The typical setup for the magnetron sputtering system is depicted in Fig. 1, which comprises a vacuum chamber, a voltage source, a target, and a substrate holder. At the bottom of the system is the sputtering target, typically a planar disc of the material to be deposited, and connected to a negative potential acting as a cathode. Directly above the target, the substrate is mounted, which serves as the anode, where the sputtered material is deposited. The chamber possesses an inlet for sputter gas, which is introduced at controlled flow rates. An outlet is also present to maintain the desired vacuum conditions. During operation, a high voltage is applied between the target and the substrate, ionizing the sputter gas, and the sputter gas glows with a characteristic glow upon conversion to a plasma state within the chamber. The plasma contains Ar⁺, accelerated towards the negatively biased sputtering target.

Figure 1. Schematic of ionization of the Ar and the bombardment, to sputter the target atom, and deposition on the substrate surface

The four modes of the RF sputtering are (i) DC, (ii) RF, (iii) Pulsed DC, and (iv) reactive sputtering. The first three modes are based on the power source used, depending on the type of target material, whereas reactive sputtering uses any power source. DC Sputtering is straightforward and cost-effective, offering easy controllability and relatively low operation costs. In DC non-magnetron sputtering mode, the potential applied to the cathode is constant, usually from − 2 kV to -5 kV; however, the DC magnetron sputtering potential level varies from 200 V to 1 kV [10]. The major limitation of DC sputtering arises during the sputtering of non-metals; arcing occurs due to the charge built up over time, eventually leading to uneven voltage drops, resulting in system breakdown or uneven film deposition [11].

Radio frequency (RF) Sputtering uses AC power with a fixed frequency of 13.56 MHz [7]. The RF sputtering solves arcing due to charge buildup in DC Sputtering and allows non-metal targets. Due to the continuous switching of voltages, passive buildup of charges is prevented on the target surface. RF sputtering is relatively expensive and requires technical expertise. RF sputtering operates at a lower chamber pressure than DC sputtering, resulting in fewer collisions, higher deposition efficiency, and improved film quality. RF sputtered films generally exhibit smoother morphology with better packing density than DC sputtered films.

Pulsed DC sputtering combines key benefits of DC and RF techniques—minimizing arcing, enabling deposition of challenging materials (dielectrics), and maintaining high deposition rates. Pulsed DC sputtering is more straightforward to implement and operate than RF sputtering. The source is a pulsed DC with a frequency between 10 kHz and 350 kHz [11]. Pulsed DC sputtering periodically reverses the target polarity by applying a brief positive voltage pulse after the main negative sputtering pulse. The polarity reversal neutralizes positive charge buildup on the target surface, effectively suppressing arcing and enabling continuous deposition of dielectric materials [12]. Unlike conventional DC sputtering, which is unable to handle charge accumulation on non-conductive targets, pulsed DC alternating pulses maintain process stability and improve film quality, which is advantageous for reactive and dielectric film deposition.

For reactive sputtering, the process gas (Ar) is released along with reaction gases to form respective compounds deposited on the substrate. The compound formation occurs at the substrate and target levels [13]. The reactive sputtering produces compound films such as nitrides and oxides of the target materials. The ratio of Ar to reactive gas is maintained at a constant ratio. These processes are tricky and often show hysteresis effects; hence, system control becomes complicated.

Sputtering involves complex, multi-variable interactions, such as power, pressure, and target material, which are challenging to control fully with traditional experimental methods [14]. By leveraging real-time data (like voltage and deposition rate measurements), machine learning rapidly identifies suitable process conditions, optimizes parameters, and predicts outcomes such as film composition or quality, while minimizing material waste and experimental time [15]. Machine learning enables automated, efficient exploration of the vast process parameter space, allowing researchers to achieve optimal results with fewer experiments than manual trial-and-error approaches, and is particularly valuable as sputtering systems and material requirements become increasingly intricate [13].

