- Email: [email protected]
Theoretical investigations on closed-shell silicon clusters doped with Cu atoms
Journal of Molecular Structure (Theochem) 487 (1999) 183–192
Theoretical investigations on closed-shell silicon clusters doped with Cu atoms F. Hagelberg a,*, I. Yanov b, J. Leszczynski b a
Computational Center for Molecular Structure and Interactions, Department of Physics, ATM and General Sciences, Jackson State University, Jackson, MS 39217, USA b Computational Center for Molecular Structure and Interactions, Department of Chemistry, Jackson State University, Jackson, MS 39217, USA
Abstract Silicon clusters doped with a single copper impurity (CuSiN), which were detected previously by mass spectrometric experiment, are explored by means of ab initio analysis. Features related to geometries, stabilities and adsorption energies of the species CuSiN, with N 4, 6, 8, 10, 12, 14 are discussed. The sensitive dependence of the physical properties of CuSiN clusters on the geometric arrangement of the respective SiN subsystem, as emerging from our research, is emphasized. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Atomic clusters; Electronic structure; Isomers; Composite systems; Stabilities
1. Introduction Ever since carbon clusters with geodesic structures, epitomized by C60, were first detected, questions on the existence of similar species based on Si have been asked [1–5]. According to both, theoretical and experimental studies done on SiN clusters to this day, however, these units display features of architecture and related physical and chemical properties that distinguish them strongly from the corresponding CN species. Thus, no evidence for a geodesic cage-like ground state structure has been reported for any SiN system, which may be attributed to the fact that a threefold coordination, involving sp 2 bonding as found in fullerenes, is energetically more favorable for CN than for the SiN clusters. It still appears interesting to explore the characteristics of cage-like * Corresponding author. Tel.: 1 1-601-968-3638; fax: 1 1-601968-3630. E-mail address: [email protected] (F. Hagelberg)
isomers of SiN units; recently, first results of an ongoing research effort aimed at identifying stable quasi-spherical SiN structures have been published [6]. While it has turned out as rewarding to study these units under the aspects of geometry and stability, they also have importance as potential matrices of impurity atoms. Numerous projects have been devoted to the examination of metal doped fullerenes [7,8], leading to discoveries of unprecedented phenomena related to geometries, bonding and electronic structure. Few studies, on the contrary, have dealt as yet with metal doped SiN clusters [9,10]. This is all the more surprising, as these clusters are the microscopic counterparts of the materials with highest relevance to modern electronic devices. Simetal contacts and their controlled manipulation are essential elements of microelectronic engineering. It appears to be a question of interest, in what ways these well described and frequently used systems will transform as they are scaled down to cluster dimension.
0166-1280/99/$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00153-0
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Among the few mass-spectrometric observations of doped SiN clusters are the experiments of Beck [9], who detected mixed silicon–metal clusters formed by chemical reaction in a supersonic molecular beam [9,11]. Beck’s measurements were stimulated by the need for detailed knowledge of the physical and chemical processes at the silicon–metal interfaces. Experimental investigation of small complexes containing both Si and metal species could provide theory with information on units accessible to first principles quantum chemical computation, and thus promote the basic understanding of the silicon– metal bond. In a series of measurements, Beck used the laser vaporization supersonic expansion technique [12] to generate MSiN clusters with M Cr, Mo, W and Cu. In this work, we focus on units of the form CuSiN. The CuSiN spectra recorded in the laboratory show a strong abundance peak at N 10. Besides the dominating species CuSi10, several other units with 6 # N # 12 were found. In this paper, we will present ab initio electronic structure calculations for several CuSiN clusters in the experimentally investigated mass region. We will depart from our preceding work on quasi-spherical SiN isomers with N 4, 6, 8, 10, 12, 14, which restricts us to the CuSiN systems with even numbers N of Si constituents. In each individual case, the question will be asked, in what ways and to what extent incorporation of a Cu impurity changes the geometric and electronic features of the SiN unit under study.
