A kinetic Monte Carlo method for the atomic-scale simulation of chemical vapor deposition: Application to diamond

Abstract

We present a method for simulating the chemical vapor deposition (CVD) of thin films. The model is based upon a three-dimensional representation of film growth on the atomic scale that incorporates the effects of surface atomic structure and morphology. Film growth is simulated on lattice. The temporal evolution of the film during growth is examined on the atomic scale by a Monte Carlo technique parameterized by the rates of the important surface chemical reactions. The approach is similar to the N-fold way in that one reaction occurs at each simulation step, and the time increment between reaction events is variable. As an example of the application of the simulation technique, the growth of {111}-oriented diamond films was simulated for fifteen substrate temperatures ranging from 800 to 1500 K. Film growth rates and incorporated vacancy and H atom concentrations were computed at each temperature. Under typical CVD conditions, the simulated growth rates vary from about 0.1 to 0.8 μm/hr between 800 and 1500 K and the activation energy for growth on the {111}: H surface between 800 and 1100 K is 11.3 kcal/mol. The simulations predict that the concentrations of incorporated point defects are low at substrate temperatures below 1300 K, but become significant above this temperature. If the ratio between growth rate and point defect concentration is used as a measure of growth efficiency, ideal substrate temperatures for the growth of {111}-oriented diamond films are in the vicinity of 1100 to 1200 K.

Locally activated Monte Carlo method for long-time-scale simulations

“…The global evolution of the system is separated into single atom events ͑generic moves͒ for which the typical barriers are predetermined and assumed to remain unchanged as the system relaxes. Usually the barriers are calculated for the generic moves of an atom in an otherwise ideal host matrix by the most accurate methods available 16,17 before actually doing any structural optimization of the model. A Monte Carlo step consists of randomly selecting one of the atoms and one of the generic moves and of evolving the system according to the transition rate for this move.…”

“…This time increment ⌬t hop yields a lower limit of the time duration while it assumes that any of the diffusion jumps has taken place. An alternative way to define the time increment is given by Battaile et al 17 However, in the LAMC, the pool of the escape rates may change after every diffusion jump, so it is not clear that the time increment suggested by Battaile et al converges to the correct value.…”

A mechanism for crystal twinning in the growth of diamond by chemical vapour deposition

“…Atomistic modelling has been performed of the diamond CVD growth using the kinetic Monte Carlo method (Battaile et al 1997a(Battaile et al ,b, 1998. A key observation was that growth rate on the diamond (111) surface was limited by the rate of nucleation of the next layer of growth and that once a step edge exists, growth proceeds rapidly by single and two carbon addition events at the step edges (see figure 4).…”

Effective transition rates for epitaxial growth using fast modulation

“…11,13 We perform kinetic Monte Carlo (KMC) simulations in this paper, using the formalism of Bortz 14 to capture the correct evolution in time. Kinetic Monte Carlo simulations provide useful predictions of thin-film growth, but the rule-based simulations are not conducive to mathematical analysis.…”