Ion Implantation Distribution Modeling with Unique Tail Parameters
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Solution Overview
Problem
The existing methods for modeling ion implantation distributions in semiconductor manufacturing face challenges in accurately predicting distributions under different conditions due to the lack of uniqueness in the moment parameters (γ, β) of the Pearson distribution, leading to arbitrariness and difficulties in building a reliable database for interpolation.
Innovation Solution
An information processing apparatus that uses a joined tail function to fit ion implantation distribution data, allowing for the determination of unique moment parameters by adjusting the parameters of the joined tail function to minimize errors, which are then used to generate a Pearson distribution for predicting ion implantation distributions under different conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If Pearson distribution moment parameters (γ, β) are used to model ion implantation distributions, then the distribution can be represented mathematically, but the parameters lack uniqueness leading to arbitrariness in the database
Solution Approach 1:
The patent transforms the moment parameters (γ, β) into alternative parameters (α1, α2) that have unique determination properties. By changing the parameter representation from moment parameters to tail shape parameters, the patent resolves the non-uniqueness issue while maintaining the ability to model ion implantation distributions accurately.
Solution Approach 2:
The patent introduces a joined tail function as an intermediary mathematical model that connects the Pearson distribution to uniquely determined parameters. This intermediate function serves as a bridge that allows transformation from the non-unique moment parameters to unique tail shape parameters, enabling reliable database construction.
2Measurement precision
If traditional Pearson distribution is used for ion implantation modeling, then existing distribution data can be fitted, but accurate prediction under different conditions is difficult due to parameter arbitrariness
Solution Approach 1:
By changing from moment parameters to tail shape parameters (α1, α2), the patent enables both accurate fitting of existing data and accurate prediction under different conditions. The new parameters maintain fidelity to the original distribution shape while providing unique, deterministic values for interpolation and prediction.
3Adaptability or versatility
If moment parameters are used to represent ion implantation distributions, then the Pearson distribution can be applied, but building a reliable database for interpolation becomes difficult
Solution Approach 1:
The patent changes the parameter representation to eliminate arbitrariness, making database construction straightforward. The unique tail shape parameters (α1, α2) can be directly stored and interpolated without the complexity of dealing with non-unique moment parameters, simplifying the database structure while maintaining Pearson distribution applicability.
Data Source
AI summary
An information processing apparatus includes: a receiving device receiving a distribution data series; first adjusting device adjusting first function parameter set to reduce an error, the first function parameter set specifying the position of the extreme value, and the ratio of a value at first distance on the coordinate axis from the position of the extreme value in first direction to the extreme value; second adjusting device adjusting second function parameter set to reduce an error, the second function parameter set specifying the position of the extreme value, and the ratio of a value at second distance on the coordinate axis from the position of the extreme value in second direction to the extreme value; a calculator calculating a characteristic coefficient identifying a Pearson function from a moment of a function including the first and second functions; and a distribution data calculator for calculating distribution data by a Pearson function.