Wafer Yield Factor Attribution Using Embeddings and Shapley Approximation
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Solution Overview
Problem
Existing methods for determining the contribution of factors in wafer manufacturing processes face significant computational challenges, particularly in calculating Shapley values for large numbers of features, which hinders efficient analysis of wafer yield.
Innovation Solution
A method and system utilizing an embedding layer and model explainer to convert categorical data into embedding vectors, enabling the use of gradient explainers to approximate Shapley values, thereby reducing computational demands and accurately determining factor contributions to wafer yield.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Shapley values are calculated for all input features to determine factor contributions, then measurement precision of factor contribution is improved, but computing time and computational resources increase exponentially
Solution Approach 1:
The patent segments the computational task by dividing input features into categorical and numerical types, applying different processing methods to each segment. Categorical features are converted to embeddings while numerical features are processed directly, allowing parallel and optimized computation paths that reduce overall computational complexity while maintaining contribution measurement precision.
Solution Approach 2:
The patent transforms categorical feature parameters into continuous embedding vectors, changing the parameter representation from discrete categories to continuous numerical spaces. This parameter transformation enables the use of gradient-based methods for contribution calculation, significantly reducing computational requirements compared to traditional Shapley value calculation while preserving measurement accuracy.
2Measurement precision
If traditional Shapley value calculation is used for categorical data, then contribution accuracy is maintained, but computational complexity increases
Solution Approach 1:
The patent substitutes the mechanical computation process of traditional Shapley value calculation with a neural network-based gradient computation system. By using embedding layers and gradient explainers, the system replaces exhaustive combinatorial calculations with differentiable neural network operations, reducing computational complexity while maintaining contribution accuracy through the mathematical properties of gradients.
3Productivity
If embedding vectors are used to represent categorical data, then computational efficiency is improved, but data transformation complexity increases
Solution Approach 1:
The patent performs preliminary action by pre-training embedding layers to convert categorical data into meaningful continuous vectors before the main contribution calculation process. This preprocessing step creates reusable embedding representations that can be applied across multiple predictions, improving computational efficiency during inference while the initial transformation complexity is amortized over subsequent operations.
Data Source
AI summary
A method, a device, and a system that determines a plurality of partial contributions from process data of a target wafer and process data of a background set wafer to a yield using a trained yield prediction model, and determines a contribution of a factor in a manufacturing process of the target wafer to the yield by summing the plurality of partial contributions are provided.