2. Procedure For every system examined, a full Hartree–Fock geometry optimization was carried out using the program gaussian 94 [13]. In view of the size and the number of species investigated in the present context, a 3-21G p basis set was employed for the description of the electronic states. Attempting to evaluate the validity of this approach, we compared this basis with the more complex 6-31G p basis, which has been shown to yield very adequate results for the SiN clusters [14,15]. Using both the basis sets in optimizations of SiN, with N 4, 6, 8, 10, we find only small differences in the per cent range between the bond distances in the optimized geometries derived
from the two approaches. Further examinations of our computational procedure were performed using the smallest Cu-containing unit treated in this work, as explained below. All the CuSiN clusters which form the topic of this work were investigated as spin doublets (s 12 ). In order to impose well-defined spin conditions on the respective systems, the Restricted Open Shell Hartree–Fock method (ROHF) was used throughout. Among the criteria for the comparison of the SiN and CuSiN cluster series inspected here is the binding energy, DE, per particle of the species under consideration, defined as the difference between the total energies E of the atomic cluster constituents and the total cluster energy, i.e. for CuSiN: DE E Cu 1 N E Si 2 E CuSiN =N 1 1: As SiN and CuSiN represent species of different particle number and composition, a more meaningful basis for comparison than the binding energy is the energy difference associated with the adsorption of an additional Si or Cu atom by an SiN unit, reflecting the propensity of the latter system to take up preferentially an Si or a Cu atom. This quantity is defined for CuSiN as DEad CuSiN E Cu 1 E SiN 2 E CuSiN ; and for SiN11 as DEad SiN11 E Si 1 E SiN 2 E SiN11 : In order to apply these relations, we carried out additional geometry optimizations for the systems Si7, Si9 and Si11, where the equilibrium structures were derived from units of threefold symmetry, as suggested in Ref. [16]. To extend the use of the adsorption energy criterion to the systems CuSi12 and CuSi14, Si13 and Si15 have to be optimized as well, employing the same basis set as for the other systems; the respective computations are currently performed. The work presented here does not aim at a definitive quantitative analysis of the CuSiN cluster under study, but is rather meant as a qualitative preparation of such a research effort. More specifically, we cannot claim to arrive at accurate binding energy values, as our calculations are based on the Hartree–Fock model, and thus neglect the effects due to electronic correlation. Further, the Hartree–Fock method tends
F. Hagelberg et al. / Journal of Molecular Structure (Theochem) 487 (1999) 183–192 Table 1 Comparison between binding energies, DE, of CuSiN and SiN system, with N 6, 8, 10, 12, 14 CuSiN system
DE for CuSiN (eV)
DE for SiN (eV)
CuSi6 CuSi8 (Td) CuSi8 (D4d) CuSi10 (Td) CuSi10 (D4d) CuSi10 (D5d) CuSi12 CuSi14
3.25 3.64 3.44 3.47 3.81 3.43 3.67 3.66
3.51 3.56 2.71 3.73 3.73 3.11 3.41 3.38
to overestimate the size of energy gaps between the occupied and unoccupied states, which affects our discussion of HOMO–LUMO energy differences. Still, from qualitative comparisons between the various species isolated here, one can extract tendencies, which are likely to be useful in ensuing research at a higher level of numerical accuracy. 3. Results and discussion In the following paragraphs, we want to present our results obtained so far for individual systems of the form CuSiN, with N 4, 6, 8, 10, 12, 14. Comparison is made with the corresponding pure SiN cluster in each case considered and, wherever possible, with experimental observations. 3.1. CuSi4 and CuSi6 In the mass spectrometric measurements given in Ref. [9], no CuSiN species with N , 6 was isolated. When we nevertheless include CuSi4 in our work, it is done for the purpose of assessing our methodology. Due to its small size, this molecule can be used as a testing ground for potential effects related to the extension of the basis sets employed. We, thus, performed two geometry optimizations of CuSi4 using two different sets of basis functions, namely first the 3-21G p set adopted in this work, and secondly a 6-31G p set on the Si cluster atoms in conjunction with a set of composition (8/6/4/1) [17] on the Cu atom. The results of both computations show only minimal deviations in the optimum geometries found for the Si4 cluster subsystem. While the ground state structure of Si4, is known to be a flat rhombus
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(D2h symmetry) [7,14], addition of a Cu atom distorts this structure into a bent rhombus (D2d symmetry). Comparing the first and the second calculation under the aspect of Si–Si bond lengths, we obtain differences of less than 2% in both the cases, the opening angle of the bent Si4 rhombus amounts to 139.98. Whereas we find from both calculations the Cu atom situated on the D2d symmetry axis, the more complex basis yields larger Cu–Si bond distances by about 20%. These results indicate that the present 3-21G p approach, while comparing favorably with many results derived from more extended basis sets, should rather be used for the evaluation of tendencies and qualitative features than for quantitatively accurate analysis. It seems worthwhile to point out that we find a strong destabilization going from Si4 to CuSi4, as reflected by a drop in the binding energy per particle from 3.19 to 2.57 eV, and associated with a narrowing of the HOMO–LUMO gap from 7.40 to 2.38 eV. This observation is in accordance with the total absence of the species CuSi4 from the mass spectrum [9]. The most symmetric shape the Si6 unit can adopt is obviously the one of a regular octahedron. A geometry optimization of this cluster, using the 3-21G p basis set, yields a distorted octahedron, compressed along one of its fourfold axes. As a Cu atom is inserted into the center of this complex, the distortion is markedly reduced. While for the pure Si6 unit, the Si distances from the cluster center was found to deviate by 29%, for the Cu–Si distances, these deviations were reduced to about 4%. The tendency of regularization as one goes from Si6 to CuSi6, is also reflected by the atomic charges obtained from Mulliken population analysis. In Si6, the two Si atoms located on the fourfold axis acquire negative charges of 2 0.250 a.u. each, whereas each of the four remaining atoms carries a charge of 0.125 a.u. In CuSi6, as a result of electron transport from the Si6 subsystem to the Cu center, all the Si atoms adopt positive charges of magnitude 0.11 or 0.16 a.u. The observed electron transport from the SiN cage to the central metal impurity is in contrast to observations made on small carbon fullerenes doped with metal atoms [18], where the opposite trend was found. Although our results related to the charge transfer between the two subsystems require careful reexamination in the light of a method more advanced than the one used here, it has to be
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Table 2 Comparison between adsorption energies, DEad, of CuSiN and SiN11 systems, with N 6, 8, 10 CuSiN system
DEad for CuSiN (eV)
DEad for SiN11 (eV)
CuSi6 CuSi8 (Td) CuSi8 (D4d) CuSi10 (Td) CuSi10 (D4d) CuSi10 (D5d)
1.69 3.50 7.41 0.84 4.61 3.43
2.82 3.12 9.92 2.19 2.19 8.39
pointed out that the present finding is in keeping with the electronegativity difference between the elements Cu and Si. The Si6 system can thus be seen to approach quasispherical structure as a Cu atom is added to it. As shown in Tables 1 and 2, however, both the binding and the adsorption energies of CuSi6 are clearly lower than those of the Si6 matrix, which may be among the factors determining the low abundance of CuSi6 in the mass spectrum.
