Island-size distribution and capture numbers in three-dimensional nucleation: Comparison with mean-field behavior

The scaling of the monomer and island densities, island-size distribution sISDd, capture-number distribution sCNDd, and capture-zone distribution is studied as a function of the fraction of occupied sites scoveraged and ratio D /F of the monomer hopping rate D to the sper sited monomer creation rate F in a three-dimensional s3Dd point-island model of irreversible nucleation and island growth. Our model is a 3D analog of submonolayer growth and may also be viewed as a simplified model of the early stages of vacancy cluster nucleation and growth under irradiation. Good agreement is found between mean-field sMFd rate-equation results for the average island and monomer densities and our simulation results. In addition, due to the decreased influence of correlations and fluctuations in 3D, the scaled CND depends only weakly on the island-size. As a result, the scaled ISD is significantly sharper than obtained in 2D and diverges with increasing D /F. However, for large D /F both the scaled ISD and the scaled CND differ from the MF prediction. In particular, the scaled ISD diverges more slowly than the MF prediction while the asymptotic divergence occurs at a value of the scaled island size which is larger than the MF prediction. These results are further supported by an analysis of the asymptotic scaled capture-number distribution.