Three-dimensional kinetic Monte Carlo simulations of cubic transition metal nitride thin film growth

Abstract

A three-dimensional kinetic Monte Carlo (KMC) model has been developed and used to simulate the microstructure and growth morphology of cubic transition metal nitride (TMN) thin films deposited by reactive magnetron sputtering. Results are presented for the case of stoichiometric TiN, chosen as a representative TMN prototype. The model is based on a NaCl-type rigid lattice and includes deposition and diffusion events for both N and Ti species. It is capable of reproducing voids and overhangs, as well as surface faceting. Simulations were carried out assuming a uniform flux of incoming particles approaching the surface at normal incidence. The ballistic deposition model is parametrized with an interaction parameter ${r}_{0}$ that mimics the capture distance at which incoming particles may stick on the surface, equivalently to a surface trapping mechanism. Two diffusion models are implemented, based on the different ways to compute the site-dependent activation energy for hopping atoms. The influence of temperature (300--500 K), deposition flux (0.1--100 monolayers/s), and interaction parameter ${r}_{0}$ (1.5--6.0 \AA{}) on the obtained growth morphology are presented. Microstructures ranging from highly porous, [001]-oriented straight columns with smooth top surface to rough columns emerging with different crystallographic facets are reproduced, depending on kinetic restrictions, deposited energy (seemingly captured by ${r}_{0})$, and shadowing effect. The development of facets is a direct consequence of the diffusion model which includes an intrinsic (minimum energy-based) diffusion anisotropy, although no crystallographic diffusion anisotropy was explicitly taken into account at this stage. The time-dependent morphological evolution is analyzed quantitatively to extract the growth exponent $\ensuremath{\beta}$ and roughness exponent $\ensuremath{\alpha}$, as indicators of kinetic roughening behavior. For dense TiN films, values of $\ensuremath{\alpha}\ensuremath{\approx}0.7$ and $\ensuremath{\beta}=0.24$ are obtained in good agreement with existing experimental data. At this stage a single lattice is considered but the KMC model will be extended further to address more complex mechanisms, such as anisotropic surface diffusion and grain boundary migration at the origin of the competitive columnar growth observed in polycrystalline TiN-based films.