3.2. CuSi8 As has been shown earlier [7], the Si8 structure of highest symmetry, i.e. a regular cube, relaxes into a unit consisting of two distorted concentric tetrahedra of different size: a negatively charged “core tetrahedron” surrounded by a positively charged “shell tetrahedron”. By placing a Cu atom into the center of this cluster and optimizing the geometry of the emerging CuSi8 unit, we make similar observations as in the case of CuSi6. Electron transport to the Cu atom results in a positively charged Si8 shell of nearly even charge distribution, deviating from quasi-sphericality distinctly less than the pure Si8 matrix (Fig. 1(a)). Comparison between the binding energies of CuSi8 and Si8 from Table 1 yields a slightly enhanced value for the former species, a trend which is also reflected by the adsorption energy. For a better insight into our result, we contrast it with a less compact model of CuSi8 (Fig. 1(b)) which is derived from a structure of D4d symmetry. In this case, the Si8 matrix is sizeably lower in binding energy (see Table 1) and markedly higher in adsorption
Fig. 1. The two geometries derived for CuSi8. (a) CuSi8 (Td), (b) CuSi8 (D4d). Central atom: Cu.
F. Hagelberg et al. / Journal of Molecular Structure (Theochem) 487 (1999) 183–192
energy (see Table 3). At the same time, a nearly vanishing HOMO–LUMO energy gap found for the CuSi8 variant under study seems to be indicative of metallic characteristics. This view is supported by the small amount of charge transport between Cu and Si8 subsystems, which is diminished by a factor of nearly 2 as compared with the quasi-spherical variant of the same species discussed above. 3.3. CuSi10 Among all the recorded CuSiN units, the CuSi10 cluster has been detected with highest abundance. This predominance seems to be well compatible with the finding that Si10 is the most stable of the small SiN species with N # 14 [7,14,15] under the aspect of binding energy. However, for deeper understanding, one has not only to show that CuSi10 is of pronounced stability among other CuSiN species, but also that relative stabilities of the pure Si10 matrix and CuSi10 make the formation of the latter species out of Si and Cu components probable.
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Table 3 Comparison between HOMO–LUMO energy gaps, DEHL, of CuSiN and SiN systems, with N 6, 8, 10, 12, 14 CuSiN species
DEHL for CuSiN (eV)
DEHL for SiN (eV)
CuSi6 CuSi8 (Td) CuSi8 (D4d) CuSi10 (Td) CuSi10 (D4d) CuSi10 (D5d) CuSi12 CuSi14
3.54 2.64 1.88 0.65 2.41 1.88 2.17 2.32
7.91 6.03 4.45 8.17 2.82 1.70 4.12 4.10
For Si10, a tetracapped octahedron (Td symmetry) structure has been demonstrated to be the geometry of a stable isomer [7], and possibly the ground state geometry [15]. This structure may be interpreted as a “core octahedron” of net charge q 2 1.1 a.u. inscribed into a “shell tetrahedron” with a corresponding net charge of q 1 1.1 a.u. Incorporation of a Cu atom into Si10 (Fig. 2(a)) does not induce a change in the symmetry of the species, but leads to an exchange
Fig. 1. (continued)
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Fig. 2. The three geometries derived for CuSi10. (a) CuSi10 (Td), (b) CuSi10 (D5d), (c) CuSi10 (D4d). Central atom: Cu.
