A tight - binding molecular dynamics study of Ni Si binary m n clusters

A transferable tight-binding parametrization of the Ni–Si interactions, from small binary Ni Si clusters to bulk NiSi , m n 2 Ž . is presented within a minimal parameter basis. The data base for fitting the parameters is obtained from i ab initio results for the NiSi dimer obtained using the density functional method and the single, double and triple coupled clusters method, Ž . and ii band structure results for the bulk NiSi . The parametrization is incorporated into the tight-binding molecular 2 dynamics scheme to study medium size Ni Si clusters. Our results are in very good agreement with experiment. q 1998 m n Published by Elsevier Science B.V. All rights reserved. Metal-semiconductor interfaces and, in particular, Ž . transition metal silicides TMS’s grown on Si surfaces have attracted major research interest due to their technological importance in semiconductor fabrication. An attractive feature is that they exhibit abrupt interfaces and very low sheet resistance. Furthermore, transition-metal silicides offer high temperature materials for Si metalization as well as rectifying junctions with a variety of Schottky barrier Ž . Ž heights SBH’s . Also, transition metal silicides and 1 E-mail: [email protected] 2 E-mail: [email protected] . in particular NiSi and CoSi constitute prototype 2 2 systems in surface science studies for understanding the effect of the transition metal atoms in surface reconstruction and hetero-diffusion. However, despite intense research efforts, the growth mechanism of metal silicides on Si has not yet been completely understood. Thus, the epitaxially grown NiSi on 2 Ž . Ž . Si 111 and Si 100 surfaces exhibits SBH’s which depend not only on the substrate orientation but also w x on the growth conditions 1–3 . It has been shown that the different SBH’s measured for NiSi reveal 2 various local structural interface variations which are associated with various degrees of interfacial reconw x structions 1,2 . Furthermore, the problem of NiSi2 0009-2614r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved. Ž . PII: S0009-2614 98 00665-4 ( ) A.N. Andriotis et al.rChemical Physics Letters 292 1998 487–492 488 Ž . or CoSi growth on Si surfaces poses a number of 2 questions that have not been answered yet. For example, the nature and the identification of the initial Ž . Ž . nucleation sites for Ni Co on the Si surfaces and their subsequent evolution into forming silicide comw x pounds as well as the observed 1 multiple phase Ž . structures of the NiSi during its growth on Si 100 , 2 constitutes some of the most important questions that have been the focus of intense theoretical and experimental interest recently. Experimentally, the key factors controlling the initial stages of growth of NiSi on Si substrate 2 appear to be the misfit between the silicide and the Si substrate as well as the diffusion rate of Ni into Si and that of Si into Ni. The theoretical calculations Ž . performed at Ts0 , however, appear to be inadequate in supporting the experiments which indicated an increased tendency for Ni to diffuse into Si. Theoretical results indicate that at Ts0 the diffuŽ sion of Ni into Si is not favorable or at least the . activation energy for diffusion is too large . The diffusion mechanism, therefore, is thought to be assisted by the presence of surface defects andror the elevated substrate temperature at which experiments are performed. The use of the scanning tunneling microscope Ž . STM has helped in identifying the most stable sites w x for Co and Ni nucleation on Si surfaces 4,5 . In particular, Co atoms have been found to indiffuse Ž . Ž . into the Si 111 7x7 substrate occupying a position close to a subsurface interstitial site without affecting . the surface reconstruction ; these sites were proposed w x as precursors to silicide formation 4 . Similar behavior has also been suggested for Ni atoms on Si w x surfaces 4 . Also, STM pictures have shown the Ž . formation of a Ni-induced 2x1 surface structure Ž . w x during the initial growth of Ni on Si 100 1,6 . Other experimental findings have suggested that it is possible for the initially formed Ni clusters to react with the Si surface, releasing sufficient energy to promote Si atoms over the Ni clusters suggesting, thus, a possible mechanism for silicide formation w x 7,8 . Such a mechanism was proposed earlier by w x Zunger 9 for the case of Al clusters grown on GaAs. The theoretical investigations of the Si–silicide interfaces are usually based on band structure calculations applied on various slab geometries, the latter w x used to model the Si–silicide interfaces 3,5,10–14 . Some cluster calculations have also been reported for Ž . Ž . modeling the CoSi rSi 111 and NiSi rSi 111 in2 2 w x terfaces 15 . All these calculations have been performed using either the density functional theory Ž . Ž . DFT within the local density approximation LDA Ž . or the tight-binding TB scheme. There appears to be a noticeable preference for the TB calculational schemes because of the computational complexity associated with large scale calculations of the Si– silicide interface with ab initio methods. Also, to the best of our knowledge, ab initio calculations at the Ž . configuration interaction CI level have not been reported for the Ni–Si system. This is mainly due to the calculational difficulties associated with the Ni species even in its free atom state. In particular, Ni exhibits sensitivity to the electron correlation effects Ž . due to its open d-shells and the results depend Ž strongly on the CI-level used, see for example, w x. discussions in Ref. 16 . In this Letter, we report on results derived from a theoretical investigation of the binary Ni Si clusm n ters using the tight-binding molecular dynamics Ž . TBMD scheme based on data obtained from ab initio calculations. Our approach is an application of the TBMD calculational scheme as used earlier in our studies of covalent and metallic systems. The successful applications of the TBMD method in the w x studies of clusters of both semiconductor 17 and w x transition metal atoms 16,18–20 allow us to draw useful conclusions from studies of more complex systems such as the large binary clusters of Ni Si m n which, at the present, are beyond the domain of ab initio theories. Our approach allows us to perform both symmetry unconstrained and spin unrestricted optimizations simultaneously for the determination of the ground state geometry of the binary cluster in a computationally efficient manner. The TBMD w x scheme employed 16,18–20 is semi-empirical and requires only a minimal number of fitting parameters which include the experimental or the theoretical bond lengths and the vibrational frequencies of the dimers Si , Ni and NiSi as well as the ab initio 2 2 total energy results of small Ni Si clusters with m n Ž . nqm-4. The fitting parameters include i the strength f Ay B of the pair repulsive interaction be0 Ž . tween A and B atoms, A,BsSi,Ni, and ii the scaling factor, a , for the distance dependence of Ay B ( ) A.N. Andriotis et al.rChemical Physics Letters 292 1998 487–492 489