Modeling catalyst nucleation for carbon nanotube growth by chemical-vapor and plasma-enhanced chemical-vapor deposition methods

The nucleation of the nickel nanoparticles on substrates, a critical process in the growth of carbon nanotubes, has been modeled analytically using thermodynamic and statistical theories. It was hypothesized that during the initial stages of the annealing process smaller nanoparticles with the size of about 5 nm form and, subsequently, randomly hop to make larger nanoparticles. The minimum and maximum diameter of the nickel nanoparticles can be obtained from the derived expressions. In addition, the size-dependent probability of forming the nanoparticles was examined at various temperatures and plasma power densities in chemical-vapor deposition and plasma-enhanced chemical-vapor deposition methods, respectively. The theoretical results presented agreed very well with experimental data.