A theoretical study of the growth of metals on silicon

Applied Surface Sciencef~l/hl (1092) 136-145 North-Holland

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A theoretical study of the growth of metals on silicon | n d e r P. B a t r a IBM Rc~e~lrc'h Dlt t.~ion. Abnadrn Rest'arch (~'mt'r K62 / 802, 650 Ihtrrt Road, 3an Jaw. t'.4 o512n, UA~4

Received 20 November 1001;accepted b~r publicatinn 3 December lUUl

The structures of ordered nverlaycrs of ~llkali~1~=1,u.:,'~lemelals on Si(01)l}-2 × I nix.studied thcorelically.Compandive studies enable us to nnderstand btmding and slabililyof Peierls distorlcd structures. Results deduced from computed Iotal cuel'gle~are emplosed to explain u~rneselected experimentalobser.,alions.

l,|ntruductJon An understanding of the growth of metals on semiconductors can impact a variety of application areas besides Schottky barrier formation and metallization [1]. To achieve this it is helpful if one is armed with the knowledge of the geometrical arrangement of metallic overlayers. The computation of atomic arrangement is a challenging theoretical endeavor not only due to coverage-dependent effects but in many cases the grown structure depends strongly on the substrate temperature. The level of theoretical complexity is not difficult to appreciate considering that the atomic reconstruction of various Si surlS_ees have involved efforts extending over several decades. In the year 1991, there are still publications dealing with this very, subject. The adsorption of metals on Si can lead to removal of reconstruction of the substrate or it may lead to some other complex rearrangements. It is therefore not surprising thai our knowledge at this point is limited at best to a handful of systems. in this paper, we primarily concentrate on providing the atomic structure of alkali metals (AM) on Si(001)-2 × 1 surface a, initial coverages. The adsorption of simple metal like AI is only included for elucidating certain aspects of A M - S i interactions by comparison. In our work, one

monolayer (1 M L = 6.78 × 10 l~ adsorbates/cm -~1 corresponds to a metal atom : Si ratio of 1 : 1. Numerous investigations [1-4] have been carried out recently for understanding the nature of interaction of A M with semiconductor surl~ces. The Si(001)-2x 1 substrate has attracted much attention because this is among one of the tow surfaces which can be driven into a negative electron affinity [5,b] (NEA) state. It is somewhat ironic that even after many total energy calculations [1,7-15] no clear consensus exists regarding the optimum adsorption site. The nature of AM-semiconductor bond aP,~ continues to be a topic of debate. Extreme views exist [IA2,13A6-18]. The bond has been characterized as strong and ionic, weak and covalent, as well as various shades of gray in between. For alkali metals adsorbed on other metals, Langmuir [19], Gurney [21)] and more recently Lang [21] presented a model inw~Iving an ionic to metallic transition as a function of increasing coverage. Muscat and Bairn [22] went further in developing those models. Based on the ab inito results of Batra and Ciraci [23], they introduced bond length relaxation as a companion to the transition. This enabled them to obtain quantitative agreement with the change in the work function data [22]. Bond length relaxation has recently been confirmed experimentally [24].

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At low coverages tile A M atoms are believed to be mostly ionized. The A M overlayer turns metallic at higher coverages. This intuitively plausible picture of ionic to metallic transition is being questioned [25] for A M adsorption on metals, It is suggested that even at very low coverages the bond has a significant covalent component. For AM-semlconductors systems the situation is more complex. Some of the publications [1,18,26] have argued that the origina; Langmuir [19] and Gurney [20] proposal fi)r A M - m e t a l irlteraetious call be literally taken over for A M semiconductors interactions as well. Another school of thought [I,8] is that the presence of active dangling bonds on semiconductor surfaces makes a key difference. These empty dangling bonds near the Fermi level continue to soak charge from A M overlayer even up to 1 M L coverage. The overlayer metallization, therefore, does not take place well beyond I_~ M L coverage. Others [16A7] have interpreted their results in the light of a completely metallic bonding in the overlayer at 1 M L coverage. Thus values of charge transfer ( . A Q ) from A M to Si have been obtained [2] in the range (1 < .AQ < 1.