of the charge assignments between the two geometric subunits: owing to the electron transport to the central Cu atom, the octahedron now acquires positive charge, while the tetrahedron acquires a negative
charge. It should be pointed out, however, that the net charges on any of these cluster elements are comparatively small, amounting maximally to 0.44 a.u. This reduction of charge transfer, as one
Fig. 2. (continued)
F. Hagelberg et al. / Journal of Molecular Structure (Theochem) 487 (1999) 183–192
Fig. 2. (continued)
goes from Si10 (Td) to CuSi10, is accompanied by a dramatic narrowing of the HOMO–LUMO energy gap (see Table 3). Both the features may be viewed as fingerprints of metallic behavior. A strong drop in the binding energy from Si10 to CuSi10, as is obvious from Table 1, makes the
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discussed unit an unlikely candidate for the actual structure of CuSi10. In analogy to our treatment of CuSi8, we investigate a further, less compact variant of the CuSi10 species, namely a unit derived from D5d symmetry, as shown in Fig. 2(b). In this case, we find not only the binding energy slightly enhanced as compared with the one of the D5d matrix, but also somewhat widened HOMO– LUMO energy difference. However, as in the case of the Td unit, the values of the adsorption energy result are smaller than those of the corresponding Si11 unit, hence, none of the quantities considered, i.e. binding and adsorption energy, are capable of accounting for the spectroscopically confirmed high abundance of the CuSi10 species. For a third variant of CuSi10 investigated in the context of this work, however, the situation is somewhat different. As we optimize the geometry displayed in Fig. 2(c), which is based on a model of D4d symmetry, we arrive at a binding energy, as well as adsorption energy, that is sizably enhanced as compared to the respective findings for the pure silicon systems. From Table 1, it can be seen that the binding energy value of CuSi10 (D4d) surpasses the one of the highly stable Si10 (Td) unit. Frequency analysis of CuSi10 (D4d) reveals three imaginary frequencies, indicating some additional lowering of the binding energy through further structural modification of CuSi10 (D4d). In the light of these findings,
Fig. 3. The DOS distributions calculated for the three variants of CuSi10 discussed in the text. (a) CuSi10 (Td), (b) CuSi10 (D4d), (c) CuSi10 (D5d). The Fermi energies are indicated by FE.
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Fig. 3. (continued)
high abundance of CuSi10 complexes derived from a model of D4d symmetry in copper–silicon mixtures is conceivable. It should be pointed out that the three alternative CuSi10 structures investigated here differ very markedly in adsorption energies. In the case of the corresponding Si11 system, nearly equal adsorption energies are found for the species generated from Si10 (Td) and Si10 (D4d) which is obvious in view of the very similar binding energies of the two latter
species (Table 1). The Si10 (D5d) variant, in contrast, is associated with a strongly enhanced adsorption energy. The crucial differences between the CuSi10 variants discussed in this subsection are also reflected by the respective density of states (DOS) distributions, as shown in Fig. 3(a)–(c), which were calculated according to the outline given in Ref. [19]. Whereas the Fermi energies of the D5d and D4d CuSi10 species are found to fall into clearly pronounced energy gaps, in
Fig. 3. (continued)
F. Hagelberg et al. / Journal of Molecular Structure (Theochem) 487 (1999) 183–192
the case of the Td species, the Fermi energy is located on the rising side of a steep DOS maximum. This feature is considered indicative of metallicity [19]. 3.4. CuSi12 and CuSi14 For both the types of clusters, a highly symmetric closed-shell SiN configuration was chosen as initial geometry, i.e. icosahedral symmetry (Ih) for N 12 and Oh symmetry for N 14, corresponding to a triakis octahedron structure. Geometry optimizations have been performed for both the pure as well as the Cu doped SiN structure. Although the comparison of the binding energies for SiN and CuSiN (N 12, 14) in Table 1 indicates an increase of binding energy from the pure to the doped cluster, it cannot be inferred that the clusters SiN (N 12, 14) are less stable than their Cu containing counterparts. Such a conclusion would be justified only with respect to stable SiN isomers, as they are produced in the laboratory. While research on such isomers with N 12, 14 is in progress, the present work does not deal with them.
4. Conclusion
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behavior can be linked to an impurity-induced metallization of the unit under study. In the planned further investigations on CuSiN clusters, we will remove successively the constraints imposed on the present work. Most importantly, the present results have to be reexamined in the light of the unrestricted Hartree–Fock approach in conjunction with a correlated computational method to account for the impact of many body effects on the conclusions drawn here. Further, we will investigate possible structural isomers of CuSiN in which the Cu atom does not occupy the center position; also, the assumption of spin 12 made for the CuSiN considered here has to be critically examined. Lastly, larger species and those with odd numbers of Si atoms will be studied in the future, partly in an attempt to link the present research effort to the extensive work [20] done on Cu impurities in the Si bulk as well as in the Si surfaces. Acknowledgements The support given to this work by the National Science Foundation through the CREST program (HRD-9805465) is gratefully acknowledged.
