Application of the bond valence method to Si/NiSi 2 interfaces
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It is shown how the bond valence method can be used to estimate expected interatomic distances in coherent interfaces. The method is illustrated by application to the Si/NiSi 2 ( H I ) interface with results generally in accord with experimental data.
I. THE BOND VALENCE METHOD Recent developments in the bond valence method (briefly reviewed below) have made it possible to make rather accurate predictions of interatomic distances in crystals, even those with very complex structures.1 The purpose of this paper is to show that the same method can also be applied to coherent interfaces to estimate expected relaxations of atomic positions in the interface region. The method is conceptually very simple and can readily be applied to structures involving a large number of atoms and, although empirically based, has considerable heuristic value in predicting the nature of interface relaxations that might reasonably be expected. The only parameters entering into the problem are the atomic valences (usually unambiguous) and a parameter (usually considered "uniyersal") that expresses the dependence of bond lengths on bond valence. Here the method is illustrated by application to (111) NiSi 2 and CoSi2 interfaces with Si, which have been the subject of considerable investigation because of their technological interest.2 Central to the method is the idea, long established in chemistry, that associated with bonds between atoms i and j there is a bond valence Vy such that their sum over bonds to i is the valence V> of that atom:
To an excellent approximation the length of the bond dtj is a unique function of the valence. It has been shown3 for very many bonds that a suitable form of this function is: ij = Rij
- b i n
Vij
(2)
with b empirically observed4 to be a "universal" constant equal to 0.37 A. Equation (2) is used with this value of b in this work. The prediction of bond lengths requires first a prediction of bond valences which are then converted into predicted bond lengths using Eq. (2). Unfortunately, except for the very simplest of structures, Eq. (1) is not sufficient to determine unique bond valences. A major advance was the proposal5 (the "equal valence rule") that one should require valences of bonds between like pairs J. Mater. Res., Vol. 6, No. 11, Nov 1991
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of atoms to be as nearly equal as possible subject to the constraints, Eq. (1). It has been shown6 that these conditions lead to additional linear relationships that uniquely determine the individual bond valences, and an algorithm for obtaining the predicted valences from the connectivity matrix of the structure has been described.1 The equal valence rule has been shown1'5'6 to correctly predict bond lengths in large numbers and varieties of crystal structures. Bond valence parameters, Ry, for a large number of atom pairs are now available.3'47'8 From Eq. (2) it should be clear that Rtj is, in a formal sense, the length of a unit ("single") bond between i and j . II. BONDING IN NiSi2 NiSi2 has the fa
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