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2. Discussion of structural models[or alkali metals-Si Let us recall that atoms in the top Si layer of a clean St(001) surface nurmaily have two dangling bonds each for an ideal bulk truncated structure. The 2 × I structure is obtained when the:~e atopis dimerize along the x-direction (generating a o'bond) resulting in rows of dimers along the y-[110] direction. Each surface atom nominally has a single dangling bond. Since there are two Si atoms per surface unit cell, one gets two bands (~- and 7r*) in the gap region which are only partially occupied. The A M atoms interact with these dangling bond orbitals located near the Fermi level. Six probable adsorption sites labelled by the letters H. B, C, D, T and Y are shown in fig. 1. At ½ M L coverage there is one AM atom per 2 × 1 cell (3.39× 10 ~4 atoms/era-') in one of the above mentioned sites.

Fig I. Tt~pvie~s descrihalg the positionsof metalson $i((}()1)2x I. Filled and empty circle~ denote metal and Si atoms. respecli~ely Numeralsin the circles indlealc Si ulumic layers. (al ]I. B. Y C D ;tad T sdes have been labelled in the 2× 1 unil cell ~ht~,n hy dotted I~nes.AI ~ ML coverage only c~neof Ihese silos is o=:cupied h,r /.M. At 1 ML H-B or H-C are simullancuus[y ,'coupled. (b; Tile 2×2 una cell shown by dotted lineL,use[ tu stud~ Jx Peierls dislorted structure of metals lit i ML. ~c) ] he 2 × 2 unit cell shown by dotted lines used nl study dim.,riz~tion of metal atoms (J.~ disto[tion) at ML.

Levine [27] in 1973 proposed tbr Cs adsorption on St(001) that al low coverages this metal occupied a quasi-hexagonal hollow site (H) above the rows of dimers. The H-slte occupancy offered [27] a simple explanation for N E A because it left the

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long bridge (B) sites, where the adatom connects two dimers in adjacent rows, unoccupied. The coadsorption permits the o~.ygen atoms to sub- ergo under the B-sites to cause additional (beyond that produced by AM) [ov,ering of the work function required to achieve NEA. The C-site has adsorbatcs above the third layer of Si and due to reconstruction this is a more open site than H. Others trove called [I 1,13] the C-site as a valley bridge site (T3) and B-site as a cave site (T4). The dimer bridge site, D locates the adsorbate above the mid point of the Si dimer. In the lop site, T adsorbate is above one of the dimer forming Si atoms. The Y-site is an off centered site between the H- and the C-sites. Scanning tunneling microscopy {STM) work [28-32] on alkali metals at low coverages is responsible for revealing the Y-site [31]. The pioneering work [28-311 of deducing structure from the STM data [or AM on Siiflll[)-2 × 1 has been carried out by our Japanese colleagues. Since STM approximately probes the local density of states around the Fermi level, the detection of alkali metals on Si(01)l)-2 × 1 surface is a non-trivial issue. The difficulty arises from the fact that the Si~,00t)-2 × 1 surface has partly "occupied dangling bond states. The local density of states around E} are thus dominated by these states. Furthermore, the valence (ns) orbital of the AM atom which is obliged to interact with these states is rather diffuse. In the extreme ionic iuteraeti:m picture, these AM atoms will decorate the dangling bond states to be detected by STM. In the weak interaction case, the dangling bond states and the valance states of the metallic overlayer occupy" the same narrow region around El: making discrimination difficult. In spite of all these complications, STM work [28-32] has provided valuable information about the geometrical arrangement for AM on Si(001). 2 × L By carefully monitoring the density ef bright spots and deposition time the adsorbed AM atoms have been identified. Hashizume et al. [28] from their STM data suggested earlier that at low coverages, Li, K atoms are adsorbed on top (T) site above one of the dimer forming Si atoms. This data has been reinterpreted [29] in term of the Y-site adsorption.