From our analysis of Cu doped SiN clusters, with N 4, 6, 8, 10, 12 and 14, several salient features of these species emerge:
References
• The presence of a Cu impurity leads to a restructuring of the SiN unit, related to charge transfer from the SiN subsystem to the Cu center. For the smaller of the doped units examined here, chiefly those with N 4, 6, 8, this implies a transition of the SiN subsystem into a more regular, quasi-spherical shape than is found for the pure species. • In accordance with experiment, destabilization is found for N 4, 6, 8 and stabilization for N 10 as one goes from SiN to CuSiN. • For a particular CuSiN unit, binding energies, adsorption energies and physical properties, such as metallicity, seem to depend sensitively on the geometry adopted by the SiN subsystem. • In the majority of cases investigated, addition of a Cu center to SiN is associated with a pronounced HOMO–LUMO energy gap narrowing. A continuation of this research will have to show if this
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Theoretical investigations on closed-shell silicon clusters doped with Cu atoms F. Hagelberg a,*, I. Yanov b, J. Leszczynski b a
Computational Center for Molecular Structure and Interactions, Department of Physics, ATM and General Sciences, Jackson State University, Jackson, MS 39217, USA b Computational Center for Molecular Structure and Interactions, Department of Chemistry, Jackson State University, Jackson, MS 39217, USA
Abstract Silicon clusters doped with a single copper impurity (CuSiN), which were detected previously by mass spectrometric experiment, are explored by means of ab initio analysis. Features related to geometries, stabilities and adsorption energies of the species CuSiN, with N 4, 6, 8, 10, 12, 14 are discussed. The sensitive dependence of the physical properties of CuSiN clusters on the geometric arrangement of the respective SiN subsystem, as emerging from our research, is emphasized. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Atomic clusters; Electronic structure; Isomers; Composite systems; Stabilities
1. Introduction Ever since carbon clusters with geodesic structures, epitomized by C60, were first detected, questions on the existence of similar species based on Si have been asked [1–5]. According to both, theoretical and experimental studies done on SiN clusters to this day, however, these units display features of architecture and related physical and chemical properties that distinguish them strongly from the corresponding CN species. Thus, no evidence for a geodesic cage-like ground state structure has been reported for any SiN system, which may be attributed to the fact that a threefold coordination, involving sp 2 bonding as found in fullerenes, is energetically more favorable for CN than for the SiN clusters. It still appears interesting to explore the characteristics of cage-like * Corresponding author. Tel.: 1 1-601-968-3638; fax: 1 1-601968-3630. E-mail address: [email protected] (F. Hagelberg)
isomers of SiN units; recently, first results of an ongoing research effort aimed at identifying stable quasi-spherical SiN structures have been published [6]. While it has turned out as rewarding to study these units under the aspects of geometry and stability, they also have importance as potential matrices of impurity atoms. Numerous projects have been devoted to the examination of metal doped fullerenes [7,8], leading to discoveries of unprecedented phenomena related to geometries, bonding and electronic structure. Few studies, on the contrary, have dealt as yet with metal doped SiN clusters [9,10]. This is all the more surprising, as these clusters are the microscopic counterparts of the materials with highest relevance to modern electronic devices. Simetal contacts and their controlled manipulation are essential elements of microelectronic engineering. It appears to be a question of interest, in what ways these well described and frequently used systems will transform as they are scaled down to cluster dimension.
0166-1280/99/$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00153-0
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F. Hagelberg et al. / Journal of Molecular Structure (Theochem) 487 (1999) 183–192
Among the few mass-spectrometric observations of doped SiN clusters are the experiments of Beck [9], who detected mixed silicon–metal clusters formed by chemical reaction in a supersonic molecular beam [9,11]. Beck’s measurements were stimulated by the need for detailed knowledge of the physical and chemical processes at the silicon–metal interfaces. Experimental investigation of small complexes containing both Si and metal species could provide theory with information on units accessible to first principles quantum chemical computation, and thus promote the basic understanding of the silicon– metal bond. In a series of measurements, Beck used the laser vaporization supersonic expansion technique [12] to generate MSiN clusters with M Cr, Mo, W and Cu. In this work, we focus on units of the form CuSiN. The CuSiN spectra recorded in the laboratory show a strong abundance peak at N 10. Besides the dominating species CuSi10, several other units with 6 # N # 12 were found. In this paper, we will present ab initio electronic structure calculations for several CuSiN clusters in the experimentally investigated mass region. We will depart from our preceding work on quasi-spherical SiN isomers with N 4, 6, 8, 10, 12, 14, which restricts us to the CuSiN systems with even numbers N of Si constituents. In each individual case, the question will be asked, in what ways and to what extent incorporation of a Cu impurity changes the geometric and electronic features of the SiN unit under study.
