in their positions. The optimized K-Si bond length was 3.18 Å. Four topmost Si atoms relaxed upward by 0.1 Å from their positions in the clean surface, defined in Refs. 38 and 39. Although the clusters chosen to represent this complicated surface are very small, the main aim of this calculation is to show applicability of the proposed method to different surfaces. It would be shown in Sec. V that the K-Si bond is

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FIG. 3. Clusters simulating the adatom site in Si(111)737 surface: ~a! clean adatom site, ~b! adatom with the K atom adsorbed on top. Shaded circles denote Si atoms, small open circles denote H atoms, and a large black circle denotes the K atom.

indeed localized and, thus, at least qualitative conclusions are not affected by the smallness of the clusters. B. Method of calculation

The geometric and energetic properties of the surface were calculated using an ab initio all-electron numerical total energy DMol method40 based on density-functional theory. The details of the formalism were given by Delley.41,42 For calculations of Si~001!, the Hedin-Lundqvist/JanakMorruzi-Williams ~HL/JMW! local correlation43 and the Becke44 gradient-corrected exchange functionals were chosen. For all atoms, a double numerical basis set with a frozen core approximation for the 1s2s orbitals of As, Na, Si, and for the 1s2s2p orbitals of K and Sb was used ~‘‘frozen inner core’’!. The integration grid for molecular orbitals was generated in a spherical pattern around each atomic center.41,45 Radial integration points were taken from the nucleus to an outer distance of 10 bohrs. Angular integration points were generated at each of the radial points using Gaussian quadrature schemes.46–48 In the present work the integration grid with about 1000 points per atom was used. For calculations of K/Si~111!, the Vosko, Wilk, and Nusair49 ~VWN! local functional and the Becke-Perdew44,50 nonlocal corrections after the final self-consistent-field iteration ~SCF! were used. A test run carried out using HL/JMW functional gave close results, but for VWN less SCF iterations were needed for the same level of accuracy. A double-numerical1d orbitals ~DND! basis set with the inner core frozen was used. The convergence criterion was 131026 Ry for the energy and 131023 Ry/~a.u.! for the energy gradient. The uniform external electric field was entirely included in the calculations of the self-consistent potential. III. POLARIZABILITY AND COVALENCY PARAMETER

To specify changes in the local electronic structure, we have used the polarization of the system caused by the presence of the adsorbed atom. Such a parameter reflects the nature of the adsorbate-surface bond. The clean surface does not have a permanent dipole moment. The interaction between the adsorbed atoms and the surface leads to a redistribution of a charge density, which creates a surface dipole.

FIG. 4. Schematic representation of local dipoles for calculation of the effective polarizability.

In the past, considerable attention was drawn to the analysis of the dipole moment of the system calculated with the adsorbed atom displaced from its equilibrium position.14,51,52 The resulting curves were expanded in the Taylor series. The slope and the curvature were then analyzed to deduce the degree of the ionicity of the bond. This method describes the deviation of the slope ~proportional to the net charge on the adsorbed atom! from the one calculated for the pure ionic contributions to the bond. It is useful for the predominantly ionic or covalent systems. It is, however, less informative for the intermediate cases. We will show in Sec. IV that two systems with close values of the adsorbate’s charge may have very different bonding behavior. The slope of the dipole moment curves on its own can only serve as a qualitative measure of the bond ionicity. We are, therefore, seeking for a parameter that is equally meaningful for the extreme and the mixed types of bonding and allows a quantitative description of the type of the bond. To this end, we consider the response of the surface dipole to the external electric field. Field-induced changes in this dipole can be divided into two components: polarization of the substrate and polarization of the adsorbate-substrate bond. The former does not depend on the adsorbed atom and is close to that of the clean surface. The latter can be further divided into the contribution of the electronic polarization ~redistribution of the electron density! and the ionic polarization ~changes in the positions of the atomic cores!. The relation between these two components directly depends on the nature of the bond that the adsorbed atom forms with the surface. Indeed, the dipole associated with adsorbed atom can be considered as the vector sum of a rigid dipole ~formed by an ionized adsorbed atom and a polarized surface! and a local dipole ~due to polarization of the adsorbed atom itself!: P5q a l 1 m a , where P is the polarization due to the adsorbate defined as a difference between the total dipole of the cluster with and without the adsorbed atom; q a is the effective charge of the adsorbed atom; l is the length of the rigid dipole; and m a is the local dipole of the adsorbate ~Fig. 4!. The effective charge is the difference between the electron density within the atomic radius of the adsorbate in the cluster and in the free atom. For the calculation of the rigid dipole it is taken as a point charge at the position of the adsorbate’s core. The dipole length is the distance from the adsorbate’s core to the first surface layer. The local dipole is a measure of the deviation of the effective charge distribution from spherical


