Atomic Layer Deposition (ALD) is a process crucial to the production of nanoscale electronic and photonic devices. In this process, thin films are deposited on a substrate through repeated exposure of the growth surface to a sequence of precursor species. This mode of operation allows for nearly perfect control of film thickness to atom-scale lengths, even over complex surface topographies.

Despite the performance that can be achieved in these processes and its current use in manufacturing (e.g., the HfO₂ gate oxide used in current Intel 45nm node technology [1]), fundamental gaps in our understanding of anomalous growth in even the highly studied Al₂O₃ ALD process [2] under non-ideal conditions persist. Therefore, we present in this paper our research on Monte Carlo (MC) based simulation of ALD and other thin film deposition processes to examine the fundamental growth mechanisms.

Our MC simulation methods are based on discretizing the growth surface, enumerating all possible states that can exist for each of the lattice regions and all possible transitions between these states during each of the ALD exposure half-cycles. Transition probabilities are quantified using a combination of published literature on Al₂O₃ ALD and from data obtained from our collaborators. In our work, the surface states and transitions are represented as nodes and edges of a graph, respectively. We will demonstrate the benefits of using this approach in terms of clarifying and classifying the relationships between the large number of chemical and physical processes at work in our deposition systems.

Furthermore, we consider the problem of directly computing the steady-state behavior of the ALD process, which consists of finding fixed points to limit cycle solutions. In our approach, we represent the growth surface both by the lattice of states and a lower-dimensional distribution function. At the start of a full ALD cycle, the distribution function is used to generate a microscopic realization of the growth surface, which is followed forward in time through each exposure half cycle using the Monte Carlo simulator. The result at the end of the cycle then is projected back down to the low-dimensional distribution (the lift/simulate/restrict approach of Kevrekidis and coworkers [3]), and a residual is computed from the difference between the distributions at the start and end of the full exposure cycle. This residual is used in a Newton-Raphson procedure to compute the steady-state.

This talk will focus mainly on Al₂O₃ ALD using TMA and water as precursors. The use of our fixed-point algorithm in conjunction with a reactor-scale transport model also will be presented as a demonstration of multiscale simulation of the complete ALD process.

[1] IEEE Spectrum, Oct. 2007.

[2] Rubloff, et al., 2007 AVS meeting.

[3] See, e.g., Cipria, SIAM News, June 2005, for an overview.