2. Procedure For every system examined, a full Hartree–Fock geometry optimization was carried out using the program gaussian 94 [13]. In view of the size and the number of species investigated in the present context, a 3-21G p basis set was employed for the description of the electronic states. Attempting to evaluate the validity of this approach, we compared this basis with the more complex 6-31G p basis, which has been shown to yield very adequate results for the SiN clusters [14,15]. Using both the basis sets in optimizations of SiN, with N 4, 6, 8, 10, we find only small differences in the per cent range between the bond distances in the optimized geometries derived
from the two approaches. Further examinations of our computational procedure were performed using the smallest Cu-containing unit treated in this work, as explained below. All the CuSiN clusters which form the topic of this work were investigated as spin doublets (s 12 ). In order to impose well-defined spin conditions on the respective systems, the Restricted Open Shell Hartree–Fock method (ROHF) was used throughout. Among the criteria for the comparison of the SiN and CuSiN cluster series inspected here is the binding energy, DE, per particle of the species under consideration, defined as the difference between the total energies E of the atomic cluster constituents and the total cluster energy, i.e. for CuSiN: DE E Cu 1 N E Si 2 E CuSiN =N 1 1: As SiN and CuSiN represent species of different particle number and composition, a more meaningful basis for comparison than the binding energy is the energy difference associated with the adsorption of an additional Si or Cu atom by an SiN unit, reflecting the propensity of the latter system to take up preferentially an Si or a Cu atom. This quantity is defined for CuSiN as DEad CuSiN E Cu 1 E SiN 2 E CuSiN ; and for SiN11 as DEad SiN11 E Si 1 E SiN 2 E SiN11 : In order to apply these relations, we carried out additional geometry optimizations for the systems Si7, Si9 and Si11, where the equilibrium structures were derived from units of threefold symmetry, as suggested in Ref. [16]. To extend the use of the adsorption energy criterion to the systems CuSi12 and CuSi14, Si13 and Si15 have to be optimized as well, employing the same basis set as for the other systems; the respective computations are currently performed. The work presented here does not aim at a definitive quantitative analysis of the CuSiN cluster under study, but is rather meant as a qualitative preparation of such a research effort. More specifically, we cannot claim to arrive at accurate binding energy values, as our calculations are based on the Hartree–Fock model, and thus neglect the effects due to electronic correlation. Further, the Hartree–Fock method tends
F. Hagelberg et al. / Journal of Molecular Structure (Theochem) 487 (1999) 183–192 Table 1 Comparison between binding energies, DE, of CuSiN and SiN system, with N 6, 8, 10, 12, 14 CuSiN system
DE for CuSiN (eV)
DE for SiN (eV)
CuSi6 CuSi8 (Td) CuSi8 (D4d) CuSi10 (Td) CuSi10 (D4d) CuSi10 (D5d) CuSi12 CuSi14
3.25 3.64 3.44 3.47 3.81 3.43 3.67 3.66
3.51 3.56 2.71 3.73 3.73 3.11 3.41 3.38
to overestimate the size of energy gaps between the occupied and unoccupied states, which affects our discussion of HOMO–LUMO energy differences. Still, from qualitative comparisons between the various species isolated here, one can extract tendencies, which are likely to be useful in ensuing research at a higher level of numerical accuracy. 3. Results and discussion In the following paragraphs, we want to present our results obtained so far for individual systems of the form CuSiN, with N 4, 6, 8, 10, 12, 14. Comparison is made with the corresponding pure SiN cluster in each case considered and, wherever possible, with experimental observations. 3.1. CuSi4 and CuSi6 In the mass spectrometric measurements given in Ref. [9], no CuSiN species with N , 6 was isolated. When we nevertheless include CuSi4 in our work, it is done for the purpose of assessing our methodology. Due to its small size, this molecule can be used as a testing ground for potential effects related to the extension of the basis sets employed. We, thus, performed two geometry optimizations of CuSi4 using two different sets of basis functions, namely first the 3-21G p set adopted in this work, and secondly a 6-31G p set on the Si cluster atoms in conjunction with a set of composition (8/6/4/1) [17] on the Cu atom. The results of both computations show only minimal deviations in the optimum geometries found for the Si4 cluster subsystem. While the ground state structure of Si4, is known to be a flat rhombus
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(D2h symmetry) [7,14], addition of a Cu atom distorts this structure into a bent rhombus (D2d symmetry). Comparing the first and the second calculation under the aspect of Si–Si bond lengths, we obtain differences of less than 2% in both the cases, the opening angle of the bent Si4 rhombus amounts to 139.98. Whereas we find from both calculations the Cu atom situated on the D2d symmetry axis, the more complex basis yields larger Cu–Si bond distances by about 20%. These results indicate that the present 3-21G p approach, while comparing favorably with many results derived from more extended basis sets, should rather be used for the evaluation of tendencies and qualitative features than for quantitatively accurate analysis. It seems worthwhile to point out that we find a strong destabilization going from Si4 to CuSi4, as reflected by a drop in the binding energy