Our total energy calculations lot the adsorption of Na on 8i(11111)-2× I at ½ ML coverage have been reported earlier. The symmetric dimer model given by Abraham and Batra [33] was employed. The energy ordered sequence we found for the N a / S i system in the order of decreasing stability is E ( H I = E ( B I < E ( Y ) < E ( C ) . The Dand T-sites were found [If)] to be much less stable. The computed bond length of 2.6 ,~ was smaller by ~ 0.3/~ from the L E E D [34] value. It thus emerges that the H, B, Y and C sites arc competitive adsorption sites at ~ ML coverage. Consequently we decided to study a potential energy line passing through the likely adsorption sites. The local dip in total energy at the Y-site (with the S i - N a - S i plane being perpendicular to substrate surface) suggests that the Y-site is a good candidate to be an adsorption site. We have only carried out a limited relaxation at every structural point. But wc have shown earlier [10] that the adsorption induced relaxation of Si substratc plays a key role in selecting among sites which have close energy minima on the BornOppenheimer surface. Therefore, the results shown in fig. 2 are only good for qualitative or semi-quantitative purposes. It turns out that the C-site at this level of accuracy is not a true minimum. As shown m fig. 2, it is an inflection point along the y-direction. The AM atoms may well be trapped in this site before finding an absolute minimum. A general conclusion It-,, bc drawn from fig. 2 is that even at ½ ML coverage several adsorption sites arc nearly equally favored. A detailed duster calculation [13] initially indicated strong site dependency of the energy surface. It was subsequently realized [15] that the inclusion c,f substrate relaxation [10] makes many of those sites highly competitive. Our above assertions are consistent with the conclusions drawn from the STM data. It was concluded [31] that at low coverages ~ < 0.1 ML} K and Cs adsorb near the Y-site. We note that STM data was first interpreted [28] in terms of the T-site where AM bonds dircctly with the Si dangling bonds. This site was eliminated a long time ago by Ciraci and Batra [1,8]. Now the interpretation of the STM data has been revised [31]. It is argued that K and Cs atoms form bonds

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Fig. 2. Total energy of N;i-gi((lall-2× I (referenced wilh respect Io the H-~ael at ½ ML owerage along a line passing through various compelilive sites. Positive energies correspt*nd to less stable slructure~, with two neighboring Si atoms, which belong to adjacent and parallel dimer bonds. We called this site as the Y-site. At ½ M L coverage the wellknown one-dimensional linear chains parallel to the Si dimer rows have been confirmed [32] for K on Si(001)-2 × t. Although, the3, ~,ere unable to deduce a definitive adsorption site, the H-site is fully compatible with this S T M data [32]. At ~ 0.2 M L coverage they [32] noted the coexistence of adsorption in several sites consistent with our earlier conclusions [1,8,t0] and the inference drawn from fig. 2. A detailed cluster model calculation [13] has suggested that an A M adsorbate in an H-site may be unstable towards a Peierls type of distortion. It was shown [!3] that alkali metal atoms iu a zigzag chain produced a lower energy configuration. The zigzag chain is obtained by moving alkali metal atoms away from the H-site by equal and opposite amounts ( A x ) along the x-direction as shown in fig. lb. Batra [35] proved earlier that transverse distortions do not open any Peierls gap. Furthermore, for A M - S i '.Ix distortions also

!39

do not lower the total energy. This is to be contrasted with the AI-Si sy:item te be disees,~ed later. In all our previous considerations we had thought that results for K are expected to be rather similar. We expressed our conclusions often using Na and K interchangeably, It has become clear fl'om some recent work [36] that such a position may not be defendable, It has been pointed out that K and Cs on S i ( l l l ) do sh~)w results which depend on the AM under consideration. For e~ample, Cs leads to removal of tile n-bonded red.'onstructton an S i ( l l l ) w h e r e a s K does not. Therefore we must be more cautiaus in stating our conclusions. There are some hints in the calculations which suggest AM specific results, For example, the cluster calculation by Freeman et al. [i5] and O~g [14] pointed out that the B-site is more favorable adsorption site that the It-site when K is considered. In our calculations [8,10] the H-site wt~s favored. The revised cluster model calculations by Freeman et ;~1. [15] (including full relaxation) have found that lot K / S i the binding energies at the H-site (2.39 eV) and at the B-sites (2.38) are comparable. It is therefore now stated [15] that either of the two sites can ,serve as a possible chemisorption site for K atoms. The major effect of surface relaxation was demonstrated by Batra [10] earlier. This is now being corroborated by the cluster model calculation by Freeman et al. [1.5]. Their computed value of charge transfer of ~ 0.6 e at the H-site clearly rules out the suggestion [17] that the bonding is covalent. A bonding energy of ~ 2.4 e V also argues against the proposal [17] of a weak bond. A strong ionic picture is also supported by a cluster model calculation [12] based on ab initio Hartree-Fock method. Tgte strong bonding picture is also consistent with the recent band structure calculations by Morikawa et al. [37] as well as the thermal desorption results of Tanaka et al. [38]. The C-site is preferred (over H- or B-sites) by the recent pseudopotential ea]culations by Morikawa et al. [37] for K on Si(001)-2 × l at ½ a ML coverage. All these calculations clearly suggest that the potential energy surface is rather flat. This incidentally should be the case when

