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Predicting the composition and hardness of decorative protective TixAlySizN coatings

The Customer

The customer is a company developing decorative functional PVD coatings. Decorative PVD coatings are used on a broad range of high-end products, such as lighting fixtures, watches, jewellery, cutlery or door handles. The customer has an internal R&D department, responsible for designing new PVD colors. The primary tool for growing the decorative coatings is reactive magnetron sputtering in 4-cathode coaters.

Problem Specification

The customer would like to predict the functional and color parameters of the coating depending on the coater settings.


To predict the color, one must be able to predict the atomic composition and the crystalline structure. Furthermore, a specific thickness goal has to be met to ensure that the coating is stable and wear-resistant.

All the quantities (composition, structure and deposition rate) are controlled by the power to individual cathodes, flow rates of reactive gases and the bias voltage. There are many possible combinations of these control parameters and it is extremely difficult to correlate the coater settings with the material performance parameters.

Results and Benefits

PlasmaSolve’s PVD Digital Twin model did a good job predicting the behavior of a very complex process. The customer gained

  1. 8-10x reduction or trial depositions when designing a new material.

  2. 2-3x faster turn time when transferring an existing recipe between different coated parts.

  3. Higher confidence and predictability of materials R&D

  4. The ability to design coating recipes based on desired material properties


Model performance in terms of coating composition - left part shows 8 training experiments, right part shows 4 validation experiments.

Simulation Strategy

The PVD Digital Twin model by PlasmaSolve is capable of making coater-level predictions about the performance properties of the material being grown.


This is achieved in two steps:

  1. A physics simulation predicts the poisoning of the cathodes and the coated parts. Knowing the cathode power levels, this information is sufficient for calculating the atomic composition of the coating (metals, oxide, nitride, carbide) and the deposition rate

  2. A semi-heuristic model, trained on customer’s data. It predicts the crystalline structure of the coating, and the hardness.

The Digital Twin Model typically requires a training dataset. Because it relies on rule-restricted machine learning, the training dataset is easily attainable in most industrial environments. Specifically, we recommend:

  • Binary materials = 4 training experiments

  • Ternary materials = 8 training experiments

  • Quaternary materials = 12 training experiments.

In this case, 8 training experiments were used. The type of data required for each training experiment is elaborated on below.

Digital twin model flowchart.png

Representative example of a machine log file


Cathode currents, plotted from the logs


Gas flow rates, plotted from the logs

Inputs - Process and Coater

To correctly train the Digital Twin Model to a specific use case, a reasonable amount of information about the process and the coater had to be gathered.

Firstly, machine logs/dump were provided for each training experiment. Generally, the following information should be contained in a log for optimum performance:

  • Current to each sputter cathode

  • Voltage at each sputter cathode

  • Type of cathode (DC, RF, MF)

  • Current/Voltage at auxiliary anodes (if any)

  • Bias voltage (conductive samples)

  • Bias current (conductive samples)

  • Bias frequency (if applicable)

  • Frequency of cathode driving field (if applicable)

  • Gas flow rates of all gases supplied to the system

  • Pressure reading

Secondly, the CAD assembly showing the main dimensions of the coater was provided. The following information was obtained:

  • Target-substrate distance

  • Target dimensions

  • Target type (rotary, flat)

  • Position of anodes

  • Substrate holder dimensions and loading

  • Coating zone dimensions

  • Gas inlet positions

  • Pump positions

Note: If a machine log is not readily available. The data can be provided as a table.

Note: CAD drawing can be replaced by approximate dimensions, which may, however, reduce the model accuracy.

Inputs - Material Properties

In addition to the machine logs, material properties were provided for each training experiments.

The job of the model was to predict the atomic composition, hardness and stress, so accurate measurements of these quantities were provided for each training experiment. In addition, the thickness of individual coating sub-layers was provided and used as independent validation quantity.

Various experimental techniques for characterizing materials are available. PlasmaSolve's recommendations are:

  • Atomic composition: EDX, APT

  • Thickness: SEM cross-section

  • Residual stress: Wafer bending method (single layer), XRD (stacks)

  • Hardness: measured by nanoindenter

  • Lattice constant & crystalline structure: XRD


Material characterization for the training experiments

Training the Model

The digital twin model is, by its design, aware of various physical constraints and rules – it contains a database of sputtering yields for various metal elements, metal nitrides, oxides or carbides. It also takes into account the different chemistries of various reactive gases. For this reason, only 8 training experiments were required.

The atomic composition is predicted nearly from first principles. During the training stage, the sputtering yields in the model are adjusted slightly, only within the range of values presented in literature.

When training the model to predict the performance parameters – such as hardness and residual stress more heuristics is involved but the model is still constrained by solid-state physics rules. For example, the residual stress is known to depend on the incident ion energy and flux but the expression contains 2 fitting constants.

At the end of the training procedure, the model was able to describe all the experiments from the training dataset using one set of fitting parameters. The fact that this was possible gave us the strong confidence that the model is complete and that there are no "hidden variables".

Measured atomic composition of the investigated coatings plotted against the predictions from the trained Digital Twin Model


Training and validation data, shown together

Validating the Model

The expected feature of a Digital Twin model is the ability to accurately interpolate with the space of the training experiments. However, since the PVD Digital Twin tool is highly constrained by physics rules, it also enables extrapolation to conditions outside the training dataset, provided that they are not too far outside.

In follow-up work, the customer perfomed additional depositions and characterized the samples as a “blind test” for the model. Some of these experiments even lied outside the training space of the model (e.g. higher cathode power).

The model was successful in predicting the composition and the hardness of all the validation coatings, with reasonably small offset.

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