Lang et al. [14] used a Gaussian machine learning framework to model the thickness profile, using process parameters such as pressure, RF power, and the geometry of the sputtering setup. In a statistical approach, by Akiyama et al. [16], analysis of variance found the RF power as the most critical parameter in determining the crystal orientation of the films. Kino et al. [15] used machine learning to predict sputter yield based on physical descriptors, and the heat of formation strongly affected the value of sputtering threshold energy. Kamataki et al. [17] developed a hybrid machine learning model combining classification and regression to identify boundary conditions for producing high mobility amorphous indium tin oxide film. The model identified the conditions for making films with 27% higher mobility. Bhaskar et al. [18] used a parametric approach to determine the hydrogen storage capacity of different material classes, and parameters such as temperature and pressure were considered. Although the study has no direct relevance to sputtering, it highlights the predictability of supervised models on physical effects. Models such as decision trees and random forests offered good coefficient of determination (R²) values.

Machine learning predicts the optical properties of NiO films produced using RF magnetron sputtering, utilizing Artificial Neural Networks (ANN), Support Vector Machine (SVM), Gaussian Process Regression (GPR), and Adaptive Network Fuzzy Inference System (ANFIS) [13]. ANN and GPR are preferable in predicting the optical properties compared to the other models deployed. Paturi et al. [19] used machine learning models such as ANN and SVM to estimate coating thickness for electrostatic spray deposition, using process parameters such as electric potential, powder feed pressure, and distance between the nozzle tip and the substrate. The experiment achieved R² of 0.92 and 0.99 on the ANN and SVM models, respectively. Tang et al. [20] used machine-learning-assisted Multiphysics simulations to optimize the chemical vapor deposition process of 4H-SiC epitaxial layer growth. The study investigated the effect of process parameters such as deposition temperature, inlet-flow volume, rotational speed, and pressure on the quality of films. Ant colony optimization-back propagation neural network (ACOBPNN) was used as the machine learning algorithm, and the error rate was 4.03%. Zhai et al. [21] used k-nearest neighbors (KNN), SVR, decision tree, random forest, CatBoost, and backpropagation neural network (BPNN) for the prediction of SiN_x deposition rate during PECVD. CatBoost had the maximum R² value of 0.93, and SHAP analysis proved the gas flow rate as the most influential parameter.

Predictive models, especially machine learning, are crucial for optimizing sputtering processes. The sputtering involves multiple interdependent parameters like pressure, power, and temperature, which affect the deposition properties in a complex way. Instead of a time-consuming trial-and-error approach, predictive models analyze experimental data to identify the most influential parameters and predict the best operating conditions to achieve desired film characteristics [21]. The approach allows researchers to accelerate experiments, reduce waste, and consistently produce high-quality films. Predictive models improve process efficiency and scalability for advanced material development [18].

Predictive models optimize experimental parameters by analyzing past data to understand the relationships between process variables (like pressure and power) and desired outcomes (such as film quality) [22]. The models use machine learning to predict results for different parameter combinations and identify the most successful ones. Optimization algorithms use the predictions to efficiently find the ideal settings, allowing researchers to quickly achieve the preferred results while avoiding a time-consuming trial-and-error approach.

The air from the sputtering chamber is evacuated, and the pressure develops due to the inflow of process gas. The mean free path (λ) measures the average distance an atom or particle travels before the subsequent collision. The λ is inversely proportional to the chamber pressure. MFP is inversely proportional to the chamber pressure [23]. Sputtered particles suffer more collisions at high pressure, and the number of target atoms reaching the substrate decreases [24]. Thus, the chamber ambient parameters are the base and process gas pressures. The base pressure represents the vacuum level before releasing the process gas (typically in the range of 10^− 5 to 10^− 6 mbar). The decrease in the base pressure ensures the effect of other gases (apart from process gas) on the sputtering, leading to increased controllability. The flow rate of the process gas balances the chamber pressure (also known as the sputtering pressure, typically varying in the range of 10^− 2 to 10^− 3 mbar) to form plasma under certain conditions of power and cathode-anode distance [23].

