Wafer Feature Inference via Gaussian Process Spatial Modeling
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Solution Overview
Problem
Current methods for testing and calibrating devices on wafers require individual measurement of each device, which is time-consuming and costly, especially since devices produced on the same wafer exhibit similar patterns due to shared processing steps, necessitating a more efficient approach to determine device features.
Innovation Solution
A method using a Gaussian process model to associate wafer positions with device features, allowing for the prediction of device features from a subset of sample measurements, thereby reducing the need for extensive testing and incorporating uncertainty values and operating parameters to optimize sampling for minimal testing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If individual measurement of each device is performed, then measurement precision is ensured, but measurement time and cost increase significantly
Solution Approach 1:
The wafer is divided into multiple regions or zones based on spatial correlation of device features. Instead of measuring every device individually, the wafer is segmented into areas where devices share similar characteristics, allowing representative sampling from each segment to infer properties of other devices in the same segment.
Solution Approach 2:
The patent uses Gaussian process models to create virtual copies or predictions of device features for unmeasured devices based on measurements from sampled devices. The model learns the spatial correlation patterns from measured devices and generates predicted feature values for other devices, effectively copying the measurement information across the wafer.
2Loss of information
If individual measurement of each device is performed, then complete device feature data is obtained, but measurement cost increases significantly
Solution Approach 1:
Instead of performing complete measurements on all devices (excessive action), the patent performs partial measurements on a strategically selected subset of devices. The Gaussian process model then interpolates and predicts the features of unmeasured devices, achieving sufficient information completeness without the excessive cost of universal measurement.
Solution Approach 2:
The patent changes the measurement strategy from a fixed per-device approach to a probabilistic sampling approach based on spatial parameters. By modeling device features as continuous spatial fields with specific correlation lengths and variance parameters, the system optimizes which devices to measure based on maximizing information gain while minimizing cost.
3Productivity
If sampling is reduced to minimize testing, then measurement cost decreases, but measurement precision may be compromised
Solution Approach 1:
The Gaussian process model provides uncertainty quantification for each prediction, creating a feedback mechanism that identifies regions where prediction confidence is low. This feedback guides adaptive sampling strategies to focus measurements on critical regions or devices that will most improve overall model accuracy, maintaining precision while minimizing unnecessary measurements.
Solution Approach 2:
The sampling strategy is made dynamic rather than static. The system adaptively adjusts which devices to measure based on the evolving model uncertainty and the specific characteristics of each wafer. As measurements are taken, the model updates and the sampling priorities shift dynamically to maximize information gain at each step.
Data Source
AI summary
A computer-implemented method for inferring a device feature of a device produced on a wafer. The method includes: providing a wafer feature model associating a wafer position indicating a position of a produced device on the wafer to a device feature, wherein the wafer feature model is configured to be trained by one or more wafer feature maps and particularly configured as a Gaussian process model, providing a sample device feature of at least one device at a sample wafer position, and inferring the device feature of at least one other device of the wafer depending on the provided wafer feature model.