Entropy Calculator for Interpretable Semiconductor Yield Evaluation
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Solution Overview
Problem
Conventional yield evaluation methods in the semiconductor industry, particularly those using machine learning, face challenges in interpretability and flexibility due to complex mathematical models, leading to difficulties in adapting to changing data conditions and requiring frequent retraining.
Innovation Solution
The introduction of an entropy calculator that calculates relative information entropy to evaluate product yield, replacing complex models with fixed variables and allowing for clearer understanding and more flexible application, using the extreme gradient boosting (XGBoost) model to determine packaging strategies.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If machine learning models (DNN, random forest) are used to assist yield evaluation, then evaluation efficiency is improved, but model complexity and difficulty in interpretation increase
Solution Approach 1:
The patent extracts the core evaluation logic from complex machine learning models and formulates it as a linear programming problem with explicit objective functions and constraints. This extraction transforms the black-box ML approach into an interpretable mathematical model that maintains evaluation efficiency while eliminating complexity issues.
Solution Approach 2:
The patent replaces the mechanical/algorithmic complexity of deep neural networks with a mathematical substitution approach using linear programming. The yield evaluation is transformed into an optimization problem with clear variables, constraints, and objective functions, making it computationally efficient and interpretable without requiring complex model structures.
2Measurement precision
If complex deep neural networks are used to synthesize yield functions, then fitting accuracy is improved, but model interpretability and flexibility decrease
Solution Approach 1:
The patent changes the parameter representation from complex neural network weights and activations to linear programming variables with explicit mathematical relationships. By formulating yield evaluation as an optimization problem with clear parameters and constraints, the model achieves both accuracy and interpretability through transparent parameter definitions.
Solution Approach 2:
The patent creates a simplified mathematical copy of the yield evaluation process that mirrors the functionality of complex ML models but uses interpretable linear programming formulations. This copy maintains the essential evaluation logic while presenting it in a form that is easy to understand, modify, and adapt to changing conditions.
3Ease of operation
If expert judgment is used for yield evaluation, then interpretability is maintained, but evaluation efficiency and objectivity decrease
Solution Approach 1:
The patent enables the system to automatically perform yield evaluation through linear programming optimization without requiring expert intervention. The model self-determines the optimal yield prediction by solving the mathematical optimization problem, combining the efficiency of automated processing with the interpretability of explicit mathematical relationships.
Solution Approach 2:
The patent incorporates feedback mechanisms where the linear programming model continuously optimizes yield predictions based on manufacturing data and constraints. The explicit mathematical structure allows for clear feedback loops where evaluation results can be traced back to specific constraints and variables, maintaining interpretability while achieving automated efficiency.
Data Source
AI summary
A yield evaluation method and a yield evaluation apparatus are provided. The method is described below. Wafer manufacturing data, front-end wafer test data, and back-end product yield information in a manufacturing process of a semiconductor product is collected and multiple parameters related to a yield are selected. A relative information entropy of a defective product in multiple samples manufactured using each of the parameters relative to a global constant probability defective product is calculated to establish a product entropy calculator. The global constant probability defective product represents the defective product whose yield does not vary with the parameters. The wafer manufacturing data and the front-end wafer test data of the current product are collected and substituted into the product entropy calculator to evaluate the yield of the current product.