ICMCTF 2023 Session F5-MoM: Machine Learning and Process Modeling for Coating Design and Production

Modern products require coating stacks with increased complexity and precision as well as improved throughput, reproducibility and environmental footprint. Simulation is a valuable asset to reach these goals by modelling deposition reactor dynamics as well as thin film growth on atomistic level.

The various physical scales of thin film deposition can be addressed by either model-driven or data-driven codes. The first category is based on physically accurate models, that need only few unknown internal parameters but require high computational power. Examples are the Direct Simulation Monte Carlo (DSMC) and Particle-in-Cell Monte-Carlo (PIC-MC) methods for description of gas flow and plasma processes at low pressure and Molecular Dynamics (MD) or kinetic Monte Carlo (kMC) methods for modeling atomistic processes in thin film growth. Despite of their high computational demand, these methods are useful for getting insights into the functionality of novel deposition setups and plasma sources.

A complementary approach uses data-driven simulation codes, which are based on simplified, semi-empirical models or machine learning methods. On the one hand, they need a significant amount of internal data in order to be adjusted to represent specific process conditions, on the other hand they usually require only low computational power, which enables to do parameter optimization or use them as real-time capable digital twins for model-based in-situ process control.

This talk shows various examples for model-based simulation of PVD processes. Furthermore, it demonstrates how to use data obtained by physical modeling in order to create a digital twin for prediction of the coating uniformity on 3D substrates in a sputter reactor for optical coatings.

Magnetron sputtering is a widely used technique for the deposition of metal and compound layers for numerous technical applications. However, optimizing a sputtering process is a challenging task, especially since each industrial customer has specific requirements and expectations.

In order to improve properties of deposited coatings it is essential to understand the physics influencing them. Since the physical processes in magnetron sputtering are complex, it is often necessary to employ computer simulations. There has been a lot of work done in this regard [1-3], however, the simulations typically focused only on one part of a sputtering process, such as target erosion, sputtered atom transport, or the discharge properties.

This contribution attempts to provide a bigger picture by creating a coater-scale model which is a combination of two sub-models: (1) The bulk plasma model, which is a fluid model describing the plasma between the target and the substrate. It mostly affects ion bombardment. (2) The cathode plasma model, which is a particle-based model where ions and electrons are traced in the electric and magnetic field in the close vicinity of the target where the plasma sheath resides. This model affects mostly the target erosion. Its implementation is similar to our previous model from [4].

Together, these two models provide insight into various phenomena such as ion flux distribution, which determines target erosion, and the magnitude of ion bombardment at the substrates, which is a key determiner of the coating performance properties (residual stress, hardness, composition). Moreover, parametric studies can be performed so that the influence of pressure, substrate bias voltage, position of the electrodes, and others can be studied.

This model will be validated against experimental data.

References:

[1] C. Feist, A. Plankensteiner, J. Winkler Studying Target Erosion in Planar Sputtering Magnetrons Using a Discrete Model for Energetic ElectronsProceedings of the Conference: COMSOL, 2013

[2] S. Mahieu et al. Monte Carlo simulation of the transport of atoms in DC magnetron sputtering Nucl. Instrum. Methods Phys. Res. B, 243 (2), 2006, 313-319

[3] E. Shidoji, N. Nakano, T. Makabe Numerical simulation of the discharge in d.c. magnetron sputtering Thin Solid Films, 351 (1–2), 1999, 37-41

[4] A. Rostek Simulating ion flux to 3D parts in vacuum arc coating: Investigating effect of part size using novel particle-based model Surf. Coat. Technol., 449, 2022, 128954

Managing data in an R&D lab is often tedious manual work and leads to heterogenous, incomplete data. To ensure reproducibility, information about experimental setups, process hardware, and -conditions, and sample pre-treatment, must be kept in addition to the primary results. Consolidating and harmonizing datasets for large-scale, overarching data science projects constitutes a substantial additional effort.

At Evatec we developed a system, designed to automate these things in the specific context of thin film process development and verification. Substrate information, hardware configuration, process log-data, and measurement results are linked together based on wafer-ID.

In contrast to traditional manufacturing execution systems (MES), the Evatec Fabric can dynamically reconstruct the chronology of events for each wafer without need to define a process flow in advance. This allows our scientists and engineers a wide degree of flexibility in carrying out their work.

A data-processing component, programmed in python, uses various algorithms, models, and data-fitting techniques to process the raw data, produced by process systems and metrology instruments. It extracts useful parameters and statistics that are stored in a highly structured and contextualized way, enabling data science and machine learning projects based on clean, homogenous data.

Developing, transferring, or troubleshooting reactive PVD processes has always been a challenge. This can be partly attributed to the non-linear behavior of these processes. Additionally, the fundamental variables that drive the physics (e.g., plasma density and potential, the energy of sputtered and ionic species, …) are hard to measure, thus, often unknown in practice.

Another typical challenge is the number of consistent experiments available about the process. Experiments and their analysis are expensive and time-consuming. It is not uncommon that there are only a few (< 10) experiments available. This is the main limitation of machine-learning methods as these require large data sets (> 100).

In this contribution, we describe an alternative, physics-based approach that works well even with a low number of experiments. We illustrate that it is possible to formulate such a model for a whole coater that is either free of fitting parameters or contains only a few of them and they have a clear physical meaning. These models additionally contain coefficients, such as pumping speed, sputtering yields, or effective coating areas. These parameters are either known (pumping speed), can be obtained from the literature (sputtering yields), or can be pre-computed using 2D or 3D simulations (effective coating areas) for the coater and loading at hand.

Once created, such a model can reproduce the material composition across coaters and coater conditions with the accuracy of a few atomic percent. By correlating the process model outputs with literature data, the tool can also make predictions about the performance parameters of the coating (e.g., hardness). The approach will be illustrated in the case of nitride- or carbide-based ceramic coatings.