Multiscale modeling of chemical vapor deposition and plasma etching

Abstract

In this work, a framework and a set of modeling tools capable of describing systems with key processes occurring on widely separated length and time scales has been developed. The major focus of this work is linking atomistic and continuum descriptions of gas phase transport. This problem is of considerable practical interest, as most etching and CVD processes are run at low pressures ~ 1 torr or less. Under these conditions, the continuum diffusion models used to describe flow and transport in a typical reactor will fail below scales of a few hundred microns, and thus are not useful in describing transport in and around microscale topography. This is a serious limitation, as such topography is present in most microelectronic devices. Two methods for linking discrete particle (or feature scale) and continuum models of precursor transport are presented. The discrete and continuum models are coupled by boundary conditions at their mutual interface (just above any reactive surface with microscale detail) The first approach employs an effective reactivity function e,, which is computed through a hybrid probabilistic-deterministic MC method e. can be interpreted as a representation of the average fate of molecules entering the feature scale domain from the macroscopic model. An example of tungsten CVD over a substrate with surface topography typical of modern microelectronic devices is presented. A second, deterministic technique was also developed as an improvement on the Monte Carlo approach. The deterministic method uses the matrix of transmission probabilities, or shape kernel, to summarize all microscale events in a fashion consistent with a continuum macroscopic model. The deterministic linking algorithm is over 1,000 times faster than the previously presented MC method. The speed advantage enables simulation of detailed chemistry. Plasma etching presents a very similar multiscale problem and a strategy for linked plasma etching simulations is presented. Finally, a study of ionized physical vapor deposition of aluminum is presented as an example of atomistic-continuum linking. Molecular dynamics simulations are used to represent atomistic events. The Molecular Dynamics results are summarized in a manner that allows the combination of atomistic information with a continuum (level -set) model for evolution of the deposited metal film.