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within the adsorbate’s atomic radius. Here, we consider only the z component of this dipole, which is parallel to the electric field. The external electric field causes redistribution of the electron density as well as geometry relaxation. Both factors give rise to an additional polarization: P5 P 0 1 a eff a E,

~1!

where P 0 is the polarization due to the adsorbed atom without an electric field. The polarizability of the metal atom on the surface is, therefore

a eff a 5

dl d P d m a dq 5 1 , l 0 1q 0 dE dE dE dE

~2!

where l 0 is the unrelaxed dipole length and q 0 is the effective charge of the adsorbed atom without the field. Since we are interested in the ground-state properties of the adsorbatesurface bond, only linear terms were considered. The first two terms in Eq. ~2! are related to the redistribution of the electron density. For a purely covalent bond all changes in the dipole moment are defined by this component: D e p5

d m a dq 1 l . dE dE 0

~3!

In a purely ionic bond the density distribution does not change and all changes in the dipole are due to the shift of atomic cores. Thus, D i p5q 0

dl . dE

~4!

In a mixed bond both components are present. Their relative contribution to the field-induced polarization may serve as a measure of the bonding type. We define the degree of the bond covalency ~a covalency parameter! as K c5

Dep

a eff a

.

FIG. 5. The field dependence of the adsorbed atom’s height above the surface, the effective charge q eff , and the local dipole moment m eff for different atoms on Si~001! and Si~111! surfaces. L denotes K/Si~001!, 1 denotes Na/Si~001!, * denotes K/Si~111!, n denotes As/Si~001!, and h denotes Sb/Si~001! surface. The lines are a polynomial fit to the calculated points.

~5!

This parameter has clear physical meaning and definite numerical value for all ranges from a pure ionic (K c 50) to a pure covalent bond (K c 51). Therefore, it is possible to quantify the type of the bond on the basis of K c only. In the next section we discuss our results for five different metal atoms adsorbed on Si surfaces and show that by means of K c one can reach better understanding of the nature of the adsorbate-silicon bond. In order to calculate the covalency parameter, one first has to calculate the field-induced changes in the atomic and the local electronic structure of clean and covered Si surfaces. IV. RESPONSE TO THE ELECTRIC FIELD OF THE COVERED Si SURFACES

To study the surface response to the external electric field, the geometry of all clusters @representing clean and covered Si~001! and Si~111! surfaces# was reoptimized in the presence of the uniform electric field of both polarities. The field was oriented normal to the surface. The positive direction out of the surface was chosen. Being interested only in dis-

turbing the adsorbate-Si bond, we have used field strengths up to 60.5 V/Å ~0.0095 a.u.!, so that the potential energy change was less than half of the binding energy. The field dependence of parameters important for the present discussion are shown in Fig. 5. To find some common tendencies in the surface response to the field, consider different systems in pairs. The first pair is the group-V metals. The behavior of As and Sb atoms is quite similar. The field dependence of DZ, q eff , and m eff is linear in the whole range of the fields. The geometry relaxation is very small; for As it is almost negligible. In contrast, the changes in the effective charge and the local dipole are considerable relative to their values without the field. The second group is AM’s ~Na and K! on Si~001! surface. For the Na atom, all three parameters are strongly field dependent with linear behavior in all range of the fields. For the K atom, the effective charge changes linearly with the field, but only slightly compared with its value without the field. The atomic position and the local dipole change nonlinearly. The local dipole slightly reduces for both polarities of the field. The geometry relaxation is extremely strong.

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TABLE I. The calculated covalency parameters for different adsorbed atoms. Surface

Si~001!

Si~111!

Atom

As

Sb

Na

K

K

Kc

0.98

0.90

0.75

0.4

0.93

The third pair consists of the K atoms on two different surfaces: Si~001! and Si~111!. For this pair the only common tendency is the nonlinear response to the field. The position of the K atom on top of Si~001! surface is strongly field dependent: it is pulled out of the surface by the positive field and pushed towards the surface by the negative one. In contrast, K atom in Si~111! surface is slightly pulled out of the surface for both polarities of the field. The situation is reversed for the electronic properties. Both the effective charge and the local dipole are similar for these two surfaces without the field. They only slightly change for K/Si~001! surface. In K/Si~111!, the changes are extremely strong. According to ideas presented in Sec. III, such a different response suggests different bonding behavior for these atoms. In the case of strong changes in electronic structure and weak geometry relaxation one expects covalentlike bonding. In the case of strong relaxation and small changes in electronic structure more ionic behavior is expected. When all parameters change significantly, the detailed analysis is needed. This is exactly the case when the covalency parameter defined in the Sec. III can give a quantitative answer. To calculate the covalency parameter K c , one has to calculate the field derivatives of m a , q, and l . To this end, their values obtained for different fields were fitted by the second and third order polynomials ~Fig. 5!. The calculated K c are listed in Table I. For As and Sb, K c is very close to unity, as expected. For Na, the value of 0.75 reflects the mixed character of the bond, although it is largely covalent. The most interesting is the difference in the bonding type for K on two surfaces: Si~001! and Si~111!. It is mixed, but largely ionic in Si~001!. In contrast, in Si~111! surface K atoms are bonded covalently. To understand the origin of such a difference we have studied the changes in the electronic structure in these two surfaces using density of states ~DOS! spectra, which are discussed in the next section. V. LOCAL ELECTRONIC STRUCTURE OF K/Si„001… AND K/Si„111… SURFACES

