Model-based Analysis and Design of Atomic Layer Deposition Processes

Atomic layer deposition (ALD) is a thin-film manufacturing process in which the growth surface is exposed to non-overlapping alternating injections of gas-phase chemical precursor species separated by intermediate purge periods to prevent gas-phase reactions. ALD is characterized by sequential self-terminating heterogeneous reactions between highly reactive gas-phase precursor species and surface-bound species which, when allowed sufficient conditions to reach saturation, results in highly conformal films, on both planar and topographically complex structures. ALD has already emerged as the prime candidate for depositing ultra-thin layers with high conformality in semiconductor manufacturing. With recent advances in current technologies, novel applications of ALD are expanding beyond semiconductor processing in several emerging areas, such as surface passivation layers in crystalline silicon solar cells, buffer layers in CuIn_{1-x}Ga_{x}Se_{2} (CIGS) solar cells, and diffusion barrier layers in organic light-emitting diodes and thin-film photovoltaics. This trend brings with it a growing necessity for high-throughput and low-cost production techniques. This thesis describes the modeling of the ALD process with temporally separated precursor pulsing, which is a special modification of the chemical vapor deposition (CVD) technique, with which it shares a number of phenomenological characteristics. In particular, both deposition processes are inherently nonlinear and time-dependent, and mathematical model components describing the precursor thermophysical properties, the underlying reactor-scale mass transport of the gas-phase precursor and the deposition surface reaction are strongly coupled. Thus, the integration of physical and chemical phenomena over multiple time and length scales is a fundamental requirement for the understanding and modeling of the complete reactor system. However, what distinguishes ALD from CVD is that the steady-state deposition rate in CVD does not exist in ALD. The deposition rate of ALD depends strongly on the dynamic composition of the growth surface and the local precursor partial pressure in the vicinity of the active surface, which both change continuously through each exposure and purge period. The completely dynamic nature of the ALD process adds considerably to the difficulty of developing simulators, as the entire process cycle must be modeled due to the complex interdependence between the sequential ALD half-reactions, such that the reactivity in one half-cycle is influenced by that in the half-cycle preceding it. One of the essential advantages of ALD, on the other hand is that its self-terminating nature enables uniform coating of large-surface-area substrates, thus providing an easier pathway for process scale-up compared to CVD. In the work presented in this thesis, a physically-based dynamic model of the ALD process was developed, based on a laboratory-scale, continuous cross-flow ALD reactor system (F-120 manufactured by ASM Microchemistry Ltd.) equipped with a quartz crystal microbalance for in situ deposition measurements. The mathematical model of the low-volume, continuous cross-flow ALD reactor with temporally separated precursor pulsing comprises components that describe reactor-scale gas-phase dynamics and surface state dynamics to accurately characterize the continuous, cyclic ALD reactor operation that is described by limit-cycle dynamic solutions. The model is coupled to a heterogeneous surface reaction model based on estimated kinetic parameters from ex situ and in situ deposition measurements. The heterogeneous gas--surface reactions mean that there will be a net mass consumption at the growth surface, and the total gas-phase mass flux of species at the growth surface is balanced by the net consumption rate per unit area. Likewise, the accumulated mass resulting from the epitaxial film growth, governed by the adsorption/chemisorption and surface reaction of precursor species, was conveniently expressed in terms of the spatial and temporal evolution of the fractional concentrations of surface states for each half-reaction. In this way, the film growth per cycle (GPC) and its relative uniformity were unambiguously defined. The work described in this thesis was motivated by the predictive capabilities of physically based ALD process models, as such models can be used in the design of novel reactors, the optimization of deposition conditions, and in the scale-up of laboratory thin-film process. The process model, oriented towards optimization and control, was validated experimentally, to ensure that it could adequately predict the spatially dependent film thickness profile and provide statistically reliable least-square estimates of the parameters involved in the heterogeneous gas--surface reaction mechanism that governs the thin film growth of ZnO from Zn(C_{2}H_{5})_{2} and H_{2}O precursors. However, the general formalism of the model allows it to be used to simulate other ALD process chemistries and more complex (e.g., multi-wafer) reactor systems, thereby providing a framework for model-based process design and dynamic optimization studies, as well as controller development. The primary contribution of this work is the solution strategy developed for the dynamic ALD process model, to consider the limit-cycle solutions that describe steady (but periodic) operation of the reactor system, in conjunction with numerical solvers for limit-cycle-constraint, multi-objective optimization, dynamic optimization, and dynamic parameter estimation problems. The utility of the model-based framework developed was demonstrated by a study of constrained multi-objective optimization of the incommensurable process objectives of limit-cycle deposition rate and overall precursor conversion, subject to a set of operational constraints on the uniformity of cross-substrate film thickness and the duration of the post-precursor purge. Additionally, limit-cycle dynamic optimization targeting precursor utilization was also demonstrated in a scale up-analysis of the laboratory-scale reactor, while assuring that identical deposition profiles were obtained in the scaled-up system. In these studies, the optimal solutions obtained revealed the mechanistic dependence of the process operating parameters on the proposed optimization and constraint specifications, and reduced the design space of the ALD process to a feasible set of design alternatives