Target-substrate distance is a chamber parameter limited by the chamber design. Target-Substrate Distance indirectly affects the film grain size and deposition rate [25]. Lowering the target-substrate distance increases the deposition rate and film grain (crystalline) size, and decreases the resistivity [26]. When the angle of incidence between the target surface and the argon atoms is maintained at 90°, the Ar atoms tend to graze or bounce off the target surface, reducing the sputtering probability. The sputter yield increases with an increase in angle of incidence; the maximum sputter yield is achieved between the angles 60° and 80°, and rising further decreases the sputter yield [27]. Chamber temperature affects mobility on the substrate surface; higher mobilities result in larger grain sizes and smoother films. An empirical formula by Yamamura et al. [28] is expressed in Eq. (4), where Y(θ) is the sputter yield at θ angle of incidence, and Y(0) is the yield at normal angle of incidence. θ_opt is the angle of maximum sputter yield, and f is the fitting parameter that best fits the curve with experimental data.

The adhesion strength of the substrate to the target increases the thickness of the deposited film [25]. Substrate temperature determines the atom mobility; higher mobilities result in greater grain sizes, which increase the film thickness. The atoms spread out at higher temperatures, creating larger grain sizes and clusters. The enhanced distribution is evident after the film-deposited substrate is brought to room temperature [25]. Substrate rotation is a popular technique used to increase the uniformity of deposition, evens out the effect of uneven sputtering target flux by rotating the substrate, which results in each substrate point being deposited with target atoms at different flux points at distinct instances. Substrate voltage bias is applied to induce the movement of ions towards the target surface, which helps to control the film properties [29].

Sputtering is an electrically neutral momentum transfer process; hence, for effective sputtering, the heavier targets should be sputtered using heavier sputter gases and vice versa [30]. The properties of sputter gas affecting deposition rates and film properties are its atomic weight, reactivity with the target, and gas flow rate in the chamber. Typically, Ar is used as the sputter gas; however, Ne is preferred for lighter targets, and either Xe or Kr is preferred for heavier targets [31]. The sputter gas can be mixed with either N₂ or O₂, leading to the formation of either nitrides or oxides of the target material. Compared to elemental targets, sputter yields are lower in compound materials [32]. The reactivity of the sputter gas is quantified using the ratio of noble gas to the reactive gas. Adjusting the sputter gas flow rate is a critical balancing act. A higher flow rate increases the chamber pressure, which reduces the mean free path of sputtered particles, leading to increased diffusion and a reduced deposition rate. Conversely, reducing the gas flow rate lowers the pressure and decreases the number of argon ions, which are essential for ejecting material from the target.

DC sputtering offers higher deposition rates than RF or reactive sputtering. In a comparative study of ITO layers deposited by DC power and RF power sputtering [33], non-reactive DC sputtering yielded a deposition rate of 60 nm/min at lower power density. In comparison, reactive RF sputtering yielded 20 nm/min. Deposition rates are higher in setups using non-reactive sputter gases than reactive gases. The deposition rate depends on the applied power. An increase in power increases the energy transmitted to the plasma, which results in a higher sputter yield, increasing the deposition rate irrespective of the power source (DC or RF). Higher electrical powers enhance crystallinity and resistivity [34]. A study conducted on the deposition of ZnO:Ga on glass substrates using RF power [35] showed an increase in deposition rate.

The dataset for the model has been sourced from Gencoa’s online universal sputtering calculator, which is accessible at Gencoa Sputter Rate Calculator [36]. The dataset contains material name, power(W), sputtering mode (DC or RF), target-substrate distance (in cm), and the dependent variable is deposition rate (in nm/minute). The dataset contains 3870 entries of 43 different elements and compounds, with power ranging from 10 W to 150 W, while the target-substrate distance ranges from 50 mm to 150 mm. In DC and RF settings, the target area is fixed at a diameter of 50.8 mm, and standard gas flow and vacuum pressures have been considered. The input variables (material, power, sputtering mode, distance) are used to train the model; they are the internal variables, and the output variable is deposition rate. The model is tuned using hyperparameters, which are also referred to as external variables. Table 1 lists all the models used in the evaluation and the respective hyperparameters.

