1. Descriptor Construction

For constructing a comprehensive descriptor framework for materials informatics, we first establish a set of atom-atom interactions derived from elemental parameters. These interactions are then aggregated to generate molecule-level descriptors. In this study, we implemented eleven descriptors to characterize materials, encompassing both electronic-crystallographic properties and thermodynamic stability metrics. The electronic-crystallographic descriptors include crystal systems, space group symbols, volume, density, and crystallographic sites. Thermodynamic stability is quantified using two key descriptors: Energy Above Hull (EAH) and Formation Energy (Ef). EAH is a critical metric for assessing a material’s stability relative to its possible decomposition products. It represents the energy difference, measured in eV/atom, between the material and the most stable composition of its constituent elements on the convex hull. A positive EAH value indicates that the material is metastable and less stable than its most stable constituent phases, suggesting a potential for decomposition. Conversely, a value close to zero indicates high thermodynamic stability. Formation energy, also expressed in eV/atom, quantifies the energetic change associated with the formation of a compound from its constituent elements in their stable reference states. It is mathematically defined as

Here, E_compound is the total energy of the compound, n_i is the number of atoms of element i, and E_Elementi is the total energy of a single atom of element i in its stable reference state. A negative formation energy signifies that the compound is energetically stable with respect to its constituent elements, implying that its formation is a thermodynamically favorable process. Conversely, a positive formation energy indicates an energetically unfavorable compound that may spontaneously decompose. crystal system, space group, band gap, magnetic ordering, and other quantitative and qualitative parameters are considered. After careful consideration, irrelevant parameters from the datasets are omitted.

2. Datasets

In this study, we utilize the material project ^[29] and AFLOW database ^[30]. Both are comprehensive open repositories for computational material science and contain information on inorganic crystalline properties. These two frameworks use VASP to perform DFT calculations with GGA-PBE functional for standard compounds and apply GGA+U method for systems containing d- and f- block elements. The systematic approach with a vast database with plenty of feature space makes our dataset efficient for machine learning analysis.

We selected a subset of sixty materials with dielectric constant between 2.7 and 27, and then the data are augmented to avoid overfitting. Data augmentation is done with feature permutation that breaks strong spurious correlations and can introduce variations while preserving marginal distributions. The range is selected for choosing a suitable gate oxide material for the advanced node FinFET. The lower bound is 2.7 for better subthreshold swing (SS), and the upper bound is limited to 27. By targeting this range, the ML/DL model can select an efficient gate oxide material. The dataset is divided into training, validation, and test sets for reliable evaluation. 10% is reserved for test set. The remaining 90% is split into 80% training set and 20% validation set. The reason for this splitting is to ensure equal distribution of the dielectric constant and work function in every split.

3. Model Selection

For selecting the best model, a comparative analysis of several machine learning (ML) algorithms—including linear regression, Elastic Net, Random Forest, and Extreme Gradient Boost (XGB)—was performed on a dataset. After data cleaning and feature engineering, the data was split into a 1:4 test-to-train ratio. Hyperparameter tuning was conducted using GridSearchCV to find the optimal configuration. The best model was chosen based on the lowest function loss and the highest R² score. To prevent overfitting, k-fold cross-validation was applied during training, and model stability was confirmed by validating performance across multiple random data splits.

4. Fine-tuning Model

This study analyzes both shallow machine learning (ML) and Deep Learning (DL) algorithms. The shallow ML models, ranging from Linear Regression to K-Nearest Neighbor (KNN), and the deep learning Neural Network Regression model were all fine-tuned using GridSearchCV. All models were analyzed with k-fold cross-validation.

The neural network architecture, optimized via GridSearchCV, had its hyperparameters—such as the number of hidden layers, neurons per layer, learning rate, and batch size—rigorously tuned. The Rectified Linear Unit (ReLU) activation function was used in the hidden layers, with a linear activation in the output layer. The model was optimized using the Adam optimizer to minimize the Mean Squared Error (MSE) loss function.

