Scatterometer Parameter Optimization via Global Cost Function
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Solution Overview
Problem
Current scatterometry measurement systems face challenges in optimizing configuration parameters such as polar angle of incidence, azimuthal angle, and numerical aperture, which affects sensitivity, precision, and measurement time, often relying on analytical methods that treat parameters independently and require trial-and-error, especially as the number of parameters increases.
Innovation Solution
A model-based method using a global optimization approach to define a cost function and establish constraints for both tool and modeling parameters, employing algorithms like Nelder-Mead or primal-dual methods to determine an optimal set of parameters that minimize the cost function, thereby configuring the scatterometry system for maximum sensitivity and precision while reducing noise and measurement time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If analytical methods are used to optimize scatterometer parameters independently, then the optimization process is simpler, but measurement precision and sensitivity are reduced
Solution Approach 1:
The patent segments the optimization process into two distinct phases: a global optimization phase that establishes feasible parameter ranges using analytical methods, and a local optimization phase that fine-tunes parameters using numerical methods. This segmentation allows the system to benefit from both the simplicity of analytical approaches and the precision of numerical optimization, resolving the contradiction between measurement precision and process complexity.
Solution Approach 2:
The patent applies preliminary action by performing global optimization first to establish feasible parameter ranges and initial estimates before conducting local optimization. This preliminary step reduces the search space for subsequent numerical optimization, improving both measurement precision while keeping the overall process manageable through structured progression.
2Productivity
If trial-and-error methods are used to determine parameter values, then the approach is easier to implement, but measurement time increases
Solution Approach 1:
The patent performs preliminary optimization calculations offline to determine optimal parameter settings before actual measurements begin. By pre-determining parameter values through global and local optimization, the system eliminates trial-and-error during production measurements, significantly reducing measurement time while maintaining ease of implementation through automated parameter selection.
Solution Approach 2:
The optimization system is self-service in that it automatically determines optimal parameter values without requiring manual trial-and-error adjustment by operators. The global and local optimization algorithms autonomously identify best parameters, reducing both measurement time and operator involvement, thereby improving productivity without sacrificing implementability.
3Measurement precision
If more parameters are optimized simultaneously, then measurement accuracy improves, but computational complexity increases
Solution Approach 1:
The patent segments parameter optimization into global optimization (handling all parameters simultaneously to establish feasible ranges) and local optimization (fine-tuning parameters within those ranges). This segmentation allows comprehensive parameter consideration for accuracy while managing computational complexity through structured two-phase optimization with different algorithmic approaches for each phase.
Solution Approach 2:
The patent employs dynamic optimization strategies by adapting the optimization approach based on the phase: global optimization uses methods suitable for exploring broad parameter spaces, while local optimization switches to more precise numerical methods within constrained ranges. This dynamic adaptation allows simultaneous optimization of multiple parameters with controlled computational complexity at each stage.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach allows for accurate calculation of measurement results by considering the interaction of all parameters, optimizing across various feature shapes and providing a tradeoff between measurement time and precision, improving the overall efficiency and accuracy of scatterometry measurements.
Implementation Method 1
Scatterometry refers to an optical technique that analyzes diffraction to deduce structural details of a diffracting sample
Implementation Method 2
The light emerging from illuminator 26 is polarized by a polarizer 28 to produce a polarized sampling beam 30
Implementation Method 3
the radiation originating from sampling beam 30 that is reflected by structure 16, passed through an analyzer 32 and to a spectroscopic ellipsometry (SE) spectrometer 34 to detect different spectral components
Data Source
AI summary
The present application discloses a method of model-based measurement of semiconductor device features using a scatterometer system. The method includes at least the following steps. A cost function is defined depending upon a plurality of variable parameters of the scatterometer system and upon a plurality of variable parameters for computer-implemented modeling to determine measurement results. Constraints are established for the plurality of variable parameters of the scatterometer system and for the plurality of variable parameters for the computer-implemented modeling. A computer-implemented optimization procedure is performed to determine an optimized global set of parameters, including both the variable parameters of the scatterometer system and the variable parameters for the computer-implemented modeling, which result in a minimal value of the cost function. Finally, the optimized global set of parameters is applied to configure the scatterometer system and the computer-implemented modeling. Other embodiments, features and aspects are also disclosed herein.