It is often assumed that the similarity of some important adsorption parameters suggest similar bonding properties. As such a parameter the bond length and the effective charge are used. Both parameters are very similar for K/Si~001! and K/Si~111! without the field: L K-Si53.46 Å, q eff510.56u e u in Si~001! and L K-Si53.18 Å, q eff510.5u e u in Si~111!. However, as we already discussed, the response to the external field and the type of the K-Si bond in these surfaces are completely different. Let us consider changes in the electronic structure upon the K adsorption in these surfaces. In Si~001! the changes are small ~Fig. 6!. All states char-

FIG. 6. DOS for the ~a! clean Si~001! and ~c! K/Si~001! surfaces. In ~b! and ~d! the decomposition of the total DOS into contributions of different atoms is shown. Si1 denotes the upper dimer atom, Si2 the lower dimer atom. The origin of the spectra was placed at E F of the clean surface. The position of E F in each surface is shown by an arrow.

acteristic of the surface reconstruction in the Si~001! surface are present in the DOS of K/Si~001!. The surface states related to the p dimer bond are mixed with the K 4s orbital. The dimer p * state becomes partially filled due to charge transfer from K atom to the surface. The contribution of the K 4s orbital to the p state is close to that of the low dimer atom, while its contribution to the p * state is negligible. The K 4s orbital has the largest overlap with the surface resonance just above the conduction-band edge. There is some excess charge density concentrated between the K atom and the neighboring Si atoms and in the dimer bond region. In contrast, in Si~111! the electronic structure changes drastically ~Fig. 7!. The adatom dangling-bond state that pins the Fermi level in the clean surface was removed. Instead,

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These features of the calculated electronic structure of K/Si(111)737 surface agree with conclusions drawn from the core-level photoemission experiments.24,23,22 They also do not contradict the STM data, since the gap opened near E F would result in a localized dark contrast in both filled and empty state images. It is thus justified that, at least for purposes of the qualitative analysis, one can use small clusters to study this surface. One can see that indeed the adsorption of K atoms is a complicated process that deeply affects the electronic structure of the surface. In the Si~001! surface, both dimer atoms are involved in bonding. The mixed orbitals are localized within the first surface layer and not between the K atom and some of the Si atoms. It is clear that it is not possible to define such a bond other than of a ‘‘mixed’’ type from analysis of the zero-field structure only. In K/Si~111! surface, the picture is much clearer. Two new states, directly related to the K-Si bond, are localized between these two atoms. However, the local electronic structure is far more complicated than in the diatomic molecule and involve contributions from all Si atoms surrounding the adatom. The usual methods for defining the degree of the bond polarization from the relative contribution from two atoms to the joint orbitals are inapplicable. In such a complicated case the proposed method is thus very useful. VI. CONCLUSIONS

FIG. 7. DOS for adatom in the ~a! clean Si~111! and ~b! K/ Si~111! surfaces. ~a! The upper line is the total DOS, the lower line the contribution of the adatom states into total DOS. The state marked A is an adatom dangling bond state. ~c! The decomposition of the total DOS into contributions of the K atom and Si adatom. States marked A and B are K-Si states. The origin of the spectra was placed at the E F of the clean surface.

two states with a gap of about 1 eV appear. The K and Si adatom contribute almost equally to these states. The corresponding molecular orbitals are strongly localized between two atoms, which is typical for covalent bonding. Other states are almost unaffected, although relative intensities change.

1

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In this paper we have described the method to quantify the degree of covalency of the bond the adsorbed atoms make with the Si surfaces. The surface response to the external electric field was used to define the relative contribution of the electronic and ionic components to the effective polarizability of the adsorbed atom. The covalency parameters calculated according to this approach allow one to define the As-Si and Sb-Si bonds as almost pure covalent, Na-Si bond as polarized covalent, K-Si bond in the Si(001)231 surface as largely ionic, while in the Si(111)737 surface it is predominantly covalent. ACKNOWLEDGMENTS

I am grateful to Victor L’vov and Vera Lyakhovitskaya for important comments on the manuscript. This work was supported by the Minerva Foundation, Munich, Germany, by a grant from the Basic Investigation Foundation administered by the Israeli Academy of Sciences and Humanities, and by the Edith Reich Fund.

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