Physics-based machine learning models for lithography

Traditional machine learning models depend heavily on large datasets to identify patterns and make predictions. These models are often referred to as "black boxes" because they lack transparency, making it hard to understand how they generate results. Moreover, they may have difficulty adapting to new, unseen data, particularly if the new data differs significantly from the training set. 

In contrast, physics-based machine learning models directly incorporate physical laws and principles into the machine learning framework. This approach has several benefits. First, it tends to be more interpretable, providing clearer insights into the underlying physical phenomena. Second, it benefits from built-in physical understanding, which helps the model generalize more effectively to new data. Third, it can use this knowledge to learn from smaller datasets, reducing the need for extensive data collection. 

As the semiconductor industry explores the use of machine learning models, the lack of interpretability in traditional models has slowed their adoption as a complete solution. As a result, machine learning is often used for preliminary solutions or minor adjustments. For instance, in optical proximity correction (OPC), machine learning may be used to find an initial solution, which is then refined using conventional OPC models. Similarly, in OPC model calibration jobs, machine learning techniques are typically permitted to make adjustments only up to a small margin, such as 0.5nm. 

The interpretability of physics-based machine learning models can address this issue of trust. By incorporating physical constraints, it becomes feasible to develop machine-learning OPC models that account for the optical and chemical aspects of lithography. These physics-based models can also potentially replace the most time-consuming parts of rigorous simulators. For example, the post-exposure bake (PEB) step in rigorous simulations is often time-intensive due to its sequential nature, but with a machine learning model, this process could be significantly accelerated. These examples illustrate how physics-based machine learning models can be applied across various steps in the lithography process, from design technology co-optimization (DTCO) to metrology analysis.