surface science EI.SEVIER Applied Surface Science92 (1996) 257-260 Computer simulation of nucleation on (001) Kossel crystal surface with and without diffusion Tong B. Tang * Physics Department, H.K. Baptist University, Kowloon Tong, Kowloon, Hong Kong Received 14 December 1994; acceptedfor publication2 March 1995 Abstract The Monte Carlo technique was applied to nucleation-controlled growth of a (001) Kossel crystal surface, either with or without surface diffusion. The sizes of critical nucleus, no, and of supercritical cluster, n+, have been obtained at different temperatures and supersaturations. With the inclusion of diffusion, both sizes are reduced, and this explains why the nucleation dip of nucleation growth is shortened. However, n+/n o -- 2, as predicted by the theory of Burton, Carbrera and Frank, only in the absence of diffusion. Also, when diffusion operates the kink site density along steps is no longer independent of supersaturation. It is concluded that surface diffusion brings the system further away from thermodynamic equilibrium. 1. Introduction Crystal growth involves the transportation of masses and energy from one phase to another and cannot be adequately treated by equilibrium thermo- dynamics. However, kinetic theories suffer from a problem with spatial inhomogeneity, namely the in- stantaneous distribution of clusters with different sizes. It is natural to resort therefore to computer simulation, for which the Monte Carlo method proved most effective, since we may with sufficient general- ity model the elementary steps of absorption, evapo- ration and surface migration of the growth units by a sequence of stochastic events. Indeed, since the pio- neering works by Chernov and Lewis [1] and others, ' Tel.: + 852 2 339 7036; fax: + 852 2 304 6558; e-mail: tbtang@hkbu.edu.hk. Monte Carlo simulations of crystal growth have reached increasing levels of sophistication in dealing with greater degrees of freedom and more compli- cated boundary conditions [2,3]. Nevertheless, early theoretical considerations based on reversible thermodynamics have succeeded in determining a number of equilibrium properties of the crystal surface, that serve as parameters in its growth process, but a few basic questions remain concerning their validity under various conditions. The growth of a low-index, defect-free surface at low temperature proceeds from layer to layer and is preceded by the continuous formation and disappear- ance of two-dimensional nuclei (the Zeldovich fluc- tuation regime). The critical nucleus size n o is de- fined as the size at which the probabilities to grow and to dissolve are equal. Supercritical clusters, how- ever, are those that sustain steady average growth. 0169-4332/96/$15.00 © 1996 ElsevierScience B.V. All fights reserved SSDI 0169-433 2(95)00238-3