Gaussian Process Wafer Map Generation
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Solution Overview
Problem
Conventional methods for generating wafer maps in semiconductor manufacturing are time-consuming due to the need for extensive measurements, which slows down the manufacturing process and limits the ability to quickly identify post-step errors or non-uniformities.
Innovation Solution
The use of a squared exponential Gaussian process model to generate and present a map of a semiconductor wafer's attributes by calculating non-measured data points based on model parameters and correlation models, reducing the need for extensive measurements and improving data interpolation accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional measurement methods (atomic force microscope, scanning electron microscope) are used to map substrate attributes, then measurement precision is improved, but measurement time increases significantly
Solution Approach 1:
The patent creates a computational model (copy) of the substrate attribute distribution based on limited measured data points. This model serves as a virtual replica that can be processed and analyzed without requiring exhaustive physical measurements across the entire substrate surface, thereby reducing measurement time while maintaining precision through the accuracy of the computational model.
Solution Approach 2:
The patent replaces time-consuming mechanical measurement processes (atomic force microscopy, scanning electron microscopy) with computational methods. By using iterative calculations and optimization algorithms on a computer system, the patent substitutes physical measurement mechanisms with mathematical models that can rapidly generate comprehensive substrate maps from sparse data points.
2Loss of time
If a limited set of data points is used for wafer mapping, then measurement time is reduced, but manufacturing precision deteriorates due to insufficient data coverage
Solution Approach 1:
The patent introduces an iterative computational model as an intermediary between limited measured data points and the complete substrate attribute map. This intermediary process fills in the gaps between sparse measurements by calculating non-measured attribute data points through iterative optimization, thereby achieving high-precision mapping without requiring dense measurement sampling.
Solution Approach 2:
The patent transforms the problem from directly measuring all substrate points to measuring a subset and computationally deriving the rest. By changing the approach from exhaustive physical measurement to selective measurement combined with computational inference, the patent maintains manufacturing precision while reducing measurement cycle time.
3Manufacturing precision
If exhaustive measurements are performed across the entire substrate, then manufacturing precision is improved, but productivity decreases due to extended cycle time
Solution Approach 1:
The patent extracts only the essential measured data points needed to create an accurate computational model, rather than performing exhaustive measurements. By taking out just the necessary measurements and using iterative calculations to derive the remaining information, the patent achieves high manufacturing precision while maintaining fast productivity.
4Ease of operation
If conventional spline interpolation is used to estimate values between measured points, then ease of operation is improved, but measurement precision deteriorates due to radial approximation errors
Solution Approach 1:
The patent replaces static spline interpolation with dynamic iterative optimization. Instead of using fixed radial approximation methods, the system continuously refines the estimated values by iteratively calculating non-measured attribute data points based on the measured data and optimization criteria, thereby improving measurement precision while maintaining computational tractability.
Data Source
AI summary
Described herein are technologies to facilitate the generation and presentation of a map of an attribute of a substrate, such as a semiconductor wafer. Using the data of measured attribute (e.g., thickness, temperature, etc.) of a substrate, one or more of the described implementations generate data of non-measured (i.e., calculated) attributes to complete a map of the substrate using model parameters and a correlations model, such as a squared exponential Gaussian process model.