Linear regression, the most popular machine learning model globally, is widely used for simplicity [18], establishing a linear relation between the input and output matrices, as illustrated in Eq. (6). Where [Y] is the matrix set of output variables (or dependent variables), [A] is the matrix set of coefficients of [X], [X] is the matrix set of independent variables, and B is the intercept of the linear relation, while e is the error term. The output matrix and input matrix contain single variables, which refers to linear regression; otherwise, multiple linear regression. The objective of the linear regression model is to find the optimal set of coefficients and intercept that best fits the given dataset and minimizes the error term (ε) as effectively as possible, which is done by iteratively comparing the cost function of each set of coefficients and intercept. The cost function is illustrated in Eq. (7). Y(i) and Yⁱ are the actual output values and predicted output values for the instances of [A] and B. The optimum solution is found using the gradient descent algorithm.

Polynomial regression works like linear regression models and tries to establish a nonlinear relationship between the output and input as an n^th degree polynomial in the form as illustrated in Eq. (8). Like the linear regression method, the polynomial coefficients are found using MSE, as in Eq. (2), which minimizes the error term most effectively. Where Y is the target variable, C₀, C₁, C₂…C_n are coefficients, X is the independent variable, and e is the error term.

Decision Trees regression [37] models the relationship between target and feature variables by building a tree structure. The dataset is broken down into subsets, and an associated decision tree is developed step by step. The decision tree consists of nodes and leaves, where nodes represent the decision being made and leaves are the predicted continuous value based on the feature of the decision node. The node is divided into leaves through splitting; the best split is found at every node, which minimizes the loss function. Decision Trees can handle both regression and classification tasks and are known for their versatility. Their results are independent of data scaling and preprocessing, and they handle nonlinear relationships effectively.

Random forest regression is an ensemble machine learning model to predict continuous outcomes [38], which uses multiple decision trees to achieve accuracy and overcome overfitting. Each decision tree is trained on a different subset of the data. Boosted Decision Trees [39] is a technique that combines many weak learners to come up with one strong learner. Weak learners are individual decision trees, and all the trees are connected; each tree tries to minimize the error of the predecessor, which can handle both numerical and categorical features, removing preprocessing. XGBoost (eXtreme Gradient Boosting) [40] is a tree ensemble model combining many weak prediction models to build a stronger predictive model by directly incorporating L1(Lasso) and L2(Ridge) regularization into the objective function to prevent overfitting. XGBoost is robust enough to prevent overfitting and can handle large datasets efficiently.

Support Vector Regression (SVR) is an extension of the Support Vector Machine for performing regression tasks [41]. SVR aims to find a function that best predicts the continuous output value for the input value by looking for a hyperplane that best fits all the data points. SVR handles linear and nonlinear relationships using kernel functions such as linear, polynomial, and radial basis functions. Kernels are mathematical functions that transform data into higher dimensions.

As illustrated in Fig. 2, the steps have been followed to achieve accuracy. Power, distance, and deposition rates are numerical values in the dataset, whereas the material name is categorical. Sputtering mode has been encoded as 0, 1 to denote DC, RF sputtering, respectively. A label encoder has been employed to convert character values to numeric values for the material class, which enables the model to interpret the material class. An essential step in model training is data scaling, in which data is scaled down by dividing each data column by its maximum value, to ensure the dataset variables remain well adjusted. The step especially enhances the accuracy of neural network regression and gradient-search-based models. The dataset is split into two parts, one for training the selected model and another for testing the chosen model. 80% was allocated for training the model, and 20% for testing the model. The primary step is the selection of models. Machine learning models differ in their hyperparameters.

The possible values of hyperparameters are chosen manually based on the selected model. The hyperparameters are optimized using GridSearchCV (Grid Search Cross Validation), which evaluates the performance of different combinations of hyperparameters using cross-validation to make the best selection. The cross-validation works by splitting the data into training and validation (testing) sets. The best set of hyperparameters is then chosen using a scoring metric evaluated based on the corresponding performance on the validation set. The model is trained to fit the dataset, and the performance of each is evaluated using performance metrics such as MSE, MAE, and R².