per particle from 3.19 to 2.57 eV, and associated with a narrowing of the HOMO–LUMO gap from 7.40 to 2.38 eV. This observation is in accordance with the total absence of the species CuSi4 from the mass spectrum [9]. The most symmetric shape the Si6 unit can adopt is obviously the one of a regular octahedron. A geometry optimization of this cluster, using the 3-21G p basis set, yields a distorted octahedron, compressed along one of its fourfold axes. As a Cu atom is inserted into the center of this complex, the distortion is markedly reduced. While for the pure Si6 unit, the Si distances from the cluster center was found to deviate by 29%, for the Cu–Si distances, these deviations were reduced to about 4%. The tendency of regularization as one goes from Si6 to CuSi6, is also reflected by the atomic charges obtained from Mulliken population analysis. In Si6, the two Si atoms located on the fourfold axis acquire negative charges of 2 0.250 a.u. each, whereas each of the four remaining atoms carries a charge of 0.125 a.u. In CuSi6, as a result of electron transport from the Si6 subsystem to the Cu center, all the Si atoms adopt positive charges of magnitude 0.11 or 0.16 a.u. The observed electron transport from the SiN cage to the central metal impurity is in contrast to observations made on small carbon fullerenes doped with metal atoms [18], where the opposite trend was found. Although our results related to the charge transfer between the two subsystems require careful reexamination in the light of a method more advanced than the one used here, it has to be
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Table 2 Comparison between adsorption energies, DEad, of CuSiN and SiN11 systems, with N 6, 8, 10 CuSiN system
DEad for CuSiN (eV)
DEad for SiN11 (eV)
CuSi6 CuSi8 (Td) CuSi8 (D4d) CuSi10 (Td) CuSi10 (D4d) CuSi10 (D5d)
1.69 3.50 7.41 0.84 4.61 3.43
2.82 3.12 9.92 2.19 2.19 8.39
pointed out that the present finding is in keeping with the electronegativity difference between the elements Cu and Si. The Si6 system can thus be seen to approach quasispherical structure as a Cu atom is added to it. As shown in Tables 1 and 2, however, both the binding and the adsorption energies of CuSi6 are clearly lower than those of the Si6 matrix, which may be among the factors determining the low abundance of CuSi6 in the mass spectrum.
3.2. CuSi8 As has been shown earlier [7], the Si8 structure of highest symmetry, i.e. a regular cube, relaxes into a unit consisting of two distorted concentric tetrahedra of different size: a negatively charged “core tetrahedron” surrounded by a positively charged “shell tetrahedron”. By placing a Cu atom into the center of this cluster and optimizing the geometry of the emerging CuSi8 unit, we make similar observations as in the case of CuSi6. Electron transport to the Cu atom results in a positively charged Si8 shell of nearly even charge distribution, deviating from quasi-sphericality distinctly less than the pure Si8 matrix (Fig. 1(a)). Comparison between the binding energies of CuSi8 and Si8 from Table 1 yields a slightly enhanced value for the former species, a trend which is also reflected by the adsorption energy. For a better insight into our result, we contrast it with a less compact model of CuSi8 (Fig. 1(b)) which is derived from a structure of D4d symmetry. In this case, the Si8 matrix is sizeably lower in binding energy (see Table 1) and markedly higher in adsorption
Fig. 1. The two geometries derived for CuSi8. (a) CuSi8 (Td), (b) CuSi8 (D4d). Central atom: Cu.
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energy (see Table 3). At the same time, a nearly vanishing HOMO–LUMO energy gap found for the CuSi8 variant under study seems to be indicative of metallic characteristics. This view is supported by the small amount of charge transport between Cu and Si8 subsystems, which is diminished by a factor of nearly 2 as compared with the quasi-spherical variant of the same species discussed above. 3.3. CuSi10 Among all the recorded CuSiN units, the CuSi10 cluster has been detected with highest abundance. This predominance seems to be well compatible with the finding that Si10 is the most stable of the small SiN species with N # 14 [7,14,15] under the aspect of binding energy. However, for deeper understanding, one has not only to show that CuSi10 is of pronounced stability among other CuSiN species, but also that relative stabilities of the pure Si10 matrix and CuSi10 make the formation of the latter species out of Si and Cu components probable.
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Table 3 Comparison between HOMO–LUMO energy gaps, DEHL, of CuSiN and SiN systems, with N 6, 8, 10, 12, 14 CuSiN species
DEHL for CuSiN (eV)
DEHL for SiN (eV)
CuSi6 CuSi8 (Td) CuSi8 (D4d) CuSi10 (Td) CuSi10 (D4d) CuSi10 (D5d) CuSi12 CuSi14
3.54 2.64 1.88 0.65 2.41 1.88 2.17 2.32
7.91 6.03 4.45 8.17 2.82 1.70 4.12 4.10
For Si10, a tetracapped octahedron (Td symmetry) structure has been demonstrated to be the geometry of a stable isomer [7], and possibly the ground state geometry [15]. This structure may be interpreted as a “core octahedron” of net charge q 2 1.1 a.u. inscribed into a “shell tetrahedron” with a corresponding net charge of q 1 1.1 a.u. Incorporation of a Cu atom into Si10 (Fig. 2(a)) does not induce a change in the symmetry of the species, but leads to an exchange
Fig. 1. (continued)
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Fig. 2. The three geometries derived for CuSi10. (a) CuSi10 (Td), (b) CuSi10 (D5d), (c) CuSi10 (D4d). Central atom: Cu.