1. Pipeline

The research methodology involves several key stages, from dataset creation to performance evaluation. The study began by creating a diverse dataset by combining data from the AFLOW and Materials Project databases, which contain comprehensive material properties. A meticulous feature selection process followed, identifying the most significant variables influencing the work function based on both domain knowledge and statistical analysis.

To combat bias and overfitting, data augmentation was used to expand the dataset artificially. This involved applying transformations and perturbations to the original data, creating a more diverse set for training machine learning (ML) and deep learning (DL) models. These models were trained using cross-validation to predict the work function of materials, a critical parameter for evaluating FinFET performance.

The predicted work function values from the trained models were implemented into TCAD Sentaurus simulations for a 14 nm FinFET architecture (Fig. 1). This allowed for realistic simulations of the device’s performance, bridging the gap between theoretical and material properties and real-world device behavior. From the I-V profile, the Subthreshold Swing (SS), ON-Current (Ion), and OFF-Current (Ioff) were extracted to evaluate FinFET performance. This data, combined with the predicted work function, provided a comprehensive assessment of the device’s suitability for 14 nm technology node applications.

Fig. 1. Workflow of ML/DL implementation in Advanced 14 nm Technology node. The dataset construction followed by data augmentation, and then fed to ML/DL models for work function inference. Finally, inference data implemented in TCAD.

2. Model Performance

Before modeling, exploratory data analysis (EDA) was performed to understand the dataset’s properties. A Pearson correlation analysis showed no strong linear relationships between features, with all coefficients below 0.49. However, a Variance Inflation Factor (VIF) analysis revealed high scores for ‘sites’ and ‘volume,’ indicating multicollinearity that the initial correlation analysis missed. A pair plot analysis further identified non-linear relationships and cluster formations, specifically between ‘bandgap’ and ‘work function,’ and ‘Energy Above Hull’ (EAH) and ‘bandgap,’ suggesting underlying groupings in the data beyond simple linear associations.

As for ML analysis, it starts with Linear Regression, Lasso, Ridge, and Gradient Boosting regression. After that explored with Ensemble Algorithms like Extreme Boost (XGB) Regression, Random Forest (RF) Regression, and Decision Tree regression. As for DL algorithm, Neural Network Regression. As for benchmarking ML and DL algorithms are compared with Genetic algorithm. All algorithms’ performance is depicted in Table 2.

From Table 2, we noticed that comparatively simpler regression algorithms like linear regression, Ridge, Lasso, and Elastic Net Regressor performed poorly in this regard. Their R² scores are 0.13 with high Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), which is not acceptable. As a result, these four algorithms are not suitable for this dataset. The reason for this poor performance can be the inherent behavior of the algorithms. As these algorithms approximate their prediction in a linear manner and the dataset is not linear, the prediction is wrong with a high value of RMSE and MAE. As RMSE and MAE increase, R² score will decrease. Fig. 2 exhibits the summary of all models’ performance.

Fig. 2. Visualization of predicted and true values of work function with several ML algorithms. (a) Gradient Boost Regression. (b) XGBoost Regression. (c) Decision Trree Regression. (d) Random Forest Regression. (e) Neural Network Regression. (f) Support Vector Regression. R² score is also mentioned in the images.

Boosting algorithms like Gradient Boost and Extreme Gradient Boost (XGB) perform well in this context. Gradient Boost regression has a lower value of RMSE and MAE. In the case of R² score, the value is high, which implies the model is getting overfitted. On the other hand, XGB has RMSE and MAE values within a tolerable limit. R² score of 0.88 ensures the model is not biased or overfitted. XGB identifies parameter ‘density’ as the most important feature (Fig. 3(a)).

Decision Tree regressor and Random Forest regressor are regarded as ensemble algorithms. These two algorithms have RMSE and MAE of low value, and the difference is 0.01 eV. R² scores are in an excellent range of 0.88 to 0.89, which implies these two algorithms are not biased or overfitted. In the case of feature importance, both of the models show ‘density’ feature as the most important feature to predict work function (Figs. 3(b) and 3(c)).

