Semiconductor Processing Duration Prediction via Linear Regression
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Solution Overview
Problem
Existing semiconductor fabrication line technologies face challenges in accurately predicting processing completion durations, leading to difficulties in scheduling subsequent processing steps, and require complex calculations, making it hard to support processing targets with predetermined equipment according to scheduled durations.
Innovation Solution
A processing support device and method that uses regression equations to derive intercepts and gradients from stored two-dimensional coordinate data, allowing for the prediction of processing durations and end times by substituting these values into a regression equation (Y=aX+b), where X is the unit count and Y is the processing duration, to support processing targets with predetermined equipment.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If complex calculation methods are used to predict processing completion duration, then prediction accuracy may be improved, but calculation complexity and operational difficulty increase
Solution Approach 1:
The patent transforms the complex prediction problem into a simple linear regression model Y=aX+b, where processing completion duration Y is predicted based on unit count X. By changing the mathematical approach from complex calculations to a straightforward linear equation with pre-determined coefficients a and b, the system achieves both accuracy and simplicity in prediction operations.
2Measurement precision
If complex calculation methods are used to predict processing completion duration, then prediction accuracy may be improved, but ease of operation deteriorates
Solution Approach 1:
The patent performs preliminary calculations to determine the regression coefficients a and b before actual scheduling operations. These pre-calculated parameters are stored and reused for multiple predictions, eliminating the need for complex calculations during each scheduling decision. This allows operators to simply input unit count X and obtain accurate prediction Y without dealing with computational complexity.
3Productivity
If accurate prediction of processing completion duration is achieved, then scheduling efficiency is improved, but system complexity increases
Solution Approach 1:
The patent extracts the complex prediction calculations from the operational scheduling process. By pre-determining the regression parameters a and b through initial analysis of historical data, the system separates the complex computational task from routine scheduling operations. During actual use, only simple substitution into the linear equation Y=aX+b is required, maintaining high scheduling efficiency while minimizing system complexity.
Data Source
AI summary
Using an equipment-classified processing results database, an intercept satisfying a second predetermined condition is derived from intercepts of straight lines that pass through a reference co-ordinate point, which satisfies a first predetermined condition, and respective co-ordinate points in a region bounded by: a line that passes through the reference co-ordinate point and is parallel to an x-axis representing wafer counts X; a y-axis representing processing durations Y; and a line passing through the reference co-ordinate point and the origin. Of co-ordinate points represented by an equipment and recipe-classified processing results database, a gradient satisfying a third predetermined condition is derived from gradients of lines that pass through the derived intercept and each of all co-ordinate points with wafer counts X at or above a predetermined number. A processing duration is derived using a regression equation into which the derived intercept and the derived gradient are substituted.