Machine learning-based modeling and operation for ALD of SiO₂ thin-films using data from a multiscale CFD simulation

Highlights

• Multiscale computational fluid dynamics (CFD) modeling of ALD reactor.

• Machine-learning modeling using multiscale CFD model data.

• Use of machine learning model to optimize ALD cycle time.

• Significant reduction of ALD cycle time versus fixed-time deposition.

Abstract

Atomic layer deposition (ALD) is a widely utilized deposition technology in the semiconductor industry due to its superior ability to generate highly conformal films and to deposit materials into high aspect-ratio geometric structures. However, ALD experiments remain expensive and time-consuming, and the existing first-principles based models have not yet been able to provide solutions to key process outputs that are computationally efficient, which is necessary for on-line optimization and real-time control. In this work, a multiscale data-driven model is proposed and developed to capture the macroscopic process domain dynamics with a linear parameter varying model, and to characterize the microscopic domain film growth dynamics with a feed-forward artificial neural network (ANN) model. The multiscale data-driven model predicts the transient deposition rate from the following four key process operating parameters that can be manipulated, measured or estimated by process engineers: precursor feed flow rate, operating pressure, surface heating, and transient film coverage. Our results demonstrate that the multiscale data-driven model can efficiently characterize the transient input-output relationship for the SiO₂ thermal ALD process using bis(tertiary-butylamino)silane (BTBAS) as the Si precursor. The multiscale data-driven model successfully reduces the computational time from 0.6 to 1.2 h for each time step, which is required for the first-principles based multiscale computational fluid dynamics (CFD) model, to less than 0.1 s, making its real-time usage feasible. The developed data-driven modeling methodology can be further generalized and used for other thermal ALD or similar deposition systems, which will greatly enhance the feasibility of industrial manufacturing processes.

Introduction

Deposition, along with photo-lithography and etching, is one of the most important building blocks in thin-film material development. In the semiconductor industry, the stringent demands on the scale and complexity of the electronic devices have continuously pushed the deposition techniques to be more precise and controllable. For instance, the state-of-the-art flash memory devices, such as the 3D NAND (not-and) memory and the dynamic random-access memory (DRAM), require sophisticated non-planar 3D design and ultra-thin gates (<10 nm) with demanding conformity and defect formation criteria (George et al., 1996, Schuegraf et al., 2013). Originated as a derivative of the chemical vapor deposition (CVD), atomic layer deposition (ALD) has been developed to build the thin-films that meet the demands for more uniform films and higher aspect-ratio micro-structures (Kääriäinen et al., 2013). In a typical ALD process, two precursor gases are introduced in pulses into the reactor sequentially, with inert purge gas pulse injected between the two precursor pulses. Each precursor pulse is called a half-cycle, and the inert gas pulses are called purging. In each half-cycle, ideally, only one precursor will be in contact and react with the substrate surface. Given the appropriate operating conditions and cycle-time, an ideal ALD half-cycle will be self-limiting, resulting in a highly conformal and fully covered substrate surface terminated with the desired element introduced by the precursor species (George, 2009). Following this alternating precursor scheme, ALD can precisely deposit materials layer-by-layer and effectively allow the uniform coverage on complex geometries (Tanner et al., 2007, Foong et al., 2010, Shirazi and Elliott, 2014, Ishikawa et al., 2017). As a result, ALD has been widely utilized in the field of nanoelectromechanical systems (NEMS), especially for the manufacturing of semiconductor memory devices.

The past decade has witnessed an increasing research interest on ALD and a growing market in the industrial manufacturing of thin-film materials (Raaijmakers, 2011, Kääriäinen et al., 2013). The ALD industry also holds a promising future with its global market expected to reach US$3.2 billion by 2026. Novel precursors and reaction mechanisms were discovered, making the film processing of high aspect-ratio substrate layouts more efficient and feasible. Yet, the limited throughput and the high manufacturing cost of ALD production still trouble the manufacturers, especially amid the fluctuating global semiconductor market. Despite the urgent need for further enhancement of the ALD processes, the overall cost of precursors and equipment thwarts the progression of more extensive research efforts (Shirazi and Elliott, 2014). More specifically, one of the major roadblocks to a deeper understanding of the ALD process is the coupled effect between the reactor gas-phase development and the microscopic thin-film deposition process. Beside the apparent absence of a clear and direct theoretical explanation, it is also extremely difficult to obtain an empirical database of film growth during the experiments due to the limitations in real-time in-situ sensing. Scanning electron microscopy (SEM) and scanning tunneling microscopy (STM) provide detailed film profiles but are often expensive and destructive to the deposited film, and therefore, they cannot be used to perform on-line monitoring (Chen, 1993, Goldstein et al., 2017). Quartz crystal microbalance (QCM) does a good job of measuring the overall deposition rate by examining the total mass of the substrate surface in real-time, but fails to unveil local changes within the substrate (Elam et al., 2002). Another option is the in-situ spectroscopic ellipsometry, which is capable of providing local structural information of the film. However, the operation of spectroscopic ellipsometry equipment is very complicated and thus is not prevalent in industry (Pittal et al., 1993, Dalton et al., 1994). With all aforementioned shortcomings, the existing hardware monitoring methods, despite their fidelity and capability to report the actual film profiles, are not yet applicable for a complete measurement of local film coverage profiles during the industrial ALD process. Therefore, an accurate and all-inclusive simulation model for the ALD processes could be helpful in estimating the transient film coverage and in understanding the real-time development on both microscopic and macroscopic scales, which could be of significant value to both industrial and experimental works.

