Wafer Position Reconstruction Using Gradient-Based Device Assignment
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Solution Overview
Problem
The retraceability of semiconductor devices to their original positions on a wafer is lost during the packaging process, making it difficult to assign correct positions due to the complexity of factorial possibilities, leading to thousands of unassignable devices.
Innovation Solution
A method using a gradient descent approach with a doubly stochastic matrix to ascertain an assignment rule between wafer-level test results and final test results without additional metadata, allowing for scalable and efficient assignment of semiconductor devices, even with a large number of devices, by optimizing the assignment rule through projection onto the Birkhoff polytope.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional matching methods are used between wafer-level test results and final test results, then the assignment process becomes computationally intractable, but the need for accurate position reconstruction remains critical
Solution Approach 1:
The patent transforms the discrete assignment problem into a continuous optimization problem by representing the assignment rule as a doubly stochastic matrix. This parameter transformation allows the use of gradient-based optimization methods, changing the problem from factorial complexity to a tractable continuous optimization task that can be solved efficiently with standard numerical methods.
Solution Approach 2:
The patent introduces a regression model as an intermediary between the wafer-level test results and final test results. This regression model learns a mapping function that predicts final test outcomes from wafer-level data, serving as a mediator that enables the assignment optimization without requiring direct enumeration of all possible assignments.
2Productivity
If the number of semiconductor devices increases, then the factorial complexity of the assignment problem increases dramatically, but the need for scalable solutions becomes more critical
Solution Approach 1:
By converting the assignment rule into a continuous doubly stochastic matrix parameterization, the patent enables the application of gradient descent optimization. This approach reduces computational complexity from factorial O(n!) to polynomial time complexity, making the solution scalable to large numbers of semiconductor devices while maintaining reasonable computation times.
Solution Approach 2:
The patent replaces the combinatorial search mechanism with a gradient-based optimization mechanism. Instead of mechanically enumerating all possible assignments, the system uses continuous mathematical optimization with gradient descent, substituting a computationally intensive discrete search with an efficient continuous optimization process that scales much better.
3Loss of information
If no additional metadata is added to semiconductor devices, then the devices remain simple and cost-effective, but the ability to track individual device positions is lost
Solution Approach 1:
The patent creates a virtual copy of the position information by learning a mapping model from wafer-level test data to final test data. Instead of physically marking devices with metadata, the system creates a computational model that replicates the position tracking functionality through data relationships, preserving process simplicity while recovering position information.
Solution Approach 2:
The regression model serves as an intermediary that bridges the gap between wafer-level test results and final test results. This mediator learns the underlying position relationships without requiring physical metadata on devices, enabling position reconstruction through statistical modeling rather than direct tracking.
Data Source
AI summary
A method for ascertaining an assignment rule in order to merge test results from different tests of the same semiconductor device. The method includes the following steps: adapting a model, e.g., a linear regression model, using the model to predict the test data; calculating costs based on the predictions; using a gradient descent method to minimize the costs.