Theoretical study of small silicon clusters on a graphite layer

In a series of recent experiments, the HOMO-LUMO energy gaps of small Si clusters deposited on a graphite substrate have been determined by Scanning Tunneling Microscopy (STM). The values obtained were found to be substantially smaller than the energy gaps of corresponding passivated clusters. This work considers dimensional reduction as a possible mechanism for a sizeable energy gap narrowing by the example of the system Si5. The impact of the graphite substrate on the deposited species is investigated in the framework of a pseudocluster model. PACS. 36.40.Cg Electronic and magnetic properties of clusters – 61.46.+w Nanoscale materials: clusters, nanoparticles, nanotubes, and nanocrystals A large number of contemporary research efforts, both experimental and theoretical, are concerned with the basic properties of Si clusters and nanostructures which are of high relevance to present applications in microelectronics as well as to future developments of this technology. In a recent STM study [1], small Si clusters (SiN ) have been investigated on a Highly Oriented Pyrolytic Graphite (HOPG) substrate. In these measurements, the capability of STM technique for determination of the energy gap size of deposited clusters has been used. The SiN clusters were generated through an atomic deposition procedure involving magnetron sputtering of pure Si [2]. As the atomic Si vapor is deposited on the HOPG surface, Si atoms can conglomerate through a diffusion process followed by quasi-free growth. The microscopically detected SiN clusters were classified according to their approximate diameters ranging from 2.5 to 40 Å. In all cases considered, the energy gaps determined were found to be sizably smaller than that of bulk silicon (1.1 eV). A critical cluster size of 15 Å was identified beyond which a vanishing energy gap was detected. For smaller cluster diameters, the largest recorded gap amounts to 450 meV. These results imply a reversal of the commonly assumed trend of an energy gap increase as one goes from the infinite system to its finite counterparts, as far as deposited clusters are concerned. For SiN clusters in the gas phase, a high degree of reconstruction has been confirmed [3], associated with the flexibility of cluster systems that allows for elimination of dangling bonds through geometric rearrangement. Thus, for SiN clusters with N < 20, comparatively large HOMO-LUMO energy differences in a e-mail: [email protected] the order of 3 to 4 eV have been found. For the larger ones among the SiN clusters investigated in the indicated STM experiment, the geometry of Si bulk fragments has been proposed which have been shown computationally [4] to exhibit vanishing HOMO-LUMO differences if they are not passivated through addition of hydrogen atoms. Still, the question why the deposition of Si atoms on HOPG should give rise to the formation of unreconstructed Si bulk fragments remains to be answered by computational theory. The present work follows a different purpose. We will concentrate on the regime of SiN clusters distinctly smaller than the critical size of 15 Å in diameter. More specifically, we will propose a model that in principle allows for the characterization of the interaction between the deposited cluster and the HOPG substrate, namely the Partial Density of States (PDOS) and the Partial Overlap Density of States (PODOS) analysis of SiN units attached to a pseudocluster consisting of a hydrogen passivated graphite fragment [5,6]. In the framework of this approach, we will discuss dimensional reduction as a possible mechanism of energy gap decrease by the example of the Si5 cluster. The choice of Si5 is motivated by the fact that both threeand two-dimensional stable isomers have been isolated for this species [7]. Thus, this study is guided by a twofold intention: (a) introduction of a general computational model for the interaction between SiN systems and graphite substrates, (b) application of this model to one specific case, namely Si5, in an attempt to make contact with STM measurement. For all species considered, full all-electron geometry optimizations were carried out. The quantum chemical procedure employed was Becke’s three parameter hybrid 38 The European Physical Journal D Fig. 1. (a) Equilibrium geometry of Si5. (b) Equilibrium geometry of the most stable Si5 isomer. method in conjunction with the correlation functional of Lee, Yang and Parr [8]. For the pure Si5 clusters, a 631G* basis set was used which has been demonstrated in the past to be an adequate choice for the treatment of Si clusters [9]. For the simulation of the substrate, we used a C54 planar graphite fragment terminated by 18 hydrogen atoms. This is an extension of a model that has been used in the past to investigate the reaction of various species with a graphite layer [5]. This representation of the substrate was subjected to a test in which the widths and the onset energies of the σ and π bands extracted from our model by means of PDOS analysis were compared with results of band structure calculations [10]. It was found that both approaches agree within an error margin of approximately 0.2 eV. Similarly, the transition to the sizably larger pseudocluster C96H24 introduced only minute shifts in the indicated energy band parameters. In view of their considerable size, for all composite systems to be discussed in the following section, i.e., SiC54H18 and Si5C54H18, a 3-21G* basis has been used which has been shown elsewhere [11] to yield very satisfactory approximations to the 6-31G* results for small Si clusters. In all computations reported here, the program Gaussian 98 [12] was utilized. We will first present our results on pure Si5 clusters and in a subsequent step comment on the interaction between a Si5 unit and a graphite substrate. A structure of D3h symmetry has been identified as the most stable geometry for this system [9,13]. According to the comprehensive Density Functional Theory based study of Fournier et al. [7], the geometry of second highest stability is planar, emerging from edge-capping of the highly stable Si4 rhombus with one Si atom. For a comparison of both structures, see Figs. 1a, 1b. Our calculation yields for the threedimensional ground state geometry a binding energy of 2.85 eV/atom which deviates by about 2% from the value reported by Raghavachari [9], 2.78 eV/atom, as obtained by use of the MP4/6-31G* method. For further comparison of the two geometric variants of Si5, it is instructive to study the PDOS spectra of these species in the energy region around the HOMO-LUMO gap, as displayed in Figs. 2a, 2b. Focusing first on the spectral features of the D3h alternative (Fig. 2a), one notices a large HOMO-LUMO gap size, amounting to 3.2 eV. While Fig. 2. (a) Valence electron DOS spectrum for the ground state of Si5. Shown are the contributions of pxy orbitals (solid line), pz (dashed line) and s (dotted line) orbitals. (b) Valence electron DOS spectrum for the most stable planar isomer of Si5. The assignments of the three lines shown are as in (a). the dominating peaks of the valence electron region are of s and pxy symmetry, a pronounced pz contribution can be discerned at about 2.5 eV below the Fermi energy which in this representation is equated to zero. This pz peak is attributed to a D3h doublet of the three equatorial atoms which form an equilateral triangle (see Fig. 2a). In case of the planar structure, we also find two valence orbitals predominantly composed of pz electrons. However, in contrast to the three-dimensional variant, these two orbitals, indicated by two narrow peaks in Fig. 2b, are not degenerate but exhibit an energy separation of 2.3 eV. While the lower one of these orbitals consists of a totally symmetric π bond, the one corresponding to higher energy describes bonding interaction between the atoms Si1 and Si2 as well as between Si3 and Si4 (see Fig. 1b), but the interaction between these two atom pairs is repulsive. The PDOS peak associated with the latter orbital is located in the energy gap region of the D3h variant. The resulting effect F. Hagelberg et al.: Theoretical study of small silicon clusters on a graphite layer 39 Table 1. Parameters for SiC54H18. Site of Si Spin E ads [eV] D b [Å]