Wafer Inspection Temperature Sensor Selection Using Mahalanobis Distance
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Solution Overview
Problem
Existing inspection apparatuses face challenges in accurately selecting the most suitable temperature sensor for temperature control of electronic devices on a wafer, especially when devices are arranged in uneven distributions, as the sensor closest to the average vector may not be appropriate for effective temperature control.
Innovation Solution
The inspection apparatus calculates the Mahalanobis distance between the average vector of electronic device positions and temperature sensor positions, selecting the sensor with the smallest Mahalanobis distance for precise temperature control.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If the temperature sensor closest to the average vector position is selected for temperature control, then the selection process is simple, but the temperature control accuracy deteriorates when electronic devices are arranged in uneven distribution
Solution Approach 1:
The patent changes the selection criterion from simple geometric distance to Mahalanobis distance, which incorporates the covariance structure of device positions. This parameter transformation allows the system to account for uneven distributions and correlations in device placement, thereby improving temperature control accuracy while maintaining an automated selection process
Solution Approach 2:
The patent replaces the simple geometric proximity approach with a statistical methodology based on Mahalanobis distance calculation. This substitution transforms the sensor selection from a purely spatial problem to a statistical one, enabling accurate selection even when devices are unevenly distributed across the wafer
2Measurement precision
If multiple temperature sensors are used to improve temperature control coverage, then the temperature control accuracy improves, but the device complexity increases
Solution Approach 1:
The patent introduces Mahalanobis distance as an intermediary metric that enables a single temperature sensor to effectively represent the thermal environment for multiple devices. This intermediary calculation allows one sensor to serve multiple devices accurately, avoiding the need for additional sensors while maintaining control precision
Solution Approach 2:
The patent makes a single temperature sensor universal for monitoring multiple electronic devices by using Mahalanobis distance to determine representativeness. This multi-functionality approach allows one sensor to effectively monitor temperature conditions for various devices without requiring dedicated sensors for each device, thus avoiding increased system complexity
Data Source
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AI summary
An inspection apparatus (100) includes: an acquisition part (501) configured to acquire first coordinate information indicating a position of an inspection object on a stage and a plurality of pieces of second coordinate information indicating positions of a plurality of temperature sensors (220_1 to 220_4) on the stage when performing an inspection of the inspection object; a calculation part (503) configured to calculate a Mahalanobis distance between a position specified by an average vector of the first coordinate information and the positions of the plurality of temperature sensors (220_1 to 220_4); a selection part (505) configured to select at least one temperature sensor including a temperature sensor having a smallest Mahalanobis distance, among the plurality of temperature sensors (220_1 to 220_4); and a controller (330) configured to control a temperature of the inspection object using temperature data measured by the selected at least one temperature sensor.