Overview
In semiconductor manufacturing, optimizing process steps is an essential part of maintaining and improving competitiveness.
This article provides an overview of a successful data science project that led to a better understanding of processes, optimized machine control, and starting points for automated process management.
Goal
To achieve specific transistor properties, diffusion time in the furnace during the manufacturing process is a key parameter. By applying better forecasting methods, the optimal diffusion time can be determined with greater precision, thereby improving the quality of the production process.
Starting Point
A solid data foundation of measurements from the production process, consisting of 40,000 rows and 200 columns. Control has so far been based on empirical values and the evaluation of historical data using regression models that map the relationship between diffusion time and target value for a handful of subgroups, formed on the basis of a single process parameter.
Opportunities
A large volume of data and the previously basic, yet underdeveloped use of regression methods presents a strong opportunity for success in a data science project:
- Integration of previously unused process parameters
- Use of more measurements through refined data aggregation and cleansing
- Application of more sophisticated model types (machine learning and data mining)
- Better accessibility for subject matter experts through the creation of a simulator that, after entering process details, suggests the optimal diffusion time
Environment
The use of a standardized data science environment enables the subject matter experts involved from the organization’s team to:
- Understand the analytical steps and validate them with their domain knowledge
- Carry out their own modifications and experiments
- Integrate newly generated process data (e.g., after a successful project) into the analytical process
- Independently apply this process as a template for solving new problems
What are the relevant steps?
1 - Team Enablement
Starting a project with training on an analytical software platform makes it significantly easier for the subject matter experts involved to understand the analytical steps, and enables the team to actively participate in the analysis and automation work, and ultimately take full ownership of the processes.
Using standard analytical software offers many advantages, including a NoCode/LowCode approach, documentation, training materials, integrations, standardized connectors, and reduced burden on the IT department.
2 - Analysis of the Existing Approach
The existing analytical process is replicated in order to create a basis for comparison with the new process, and to ensure the quality and consistency of the data foundation.
3 - Improved Data Aggregation
The data, originally captured at wafer level, must be aggregated to lot level. In this step, the data is consolidated. For metric measurements, the arithmetic mean can be used in this project. Categorical variables must be handled explicitly.
4 - Data Preparation
In an analytical project, new data issues tend to surface at every stage. This means that aggregation, data preparation, and feature selection steps often need to be revisited and refined. Discussions with the customer’s subject matter experts are frequently helpful here, as some phenomena can only be understood in the context of production and not from the data alone.
Typical cleansing steps include the removal of individual outliers as well as entire lots that, as it turned out, were produced solely for testing purposes.
5 - Feature Selection
A key assumption of the project is that additional information about production lots exists which was not used in the original analytical process. This could relate to chemical, physical, or process-related characteristics of the lots.
Using feature selection methods, a large number of unused attributes can be evaluated for their suitability. This results in a list of attributes that should be discussed with subject matter experts, and whose remaining candidates can then be incorporated into the models. The results become part of the data preparation process and are subsequently processed in the models.
6 - Model Selection and Comparison
More sophisticated model types are capable of drawing more precise conclusions from the data. A prerequisite is that the models remain interpretable and sufficiently transparent, so that the subject matter experts involved can validate them. The task at hand is a regression problem, that is, the prediction of a numerical value. With these requirements in mind, a preselection of the most promising candidate methods can be made.
Regression Models
Regression methods are a classic among forecasting techniques and are already established in this process. As an extension, Generalized Linear and Nonlinear Models (GLZ), with a logistic transformation function, were selected. Thanks to a stepwise model building approach, this method can evaluate a large number of influencing variables and use them where needed.
Decision Tree (CART)
Decision trees combine high robustness with fast computation and good interpretability, though they are not among the strongest forecasting models. They primarily serve to establish a baseline for the minimum expected prediction quality and are well suited for detecting and diagnosing data issues. They also offer built in feature selection, which works well in combination with the upstream feature selection step.
Multivariate Adaptive Regression Splines (MARS)
This method combines aspects of decision trees, such as stepwise model building and the ability to capture nonlinear relationships, with the favorable characteristics of regression models, including high predictive accuracy for numerical values and good interpretability.
Stochastic Gradient Boosting with Trees (Boosted Trees)
Model boosting in combination with decision trees is one of the most powerful forecasting methods in machine learning in terms of predictive accuracy. However, it is difficult to interpret and requires large amounts of data. In particular, the high data requirements mean that some relationships may not be modeled sufficiently.
Sampling Strategy
All methods are trained on the same training sample and tested on the same testing sample. The data is split into training and test sets in such a way that all values of the target variable are evenly represented in both.
Test Results
Comparing the models by mean absolute deviation, regression methods GLZ and MARS outperform the others. This is likely attributable to their more data-efficient approach and suitability for regression problems. Overall, GLZ clearly outperforms all other methods in this experiment when considering both training and test error together.
The fact that GLZ leads here is not a drawback, as the method brings additional advantages, most notably: straightforward interpretation and straightforward deployment.
Process Simulation
To further validate the models, and in particular the winning model, the fully trained model is integrated into a simulator. Users can enter the known parameters of the production process and examine the model outputs, that is, the predicted target value, in relation to diffusion time.
After successful validation by the subject matter experts, the simulator is made available to the entire team for gaining further insights into the process. For defined production scenarios, the influence of specific parameters on the required diffusion time can be explored.
Once a specific scenario has been selected, the simulator automatically calculates the expected optimal diffusion time based on the model’s predictions, which can then be used to configure the furnace.
With this step, the project can be considered complete. The simulator is then used on an ongoing basis to better understand and control the production process.
Deployment
After successful testing and validation in the simulator, a model can also be embedded directly into operational workflows. For regression methods, this is particularly flexible:
- The model can be rebuilt in other tools. The coefficients of a regression model can be extracted and reimplemented.
- Using PMML export, models can be exported in an industry standard format and imported and applied by other tools.
- Export as code in various programming languages such as Java, C#, or Visual Basic allows direct embedding in other applications.
- Predictions can be computed in batch mode on a fixed schedule and written to databases.
- Models and predictions can be made available on demand via API through a web interface.
- Model predictions, along with process details, can be dynamically generated and visualized in a dashboarding or visual data science environment such as Spotfire.
These deployment options are not mutually exclusive and can be combined as needed, depending on requirements and the stakeholders involved.
Conclusion
As with most analytical projects, the results are not limited to a single aspect but bring improvements across several areas:
- An automated data preparation process, flexible enough to be reapplied as more data becomes available. The prepared data may also prove useful in other projects.
- Identification of new relevant influencing factors on the target variable enables better process monitoring and a deeper understanding of the process.
- Comparison of multiple model types for selecting a robust and reliable forecasting model.
- The simulator gives subject matter experts broad opportunities to gain insights and allows them to run experiments without risk.
- Outlook: embedding the model in an automated process for production control has the potential to increase product quality and reduce costs.
If you are interested in an analytical project, need support evaluating your data in the semiconductor space, or are looking for a data science environment in which your team can gain new insights, we would be glad to hear from you!
