Wafer Model Selection for Lithography Process Control
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Solution Overview
Problem
Current semiconductor lithography processes face challenges in accurately monitoring and controlling process parameters such as focus and dose, which are position-dependent and time-sensitive, leading to inefficiencies in wafer patterning due to limited measurement sites and model interpolation.
Innovation Solution
A method that determines coefficients for multiple models differing in terms, approximating critical dimension values and process parameters as functions of position coordinates, and selects an updated model based on residual weights, number of terms, and order to improve process control and monitoring, using criteria like BIC and AIC, and includes Zernike or Legendre polynomials for effective interpolation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If multiple models with different terms are used to approximate critical dimension values, then manufacturing precision is improved, but device complexity increases
Solution Approach 1:
The system dynamically selects between different model types (preset model with interpolation or updated model with direct measurement) based on real-time process conditions and measurement data quality, allowing the model complexity to adapt to the specific manufacturing scenario
Solution Approach 2:
The system changes the parameter of model selection by comparing process parameter deviations and measurement data characteristics, switching between using a preset model with interpolation and using an updated model determined from actual measurements to optimize precision while managing complexity
2Device complexity
If model coefficients are determined from limited measurement sites with interpolation, then device complexity is reduced, but manufacturing precision deteriorates
Solution Approach 1:
The system creates a virtual copy of the measurement data through wafer models that can be evaluated at any position on the wafer surface, allowing full-field correction information to be generated from limited physical measurement sites without increasing measurement system complexity
Solution Approach 2:
The system transitions from discrete measurement point data to a continuous spatial model by using wafer models that represent critical dimension values as a function of position coordinates, enabling interpolation and extrapolation across the entire wafer surface
3Loss of time
If feedback loop uses low number of measurement sites, then measurement time is reduced, but manufacturing precision worsens
Solution Approach 1:
The system creates a virtual representation of the entire wafer surface through wafer models that can be evaluated at any position, allowing full-field correction values to be derived from measurements at only a few strategic locations, thus maintaining fast measurement cycles while achieving high precision
4Manufacturing precision
If process parameters are position-dependent and time-dependent, then manufacturing precision is improved, but device complexity increases
Solution Approach 1:
The wafer model serves multiple functions simultaneously: it represents critical dimension values, derives process parameter corrections, enables interpolation across the wafer surface, and adapts to different process conditions through model selection, reducing the need for separate control systems for each function
Data Source
AI summary
Critical dimension values can be obtained from wafer structures at predefined measurement sites. Coefficients of a preset model and another model with a different term are determined using critical dimension values from the measurement sites. The models approximate the critical dimension values, the process parameters and/or correction values of the process parameters as a function of at least two position coordinates. An updated model is selected from the models based on a criterion weighting the residuals between approximated critical dimension values, the number of terms of the model and/or the order or the terms of the model.