Lasso Model Term Selection for Lithography Error Correction
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Solution Overview
Problem
Current semiconductor manufacturing processes face challenges in accurately evaluating and correcting overlay and critical dimension errors due to non-uniform stress and misalignment issues, which are exacerbated by shrinking ground rules and aggressive processes like multiple patterning and high aspect ratio etching or deposition of exotic materials on semiconductor wafers.
Innovation Solution
A system and method for error corrections in the lithography step of semiconductor manufacturing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If automated model term selection with lasso regression is used to generate modeled corrections, then manufacturing precision is improved, but device complexity increases
Solution Approach 1:
The system performs self-service through automated model term selection using lasso regression and cross-validation. The automated selection process evaluates multiple model terms and automatically identifies the optimal subset that reduces residuals between modeled corrections and metrology measurements, eliminating manual model selection and improving manufacturing precision while managing complexity through automation
Solution Approach 2:
The system changes parameters by adjusting the regularization parameter in lasso regression and selecting from model terms of varying orders. By optimizing these parameters through cross-validation, the system achieves better manufacturing precision for overlay and critical dimension measurements while systematically managing the complexity of the modeling process
2Measurement precision
If the number of model terms is increased to reduce residuals, then measurement precision is improved, but computation time increases
Solution Approach 1:
The system applies partial action by selecting a subset of model terms from the complete set of possible terms up to maximum order. Lasso regression with optimized regularization parameter selects only the necessary model terms that contribute significantly to reducing residuals, avoiding the computation time penalty of using all possible terms while maintaining measurement precision
Solution Approach 2:
The system performs preliminary action through cross-validation to pre-determine the optimal regularization parameter and model term subset before actual measurement correction. This preliminary optimization reduces computation time during actual operation while ensuring measurement precision is maintained through pre-selected optimal model terms
Data Source
AI summary
Automated model term selection may use lasso regression for selecting model terms and a cross-validation scheme to optimize a regularization parameter of the lasso regression. A value of the regularization parameter may be selected by cross-validating the regularization parameter across a range of possible values using metrology measurements of a sample. A modeled correction may be generated based on the metrology measurements and the value of the regularization parameter using the regression. The regression may reduce a residual between the modeled correction and the metrology measurements. The model terms may include a sub-set of possible model terms up to a maximum order. Selecting the model terms from the possible model terms may prevent overfitting the modeled correction. The regularization parameter may control the number of the model terms which are selected.