Many efforts have been done in the past to develop an appropriate model for thermal ALD processes. Due to the limitation of computational power and the inherent differences in operational length scales, it is not economical or even feasible to develop a model that describes both the bulk gas-phase and the substrate surface processes using a single simulation method. As a result, multiscale models are often proposed and developed in which different simulation methods and techniques are adopted for gas-phase and surface processes, respectively (e.g., Ding et al., 2019). For the gas-phase model, one approach is to develop analytical or numerical solutions of the mass, momentum, and energy conservation equations with the suitable boundary conditions (Christofides et al., 2008). Nevertheless, the assumptions in these models, particularly when analytical solutions are sought, make the applicability of the results rather limited as they fail to be applicable to industrial-scale ALD systems, where complex reactor designs are often used to enhance species transport. Therefore, computational fluid dynamics (CFD) modeling may be employed instead and it has been demonstrated to be capable of computing highly accurate gas-phase profiles for complex reactor geometries (Pan et al., 2014, Crose et al., 2018). On the microscopic scale, surface reactions are the predominant processes that determine film deposition. Molecular Dynamics (MD) has traditionally been used to simulate a variety of molecular-scale microscopic events, but again it cannot be applied to simulate the industrial-size ALD system. More recently, the kMC method, which statistically determines and tracks the probability of each event instead of each particle, is proven to be able to efficiently and accurately represent ALD systems, and thereby it is a good choice for the simulation of the microscopic film-growth activities (Knoops et al., 2010, Elliott and Greer, 2004, Weckman et al., 2018, Crose et al., 2018). Therefore, utilizing and combining distinct methods for the macroscopic (gas-phase) and microscopic (film growth) simulations, we can accurately characterize the ALD system as a whole. Recently, we have investigated the thermal ALD process of SiO₂ adopting BTBAS as the precursor (Ding et al., 2019). Specifically, using a standalone 3D surface deposition kMC model, we successfully reported a growth rate that lies within the experimental range (1.4 Å ∼ 2.1 Å per cycle); and in Zhang et al. (2019), we created a 3D multiscale CFD model integrating the CFD and the kMC model, which correctly predicted the half-cycle time needed under different precursor inlet flow rates and reduced the half-cycle time needed by 39.6%, following the ALD chamber geometry optimizations.

Although the multiscale CFD model provides valuable insights to the dynamics of the ALD process, its solution is computationally time-intensive and thus infeasible to be applied in the context of industrial on-line operational optimization. Data-driven modeling adopting machine learning techniques, especially neural networks, has recently received attention in the field of deposition simulations. Djurabekova et al. (2007) and Nicolas and Lorenzo (2010) have employed an artificial neural network (ANN) to characterize the result of kMC simulation for lattice microscopic structures. Chaffart and Ricardez-Sandoval (2018) and Kimaev and Ricardez-Sandoval (2019) have looked into ANN formulations of multiscale deposition simulation on a 2D geometry. However, no machine learning-based formulation has yet been investigated for an industrial-scale ALD system. Motivated by these considerations, in this work, we first construct a database using the previously developed multiscale CFD model that incorporates the gas-phase CFD model, the microscopic kMC model, and the multiscale workflow (Zhang et al., 2019). Then, a multiscale data-driven model is developed, which consists of a linear parameter varying model approximating the gas-phase CFD model and a feed-forward ANN approximating the microscopic kMC model. By fully parameterizing the film deposition rate in terms of input variables that can be manipulated, measured or estimated in real-time, we are able to preserve the model fidelity of key input-output relationships, while greatly enhancing the computational speed. Thereby, the developed multiscale data-driven model may lead to a significant economic benefit by allowing on-line prediction of the minimum cycle-time for full coverage. By contrast, in order to conduct a thorough research on operating conditions with experiments, the precursor alone could cost about 4.08 million dollars, in addition to the operational cost for heating and running the reactor. For some other precursors, such as BDEAS, this number could be doubled due to their smaller production scale.