Fig. 3. Feature Importance from Several ML models. (a) XGB. (b) Decision Tree Regressor. (c) Random Forest Regressor.

K nearest neighbor algorithm shows similar performance to ensemble algorithms. KNN performs 0.01 eV more than ensemble algorithms in R² scores. Support vector regressor with RBF kernel performs the same in the case of RMSE and MAE. In case of R² scores, the value is lower little lower than KNN.

Neural network Regression has the lowest value of RMSE and MAE. The reason for this lowest value is neural nets. As each neural network is trained with Adam optimizer and back propagation, the model predicts work function with the least error and a high R² score. Fig. 4 depicts the performance of neural network regression. Fig. 4(a) exhibits Predicted work function Vs True Work function with 0.84 R² score. Figs. 4(b) and 4(c) depict Loss Vs Epoch and Mean Squared Logarithmic Error Vs Epoch. Both of the cases, train and test sets aligned, which implies the error is decreasing with time and learning is progressing with the least error.

Fig. 4. Neural network Regression performance. (a) Predicted work function Vs True work function. (b) Loss vs Epoch for train and test sets. Both sets aligned at the end (c) Mean Squared Logarithmic Error vs Epoch for Train and Test sets.

Genetic algorithm is initiated with four parents and each iteration, there will be six hundred generations with 5% mutation rate with random mutation. Parent selection type is ‘sss’. Crossover is the process where two parent chromosomes exchange genetic material to produce new, unique offspring chromosomes. This introduces new combinations of genes into the population, combining the best traits of both parents. For our case it is “single point” (Fig. 5). Generation Vs Fitness is a steep curve so as is Generation Vs New Solution rate (Figs. 6(a) and 6(b)). The performance is the worst in this research. RMSE and MAE values are the highest of all the models, and R² score is the lowest of all the algorithms.

Fig. 5. Some genetic evolution in the genetic algorithm.

Fig. 6. (a) Generation vs fitness in Genetic Algorithm. (b) Generation vs new solution rate.

Summary of all ML/DL models, simple linear regression models can be eliminated because of poor performance. All the ensemble algorithms, boosting algorithms and neural network regressor have high R² score values without any sign of bias and overfitting. But in the case of MAE, RMSE, Neural Network regressor has the lowest values for all. MAE, RMSE play pivotal role in bias and overfitting. So low value of MAE, RMSE indicate less possibility of bias and overfitting. Considering all the parameters, neural network regressor is the best model for this research (Fig. 7).

Fig. 7. Work function (eV) of different models.

Neural Network Regression (NNR) is selected to predict the work function. NNR model predicts monoclinic Hafnium Oxide (Hf₂O) with the work function of 4.66 eV. Implying NNR data in TCAD Sentaurus SProcess along with other process parameters like 10 nm fin thickness, 6 nm thick TiCl gate, 4e18 cm³ doping concentration, 1 nm thick HfO₂ gate oxide. 14 nm technology FinFET is simulated with Sentaurus Process (Fig. 8(a)). The Characteristics of the FinFET are analyzed with Sentaurus SDevice (Figs. 8(b) and 8(c)). With 4.6 eV (data predicted from NNR) On current is 2.5 e–6 A and Off current is 1 e-10 A. On current in different switching condition with varying work function for our 14 nm technology FinFET is depicted in Fig. 8(d). From Fig. 8(d), for 4.6 eV work function for logic 1 On current is 1.5 e–6 A. From Sprocess and SDevice simulation, it is prominent that 14 nm FinFET is working well with NNR material data, and the research pipeline is working well.

Fig. 8. FinFET TCAD simulation. (a) Process simulation of 14 nm FinFET. (b) I-V characteristics of 14 nm FinFET. (c) Logarithmic I-V. (d) Work function vs on current in different logic state.