Kinetics of cluster impingement in thin film nucleation at solid surfaces: estimation of the collision series up to the four order term

We demonstrate that the coalescence kinetics in thin film growth at solid surfaces can be properly expressed through a series expansion. By reason of the collisions among clusters each term of the series depends upon all distinct configurations of k-connected clusters, namely the bunch of order k. On the basis of the Johnson-Mehl-Avrami-Kolmogoroff (JMAK) theory and for simultaneous nucleation, we propose a computation pathway for evaluating all terms of the series. Moreover, the first three contributions are exactly computed, and an approximated expression is found fur the term of order four. The computation indicates that the collision series is rapidly convergent and, as a consequence, the sum of the first four terms well approximates the exact sum. The series is succesfully used to model the coalescence kinetics in non classical nucleation of thin films at solid surfaces. (C) 1998 Elsevier Science B.V. All rights reserved.