Formation and structural properties of the amorphous-crystal interface in a nanocrystalline system Cesar R. S. da Silva and A. Fazzio Instituto de Fı ´sica, Universidade de Sa ˜ o Paulo (USP), Sa ˜ o Paulo, Brazil ~Received 14 February 2000; revised manuscript received 31 January 2001; published 5 July 2001! Free volume Monte Carlo simulation of the melting and quenching of a Si nanosystem is used to produce an amorphous layer on top of a nanocrystal, and a completely amorphous system. The interface is kept free of any temperature gradient during the melting. We find that the crystal-amorphous transition layer is thicker than previous studies indicated, and keeps memory from the crystal structure. In amorphous bulk, the concentration of fivefold coordinated atoms is substantial, and is associated with a more open structure than fourfold- coordinated regions. All calculations were done with an empirical Tersoff potential. DOI: 10.1103/PhysRevB.64.075301 PACS number~s!: 61.43.2j I. INTRODUCTION Silicon, a very important material due to its multiple tech- nological applications, is regarded as a prototype for fourfold-coordinated covalent amorphous. Si amorphization and amorphous Si ( a -Si) have been investigated for over 30 years. Most studies, however, have focused on Si amorphiza- tion due to the impact of energetic ions, and several models have been proposed. 1–4 A substantial number of recoils gen- erate binary collision cascades, producing defects that are unlikely to be produced by other mechanisms, and even pressure-induced defect generation and amorphization have been speculated to occur. 5 The important issue is that out of thermal equilibrium, point defect accumulation plays an im- portant role in Si amorphization whether you are using ion beam or electron irradiation. 6 If the irradiation is not ther- mally assisted, the above equilibrium defects will not be an- nealed out. Consequently, this kind of mechanism probably leaves a higher concentration of overcoordinated and under- coordinated atoms. Another way to produce a -Si, which has received little attention, is fast quench from the melt. In this case the dis- order is introduced by thermally activated atomic reloca- tions. In comparison to ion beam amorphization, a smaller number of non-four-coordinated Si is expected, and the en- tire structure is likely to be different. This is produced using laser beam pulses, and during the experiment an amorphous formation was observed for Si ~Refs. 7–9! and Ge. 10 In any case, a -Si is modeled as a covalent random net- work of fourfold-coordinated atoms. The experimental aver- age bond length in a -Si is about 1.9% longer than in c-Si. Its experimental radial pair distribution function g ( r ) is not sim- ply crystalline g ( r ) with broadened and shifted peaks. 11 The peak corresponding to the crystal’s third coordination shell, which has 12 atoms, is absent in the amorphous g ( r ). Con- sequently, any model for a -Si needs to show these features to be acceptable. The structure and atomic coordination at the amorphous surface and the crystal-amorphous interface are also of great interest and are the primary concern of this study. Besides some early studies, 12–14 there are two very recent molecular- dynamics ~MD! studies especially concerned with the interface. 15,16 The work of Weber et al., 16 and the most recent work of Bernstein et al. on the subject, 17 focused strictly on the epitaxial growth of the crystalline phase, while in Ref. 15 the authors concentrated specifically on the interface proper- ties. This latter work was carried out using a tight-binding approach for the system relaxation, which ensures more ac- curate forces. Unfortunately they were limited to a small system of only 320 atoms without free boundaries. They also used the Parrinello-Rahman 18 approach to allow for cell re- laxation. The work of Weber et al., used much larger cells and a Stillinger-Weber 19 semiempirical potential. It was car- ried out using a fixed cell with a free surface, allowing for relaxation in only one direction. In order to produce the in- terface, both studies kept the atoms in a portion of the cell at a low temperature and the remaining atoms at a temperature above melting point, until a homogeneous liquid is formed. This means keeping a temperature gradient of thousands of K over interplanar distances. After that, the whole cell was cooled down to room temperature. Consequently the only effect of the crystal on the near-interface amorphous layer is the effect produced by the crystal field. Any memory that the near-interface amorphous layer could have from the crystal is lost. This is not the way a crystal melts. 20 Melting initiates at some extended defect, usually the surface, and propagates to bulk, without any sharp temperature gradient. Therefore, the near-interface amorphous layer had been in the melt for only a short time before the quench, and possibly keeps some memory from the crystal structure. An alternative way is to use a free volume approach. This will allow the crystal to melt from the surface toward the bulk. In this case, a large system is necessary to ensure that the inner bulk is not affected by the surface. Unfortunately, this will prevent the use of first principles or even tight- binding approaches. Tersoff 21,22 and Stillinger and Weber 19 created two widely used empirical potentials for Si. Despite the fact that the Stillinger-Weber produces a melting tem- perature in better agreement with experiment, we have cho- sen the Tersoff potential because it can be used for com- pounds. Thus in the future we will be able to compare Si melting and amorphous transition with Si based compounds and similar materials 23 on the same basis. The parametriza- tion used was what Tersoff called Si~C!. 22 The Metropolis method Monte Carlo 24 ~MC! is used in- stead of constant temperature MD. By choosing the MC method we do not lose great accuracy, since MD will not PHYSICAL REVIEW B, VOLUME 64, 075301 0163-1829/2001/64~7!/075301~7!/$20.00 ©2001 The American Physical Society 64 075301-1