Scaling size distribution functions of heterogeneous clusters in a linear capture coefficient model

Abstract

Balance equations of a model of irreversible heterogeneous growth at nucleation centers with linear (with respect to size) capture coefficients have been theoretically analyzed. It is shown that the exact solution of the problem can be expressed in terms of the Polya distribution. The distribution asymptotics at large sizes exactly satisfies the scaling hypothesis, which has been widely discussed in the literature for the last twenty years. The solution adequately reproduces the experimental size (length) distributions of linear chains of metallic In and Ga adatoms on a Si(100) surface.