Modeling ALD Surface Reaction and Process Dynamics using Absolute Reaction Rate Theory

Abstract

A physically based model of atomic layer deposition (ALD) surface reaction dynamics is developed and applied to alumina ALD with water and trimethylaluminum precursors. The time-dependent growth surface composition is modeled by computing the equilibrium precursor adduct surface concentrations during each half-reaction and the rate constants of the ligand exchange reactions using transition state theory. To describe the continuous cyclic operation of the deposition reaction system, a numerical procedure to discretize limit-cycle solutions is developed and used to distinguish saturating growth per cycle (GPC) from non-saturating (gpc) conditions. The transition between the two regimes is studied as a function of precursor partial pressure, exposure time, and temperature.

Dynamic Modeling for the Design and Cyclic Operation of an Atomic Layer Deposition (ALD) Reactor

“…Subsequent to either of these adsorption steps, H migration and reaction with surface Me groups releases CH 4 , which desorbs immediately [10], effectively resulting in an irreversible reaction and depopulating the surface of hydroxyl groups. The reactions taking place during the water exposure follow structurally similar reaction pathways and are described in more detail in [11]. Further details also are given in the excellent review by [13] of atomic-scale ALD reaction mechanisms and the quantum-chemical computations used to uncover the reaction mechanisms.…”

“…Empirical growth models have also been developed to describe ALD kinetics during the initial stages of nucleation [17,18] and island growth [19][20][21]. Additionally, surface reaction models have been developed to predict growth kinetics and the effects of operating parameters (e.g., temperature, pressure, precursor exposure time) during undersaturating conditions and leading to self-limiting ALD growth [11,[22][23][24][25].…”

“…An alternative to the sticking coefficient approach is to couple transient plug-flow reactor dynamics with kinetic expressions containing rate constants derived from ab initio quantum-chemical calculations and the quantum-statistical theory of chemical reactions [36]. Yet another approach is to use the absolute reaction rate theory and statistical thermodynamics to derive kinetic expressions without the use of adjustable parameters [11]. Furthermore, [37,38] developed a rigorous 2D transport model, which is coupled to a heterogeneous surface reaction model based on estimated kinetic parameters from ex situ film thickness measurements.…”

“…The two equilibrium reactions define the surface concentrations of the adduct, AX, and the transition state, AX ‡ , between the adduct and the final reaction products. A rate expression for v 0 was developed in [11]; for this study, we consider the alternative reaction mechanism of [10], written as the following reaction sequences:…”

“…The primary contributions of this paper are its use of physically-based reaction kinetics models derived from transition state theory [11] and limit-cycle calculations describing the steady operation of these reactor systems. …”