The Development of the Empirical Bond-Order Potentials for Silicon Clusters

Abstract

For the application of the Molecular Dynamics to the real system, the accuracy of the empirical interatomic potential is of key issue. In this paper, for the description of the dynamic system including small number of atoms such as gas phase and surface reaction, the empirical bond order potentials for silicon cluster structures are proposed. Since the poor description of Tersoff potential for clusters is considered to be responsible for the angle and coordination dependences of the bond order term, new original forms of the bond order term are proposed. The bulk cohesive energy, lattice parameter, the energy and especially its order of various cluster structures are set as fitting parameters. In addition, effective fitting technique by using the structural energy difference method is also proposed.
As a result, the energy order and global minimum structures of Si3-Si5 clusters and the bulk properties can be accurately described by S1b and S2b model. These potentials are excellent as compared with Tersoff type 2 and type 3 potential except for the bulk elastic constants of Tersoff type 3. The potential describing larger than Si6 cluster are created (S1c and S2c model), however it is found that it is impossible to express both bulk and large cluster properties within our scheme. It is considered that the deficiency is caused by the lack of the incorporation of the environmental effect, that is the environmental difference between cluster and bulk, by using our empirical potential forms.
Moreover, it is found that the error of structural difference method is very small (averaged error is 1.2%), therefore our proposed technique is proved to be effective for fitting procedure.