Statistical models for carbon-nitrogen film growth

Abstract

We studied models of deposition and erosion, with two species of particles, that represent quantitatively many features of amorphous carbon-nitrogen film grown under plasma enhanced chemical vapor deposition. In the original model, the columns of the deposit are independent, and particles C and N are released with probabilities p and 1-p, respectively. An incident C particle always aggregates upon contact with the surface. An N particle annihilates with a top C particle with probability q and aggregates with probability 1-q. An N particle always annihilates with a top N. A critical line separates the regimes of growth (p>q/2) and erosion (p<q/2). For fixed q, when p decreases towards the critical value p(c)=q/2, the bulk concentration of N (x(N)) increases, and the growth rate r decreases. The rxx(N) curve for q=0.25 agrees with data from films grown in acetylene-nitrogen atmospheres. In order to represent the blocking of surface bonds by hydrogen atoms, we considered a second model in which any aggregation process is accepted with probability alpha, otherwise it is rejected. For q=0.25 and alpha=0.3, the rxx(N) curve agrees with data from films grown in methane-nitrogen and methane-ammonia atmospheres. The fitting values of q and alpha were inferred from related experiments. In order to test the influence of lattice structure and spatial correlations, we also studied those models in simple cubic lattices, considering that the aggregation must satisfy the restricted solid-on-solid model conditions for the difference of heights in neighboring columns, while the erosion is random. We obtained similar results for rxx(N) curves, confirming the validity of those models to represent the kinetics of amorphous films growth. It was also observed that the surface roughness increases with x(N), which agrees qualitatively with several experiments on carbon-nitrogen films growth with ion bombardment.