Probabilistic mixed-cluster onset in GeSn:In-motivated three-species codeposition: A kinetic Monte Carlo study

Experimental studies of multicomponent codeposition show that a highly mobile deposited species can accumulate at the growth surface and promote mixed-cluster formation after relatively small changes in its supply. A representative example is GeSn:In growth, where In exhibits surfactantlike behavior and promotes Sn–In cosegregation, although early mixed-clustering onset is difficult to isolate before Sn–In-rich droplets and trails have formed. We develop a minimal kinetic Monte Carlo model of three-species codeposition where one species forms the growing matrix and two nonmatrix species have unequal surface mobilities. Reversible diffusion, attachment, and detachment allow mixed clusters to emerge from local motion and binding rather than imposed irreversible aggregation. The GeSn:In-motivated model is used to isolate mobility-assisted mixed-cluster formation. Onset is quantified by Ponset, the probability that a finite-density mixed-cluster criterion is reached before a specified target coverage. Ensemble simulations show that Ponset increases with both the supply of the more mobile species and target coverage, while the mean onset coverage shifts to earlier growth stages as mobile-species flux increases. The onset window persists upon variation of the more-mobile-species diffusion barrier, a 100-fold change in the absolute diffusion-rate scale, and ±50% variation of the neighbor-stabilization contributions. Mixed-site fractions are also statistically consistent between 64 × 64 and 80 × 80 lattices. Thus, mobility-assisted mixed-cluster formation occurs over a probabilistic onset window rather than at a sharply defined input ratio, with robustness demonstrated within the modeled kinetic regime across all parameter ranges examined in the present study, without claiming universality under arbitrary parameter assignments.