of the charge assignments between the two geometric subunits: owing to the electron transport to the central Cu atom, the octahedron now acquires positive charge, while the tetrahedron acquires a negative
charge. It should be pointed out, however, that the net charges on any of these cluster elements are comparatively small, amounting maximally to 0.44 a.u. This reduction of charge transfer, as one
Fig. 2. (continued)
F. Hagelberg et al. / Journal of Molecular Structure (Theochem) 487 (1999) 183–192
Fig. 2. (continued)
goes from Si10 (Td) to CuSi10, is accompanied by a dramatic narrowing of the HOMO–LUMO energy gap (see Table 3). Both the features may be viewed as fingerprints of metallic behavior. A strong drop in the binding energy from Si10 to CuSi10, as is obvious from Table 1, makes the
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discussed unit an unlikely candidate for the actual structure of CuSi10. In analogy to our treatment of CuSi8, we investigate a further, less compact variant of the CuSi10 species, namely a unit derived from D5d symmetry, as shown in Fig. 2(b). In this case, we find not only the binding energy slightly enhanced as compared with the one of the D5d matrix, but also somewhat widened HOMO– LUMO energy difference. However, as in the case of the Td unit, the values of the adsorption energy result are smaller than those of the corresponding Si11 unit, hence, none of the quantities considered, i.e. binding and adsorption energy, are capable of accounting for the spectroscopically confirmed high abundance of the CuSi10 species. For a third variant of CuSi10 investigated in the context of this work, however, the situation is somewhat different. As we optimize the geometry displayed in Fig. 2(c), which is based on a model of D4d symmetry, we arrive at a binding energy, as well as adsorption energy, that is sizably enhanced as compared to the respective findings for the pure silicon systems. From Table 1, it can be seen that the binding energy value of CuSi10 (D4d) surpasses the one of the highly stable Si10 (Td) unit. Frequency analysis of CuSi10 (D4d) reveals three imaginary frequencies, indicating some additional lowering of the binding energy through further structural modification of CuSi10 (D4d). In the light of these findings,
Fig. 3. The DOS distributions calculated for the three variants of CuSi10 discussed in the text. (a) CuSi10 (Td), (b) CuSi10 (D4d), (c) CuSi10 (D5d). The Fermi energies are indicated by FE.
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Fig. 3. (continued)
high abundance of CuSi10 complexes derived from a model of D4d symmetry in copper–silicon mixtures is conceivable. It should be pointed out that the three alternative CuSi10 structures investigated here differ very markedly in adsorption energies. In the case of the corresponding Si11 system, nearly equal adsorption energies are found for the species generated from Si10 (Td) and Si10 (D4d) which is obvious in view of the very similar binding energies of the two latter
species (Table 1). The Si10 (D5d) variant, in contrast, is associated with a strongly enhanced adsorption energy. The crucial differences between the CuSi10 variants discussed in this subsection are also reflected by the respective density of states (DOS) distributions, as shown in Fig. 3(a)–(c), which were calculated according to the outline given in Ref. [19]. Whereas the Fermi energies of the D5d and D4d CuSi10 species are found to fall into clearly pronounced energy gaps, in
Fig. 3. (continued)
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the case of the Td species, the Fermi energy is located on the rising side of a steep DOS maximum. This feature is considered indicative of metallicity [19]. 3.4. CuSi12 and CuSi14 For both the types of clusters, a highly symmetric closed-shell SiN configuration was chosen as initial geometry, i.e. icosahedral symmetry (Ih) for N 12 and Oh symmetry for N 14, corresponding to a triakis octahedron structure. Geometry optimizations have been performed for both the pure as well as the Cu doped SiN structure. Although the comparison of the binding energies for SiN and CuSiN (N 12, 14) in Table 1 indicates an increase of binding energy from the pure to the doped cluster, it cannot be inferred that the clusters SiN (N 12, 14) are less stable than their Cu containing counterparts. Such a conclusion would be justified only with respect to stable SiN isomers, as they are produced in the laboratory. While research on such isomers with N 12, 14 is in progress, the present work does not deal with them.
4. Conclusion
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behavior can be linked to an impurity-induced metallization of the unit under study. In the planned further investigations on CuSiN clusters, we will remove successively the constraints imposed on the present work. Most importantly, the present results have to be reexamined in the light of the unrestricted Hartree–Fock approach in conjunction with a correlated computational method to account for the impact of many body effects on the conclusions drawn here. Further, we will investigate possible structural isomers of CuSiN in which the Cu atom does not occupy the center position; also, the assumption of spin 12 made for the CuSiN considered here has to be critically examined. Lastly, larger species and those with odd numbers of Si atoms will be studied in the future, partly in an attempt to link the present research effort to the extensive work [20] done on Cu impurities in the Si bulk as well as in the Si surfaces. Acknowledgements The support given to this work by the National Science Foundation through the CREST program (HRD-9805465) is gratefully acknowledged.
From our analysis of Cu doped SiN clusters, with N 4, 6, 8, 10, 12 and 14, several salient features of these species emerge:
References
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