[Paper Review] A Novel Approach for Semiconductor Etching Process with Inductive Biases

Sanghoon Myung, Hyunjae Jang+6 more|arXiv (Cornell University)|Apr 6, 2021

Adversarial Robustness in Machine Learning6 references5 citations

TL;DR

This paper proposes a physics-informed deep learning model for semiconductor etching that embeds inductive biases—specifically Weibull-based profile evolution and cumulative etching constraints—into a Transformer architecture. The model outperforms both standard deep learning and TCAD simulations by better matching physical behavior, achieving faster inference and improved accuracy on unseen data, with a 9.4% generalization gain over baseline models.

ABSTRACT

The etching process is one of the most important processes in semiconductor manufacturing. We have introduced the state-of-the-art deep learning model to predict the etching profiles. However, the significant problems violating physics have been found through various techniques such as explainable artificial intelligence and representation of prediction uncertainty. To address this problem, this paper presents a novel approach to apply the inductive biases for etching process. We demonstrate that our approach fits the measurement faster than physical simulator while following the physical behavior. Our approach would bring a new opportunity for better etching process with higher accuracy and lower cost.

Motivation & Objective

• To address the failure of standard deep learning models in semiconductor etching due to distribution shift and lack of physical consistency.
• To improve model generalization and reliability by embedding domain-specific physical constraints as inductive biases.
• To replace or augment slow, calibration-heavy TCAD simulations with a faster, more accurate predictive model.
• To ensure predictions align with physical laws (e.g., sequential vertical etching, monotonic material removal) through architectural design.
• To enhance trustworthiness via uncertainty quantification and explainable AI, validated against domain knowledge.

Proposed method

• Introduces a Transformer-based model that predicts DTI (Deep Trench Isolation) profiles step-by-step using recipe inputs, including equipment and wafer location.
• Applies Weibull activation with learnable shape (k) and scale (λ) parameters to enforce physically plausible profile evolution per etching step.
• Imposes a cumulative etching constraint where the total etched depth increases monotonically across steps to prevent artificial re-coating.
• Uses a deep ensemble with Negative Log-Likelihood (NLL) loss to quantify prediction uncertainty across steps.
• Designs the model architecture to generate intermediate profiles without requiring intermediate measurement data.
• Validates the model by comparing predictions against TCAD simulations and assessing generalization on out-of-distribution test recipes.

Experimental results

Research questions

• RQ1 Can inductive biases improve the generalization and physical consistency of deep learning models in semiconductor etching beyond standard architectures?
• RQ2 How does embedding Weibull-based profile evolution affect the model's alignment with physical etching behavior?
• RQ3 To what extent does enforcing monotonic cumulative etching improve prediction reliability and reduce physical implausibility?
• RQ4 Does the integration of inductive biases lead to better performance on out-of-distribution test data compared to a standard deep learning baseline?
• RQ5 Can the model’s uncertainty estimates and attention maps be interpreted in alignment with domain-specific knowledge?

Key findings

• The proposed model with inductive biases achieved a 9.4% improvement in generalization performance over the baseline model on out-of-distribution test recipes.
• Without Weibull activation, the model produced physically implausible results, such as re-coating of etched trenches, indicating the necessity of the inductive bias.
• The model’s predictions showed significantly better agreement with TCAD simulations than the baseline model, especially in the final etching profile.
• The model’s uncertainty estimates increased appropriately with each step, reflecting growing prediction confidence and reliability over time.
• Attention maps confirmed that the model correctly attributed etching of the top and bottom of the trench to the appropriate steps, aligning with domain knowledge.
• The model generated accurate intermediate profiles without requiring intermediate measurements, enabling full-step-by-step prediction from recipe input alone.