Piecewise Substrate Profile Fitting for Semiconductor Process Learning
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Solution Overview
Problem
Conventional methods for describing substrate profiles in semiconductor manufacturing are inefficient, as pointwise representations are difficult to analyze and fail to accurately represent all portions of the profile, making it challenging to isolate physical effects and generate target profiles with correlated, non-linear target values.
Innovation Solution
A method involving a processing device that separates substrate measurement data into regions and fits each region with a piecewise functional fit using functions from a library, enforcing continuity and smoothness constraints to generate a complete and accurate description of the profile with fewer parameters, allowing for easier correlation of input changes to geometry.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If pointwise representations are used to describe substrate profiles, then measurement data can be collected, but the data becomes difficult to analyze and fails to accurately represent all portions of the profile
Solution Approach 1:
The substrate profile is divided into multiple distinct regions (e.g., topography regions, curvature regions) rather than treating it as a continuous pointwise dataset. Each region is independently characterized by fitting appropriate mathematical functions to segments of the profile data, enabling targeted analysis of specific geometric features while simplifying overall data interpretation.
Solution Approach 2:
The representation method transitions from raw coordinate pairs (x, y) to region-specific fitted function parameters (e.g., polynomial coefficients, curvature values). This parameter transformation condenses large datasets into meaningful geometric descriptors that are easier to analyze while preserving essential profile characteristics.
2Manufacturing precision
If conventional single-function fitting is applied to entire profiles, then the process is simple, but it fails to accurately capture varying geometric characteristics across different regions
Solution Approach 1:
The profile fitting process is segmented into multiple independent fitting operations, each applied to a specific region identified by its geometric characteristics. This allows different mathematical functions to be optimized for different regions (e.g., linear for flat areas, polynomial for curved areas) rather than forcing a single function type across the entire profile.
Solution Approach 2:
Each region of the substrate profile is assigned a locally optimized fitting function based on its specific geometric properties. The fitting approach adapts to local characteristics such as curvature, slope, and topography type, ensuring high accuracy in representing each region's unique features rather than using a uniform fitting method throughout.
3Loss of information
If detailed measurements of all profile points are taken, then complete data is obtained, but correlating input changes to geometry becomes difficult with non-linear target values
Solution Approach 1:
The complete profile information is transformed from raw measurement points to region-specific fitted function parameters. This parameter reduction maintains all essential geometric information while expressing it in a form that is linearly related to process inputs, enabling straightforward correlation analysis between manufacturing parameters and profile characteristics.
Data Source
AI summary
A method includes receiving, by a processing device, data indicative of a plurality of measurements of a profile of a substrate. The method further includes separating the data into a plurality of sets of data, a first set of the plurality of sets associated with a first region of the profile, and a second set of the plurality of sets associated with a second region of the profile. The method further includes fitting data of the first set to a first function to generate a first fit function. The first function is selected from a library of functions. The method further includes fitting data of the second set to a second function to generate a second fit function. The method further includes generating a piecewise functional fit of the profile of the substrate. The piecewise functional fit includes the first fit function and the second fit function.