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ionic bonding is predominant. Covalent bonds, being directional in nature, tend to have potential energy surfaces [39] with well defined peaks and valleys. The structural resu~lts can now be summarized for A M ;Jdsorption on Si(t~)l)-2× I at ~ ML coverage. For No. the H-site is a preferred site. For K, the H-, B-, C- and Y-sites all seem to offer thgmseh,es as pc~lential ad,sorption sites with H site still holding a bit of an edge over the other sites. The substrate relaxa,~ion plays a crucial role in arriving at these eonclusiotts. The A M - S t bond is deeid,.-dly strong ( ~ 2 cV per alkali metal atom) with bond leng;Ih [411,411 in the range of 2.6-3.3 A. The plausible struct'aral models at full ML coverage ~,hich give the observed 2 × 1 L E E D patterns are only ~ few in number. One involves simultaneous occupan,.~ of H- and H-sites, the ( H - B ) ! iodcl. An a~tcrnative, involves occupying H- and C-sites simultaneously, the ( H - C ) model. Simultaneous occupa'6on of B- and C-sltes can be ruled out on physical grounds. Enta et al. [42] and Abuka~a and Kono [43] have shown the existence of a double layer of K on Si(llfll)-2 x I. All calculations [9-15..':,7] performed to date support the formation of a double layer as far as the energetics are concerned. A substantial binding energy ( ~ 2 e V / a t o m ) is projected up to I ML coverage. All calculated structures are puckered in nature in agreement with the conclusions derived from experimental data [42,43]. Also in agreement with the experimental findings, the surface is insulating [10] due to complete occupancy of the dangling bond states. A minor unresolved issue appea:s to be the adsorption :,ites. For a fixed lattice model given by Abraham and Batra [33], the ( H - C ) structure was found [10] to be less favorable by ~ 0.1 e V per unit cell for N a / S i . Upon incorporating lattice relaxations, the ( H - B ) and the ( H - C ) could not be distinguished based on total energies. Both the ( H - B ) and ( H - C ) structures for Na/S~ obtained by us were puckered [10]; with Ah = 0.70.9 ,A. Morikawa et al. [37] have found the ( H - C ) structure to be a preferred structure tor the K - S t system with a puckering of ~ 1.1 ,~. Dilayer structures at 1 M L K coverage with a puckering

of I.I ,~ ~X-ray photoelectron diffraction [4311 and 1.~5 A ( R H E E D measurements [44]) have been proposed. T h e very fact that the ( H - B ) and ~H - C ) models are competitive in energy suggests that the potential energy surflkce is flat. This p~.qnts to substantial ionic cxlmponent in the A M - S t bond even at I ML coverage. T h e growth mode beyond 1 ML is difficult to establish because no exhaustive studies exist in that domain. T h e common wisdom is that alkali metals lbrm a saturated overlayer hetween 11.5 and I ML coverage. Further growth may be possible by going well below the room temperature.

3. Nature of alkali me t a l -S[ inleractlon There have been some suggestions [16,17] in the literature tha' the interaction between A M and Si is weak at ~ ML coverage. ]t is difficult to reconcile this with S T M data where A M atoms have been shown to form one-dimensional chains parallel to the substrate Si dimer row direction~. In the proposed geometry for say K on St(001)2 x 1, the nearest neighbor K - K interatomic dislance of 3.8 A is considerably shorter than the bulk equilibrium distance of 4.6 ~. For Cs~. the deviation from the bulk bond length (5.2 A) is even greater. This suggests that A M atoms are being forced to locate on the repulsive part ( > 0.5 eV) of the potential energy surface in the A M A M coordinate. From thermal dcsorption experiments [38] binding energies of i,6 and 1.9 eV have been obtained depending on the adsorption site. The overall stabilizati-n of the structure must then arise from A M - S t interactions. This interaction has to be substantial and in fact most theoretical calculations [1,8-15] estimate this number to be m the 2 eV range. The origin of the stabilization energy lies in the image interaction between the alkali ion and the Si surface. The predominantly covalent A M - S t interaction proposal [17] is also not being supported by the S T M data. At intermediate coverages (I).2 MLI the A M atoms have been shown [32] to occupy a variety of adsorption sites. Covalent

