Influence of multipolar electrostatic and van der Waals forces on the coagulation of silicon nanoparticles in low-temperature argon-silane plasmas

Abstract

Numerical calculations have been performed to investigate the effects of electrostatic and van der Waals interactions on coalescing silicon nanoparticles in isotropic low-temperature argon–silane plasmas. The electrostatic interaction between nanoparticles is modeled using three approaches, including the elementary Coulomb interaction, a rigorous electrostatic multipolar expansion, and an approximate form of the latter. The van der Waals interaction is described using the Hamaker expression regularized at short separation distance to manage the singularity at the contact surface. The evolution of the size and charge distributions are calculated by solving the general dynamic equation numerically for the coagulation of charged particles and using simplified approaches for nucleation, surface growth, and self-consistent plasma dynamics. A two-population size distribution, as observed in experiments, results naturally from this model. The electrostatic multipolar force is found to enhance the coagulation as compared to the elementary Coulomb force. The details of the growth process depend, however, significantly on the adopted regularization of the Hamaker expression at a short distance.