Surface diffusion: the low activation energy path for nanotube growth.

We present the temperature dependence of the growth rate of carbon nanofibers by plasma-enhanced chemical vapor deposition with Ni, Co, and Fe catalysts. We extrapolate a common low activation energy of 0.23-0.4 eV, much lower than for thermal deposition. The carbon diffusion on the catalyst surface and the stability of the precursor molecules, C2H2 or CH4, are investigated by ab initio plane wave density functional calculations. We find a low activation energy of 0.4 eV for carbon surface diffusion on Ni and Co (111) planes, much lower than for bulk diffusion. The energy barrier for C2H2 and CH4 dissociation is at least 1.3 eV and 0.9 eV, respectively, on Ni(111) planes or step edges. Hence, the rate-limiting step for plasma-enhanced growth is carbon diffusion on the catalyst surface, while an extra barrier is present for thermal growth due to gas decomposition.