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bonds are usually highly directional [39] in nature and tend to be site specific. O u r earlier total energy calculations and the Na potential energy line shown in fig, 2 support multiple adsorption sites in agreement with the S T M data. Thus both the data and the current calculations argue against a purely covalent bond. Multiple sites can be consistent with a weakly interacting metallic overlayer on $i((101)-2 x 1 surface. But we have notud above that the bond energy is ~ 2 eV which is certainly not weak. Hence, the overall interactions must have a strong ionic eontribufion. This conclusion is also supported by cluster calculations [12.13]. Tho precise quantitative value of the charge transfer, A Q , from A M to Si lacks consensus. All values ranging between 0 and 1 have been quoted in the literature. This is not tf~o surprising sincc there is no unique definition for ..~Q. T h e spatial and spectral distribution clearly suggest that the bond is substantially ionic. We believe that the STM observations are consistent with the Langm u i r - G u r n e y picture of ionic interaction at low coverages. It is clear that the values obtained by various authors are certainly correct within the framework of their models. Unfortunately, the computed charge transfer value does depend on the model used. it is therefore important that the model be stated more explicitly to avoid confusion. Finally, for what value of A Q a bond is to be called ionic, is also a matter of definition. One thinks of bulk GaAs. |or which A Q is in the range of ~ 0.1-0.3~ as an ionic compound semiconductor. We should now briefly discuss the important information about A M - S i interaction obtained from core level photoemission experiments. Recent work by Rifle et al. [45] for K on Si is prototyplcaL From a comparison of the binding energy shift (which was rather small for K on Si) with other adsorbates (F. O, CI, etc.) of presumably known ionicities, the authors [45] concluded that a .:.IQ = (I.q5e at low coverages. The low coverage regime was characterized by covalent K adsorption while at higher coverages a small degree of ionic character was suggested. This is a radically different view from the Langmuir [19]-

141

Gurney [20] model which invokes more ionic picture at low coverages. The complications associated with relating the core shift to charge transfer have been discussed [46], In particular, Bisi et al. [46] pointed out the net core shift arises from two opposing contributions. The charge transfer from A M to Si shifts the Si core level towards the vacuum level (lower binding energy). But the extra atomic Madelung contribution, of opposite sign, ea~lcels the greater part of this effect. T h u s the net core level shift may well be negligible even when ,4Q is significant. Only fl~e intra-atomic contributions of the core level shift is related to ,..,.4Q.This quantity is not directly observable and must be supplemented by either theoretical calculations or by other empirical data. This is an on going area of exploration [47] at the present tim¢. In summary, we can state that A M - S i interaction is strong and has a substantial ionic component. Perhaps a consensus on the precise value of the charge transfer from AM to Si is difficult to achieve. We continue to believe in the Langm u i r - G u r n e y picture of ionic to metallic transition only supplemented by our distance relaxation concept. The H-site at ½ ML coverage continues to be a slightly favored site. But in keeping with the concept of the ionic bond several other sites lie close in energy, Total energy permits the formation of a dilayer in either ( H - C ) or ( H - B ) configura'ion. The ordered growth beyond 1 ML is unlikely except perhaps at low temperature.

4. The a l u m i n u m - S i system We now briefly examine the atomic structure of AI on Si(001)-2 × 1 surface at initial coverages. It is expected that these results are applicable to Ga and In as well. To the author's knowledge, Lander and Morrison [48] were the first to report that at room temperature AI deposition on Si(001) leads to a disordered phase even at very low ( _< 0.5 ML) coverages. It is only recently that Ide, Nishimori and lchinokawa [49] reported a number of ordered surface structures determined by L E E D and A E S for Al-Si(001) up to 1 ML.

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DJlIerent structures appeared depending on the coverage and substrate temperature. NogamJ, Baski and Quatc [50] have produced S T M images of AI on Si(0Ol) revealing metallic dimers that run perpendicular to the underlying Si dimers rows below 0.5 M L as shown in fig. le. Beyond 0,5 ML, metallic clusters appear suggesting Stranski.-Krastannv growth mechanism. For in and Ga on Si(00 1} a transition to 3D cluster growth has been reported [51,52] only beyond a full ML. Hasan et al. [53] have grown AI overlaycrs in U H V on clean Si suhstrate kept at room temper. ature. They analyzed their data using AES. L E E D and R H E E D and concluded a layer-by-layer growth mode well beyond I ML. Thei r R H E E D data showed a continuous change from a 2 x l to an AI induced i x 1 pattern at 2 M L The L E E D data. on the other hand. continued to show a Si010l)-2× l - A l pattern (but with a degraded quality) upto 4 ML coverages. A possible explanation was offered in terms of the different depth sensitivities of the two techniques. A reasonable summary of the above experimental findings is that Al-like Ga and In is capable of producing ordered phases at low coverages but only at modest substrate temperatures. Furthermore, the ordered structures at low coverages can be explained by postulating metal dimer formet~on [49-53]. The unit cell here is 2 x 2 Si((Fdl) as opposed to 2 x I for alkali metal adsorption. S T M experiments [50] show clear evidence of dimers upto 0.5 ML. It was noted that the empty state image gives a more pronounced resolution of the Al-related features. O ~ r total energy calculations [54] support the formation of metal dimers up!o 1 ML. At ½ ML, tim structure shown in fig. Ic, where Al-dimers arc fo~med nea] the B-sites on the reconstructed surface is stable. The total charge density shown in f i g 3 explains that AI and substrate bonds are fully saturated at this coverage. State charge density a,~aciated with the lowest unoccupied state reve~,l AI atoms (it is antibonding state located on AI atoms) as concluded in the S T M work. However, there are some intriguing possibilities as to where the atoms are physically located in the unit cell! S T M experiments [50] note a change in AI growth mode at 0.5 M L and suggest that this is

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consistent with favorable bonding arrangements. We find bonding arrangements beyond 0.5 M L to explain the delayed onset of 3D cluster growth mode as seen [52] for Ga. Our calculation shows that near 1 ML the surface reconstruction is lifted. We now have ideal I × I substrate but Ai dimers are present in a 1 x 2 structure. Once again all bonds are saturated. The origin of dimers is explained in terms of standard (longitudinal) Peierls [55] distortion of a ncarly one-dimensional metallic system. The metal dimerization opens up a gap at the Fermi level and leads to an energetically more favorable state. Unlike A M - S t case, the substrate reconstruction is lifted at ~ 0.5 ML coverage of AI. O u r calculations predict some low-energy structures which have not been seen experimen-

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tally yet. These new structures may hold the key to understanding the higher order L E E D structures [49-52]. One particularly novel structure arises upon transverse Peierls type distortion [35] of AI atoms adsorbed at the quasi-hexagonal (H) sites shown in fig. lb. No A1-AI dimerization is possible at the H-sites; a strong repulsive barrier was found in our calculation. However, transverse displacements of AI atmns lead to energy lowering on a reconstructed surface as shown in fig. 4. No energy lowering is possible on an ideal Si(fl01)-I × l surface as shown in fig. 4. The low-energy configuration arises due to the formation of four strong Si-AI bonds of length 2.4 ,~. This follows clearly from the charge density distribution plots shown in fig. 5. Recall that such distorted structures were highly unfavored for AM. We take this to mean that A M - S i bonds are ionic but AI-Si bonds are covalent. The covalency is obvious from fig. 5. In conclusion we have provided the atomic structure of ordered layers alkali metals and aluminum on St(001)-2 × 1 surface. The interaction of A M with Si is primarily ionic but for AI it is covalent, Peieris distortions can explain the AI-Si structures. The basic 2 x 2 unit cell seen by L E E D

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144

L P. B a t r a / A theoretical study of the ~roa'lh oJ memlg on silk'on

arises b e c a u s e Pcierls distortions l e a d to signific a n t e n e r g y b e n e f i t for AI-Si(001), No significant b e n e f i t a r i s e s in t h e A M - S i system.

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LP. Batra / A theoretical study of the growth oJ mclols ~l silicon

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