Constrained Voxel Model for Tomographic Semiconductor Metrology
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Solution Overview
Problem
Current tomographic techniques in semiconductor metrology face challenges due to underdetermined optimization problems, leading to inaccurate reconstructions and convergence issues, especially with increasingly complex structures and small resolution requirements, as generic regularization methods often result in local minima or lack sufficient detail.
Innovation Solution
The implementation of data-driven regularization based on a constrained voxel model that captures known process variations, using simplified geometric or process models, reduces the number of independent variables and enables more accurate reconstructions with fewer measured angles and reduced computational effort, by synthesizing a constrained voxel model from measurement data and updating voxel model values based on differences between measured and simulated images.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If generic regularization is employed in tomographic optimization, then the optimization process can proceed, but it leads to convergence in local minima and incorrect reconstruction
Solution Approach 1:
The patent transforms the regularization approach by changing from generic parameter-based regularization to data-driven constraints that incorporate process knowledge. The constrained voxel model uses parameters derived from actual manufacturing processes (such as known material properties, geometric constraints from fabrication steps) to guide the optimization, thereby achieving both convergence reliability and measurement precision simultaneously
Solution Approach 2:
The patent introduces a constrained voxel model as an intermediary between the raw measurement data and the final reconstruction. This intermediary incorporates process knowledge and physical constraints to mediate the optimization process, preventing convergence to incorrect local minima while maintaining accuracy in the final measurement results
2Measurement precision
If a voxel model with one million or more voxels is used to provide sufficient resolution, then measurement detail is improved, but the optimization problem becomes mathematically underdetermined
Solution Approach 1:
The patent changes the parameter representation by constraining the voxel model based on process knowledge. Instead of treating each voxel value as an independent parameter, the constrained model reduces the effective number of parameters by incorporating relationships between voxels that are known from manufacturing processes, thereby maintaining high resolution while making the optimization problem solvable
Solution Approach 2:
The patent segments the optimization problem by dividing it into two stages: first establishing a constrained voxel model with reduced degrees of freedom based on process knowledge, then using this constrained model to guide the full-resolution reconstruction. This segmentation prevents the optimization from becoming underdetermined while preserving measurement detail
3Stability of the object's composition
If generic regularization terms are applied strongly, then optimization stability is improved, but measurement results lack sufficient detail
Solution Approach 1:
The patent applies local quality by using data-driven constraints that are specific to different regions of the structure based on process knowledge. Instead of applying uniform strong regularization across all voxels, the constrained voxel model applies appropriate constraints locally where process information is available, maintaining stability only where needed while preserving detail in other regions
4Measurement precision
If conventional tomographic techniques are used with increasingly small resolution requirements, then measurement capability is maintained, but convergence issues and local minima become more frequent
Solution Approach 1:
The patent performs preliminary action by establishing the constrained voxel model before the main optimization process. This preliminary step incorporates process knowledge and physical constraints into the model structure, preparing the optimization to converge reliably even at small resolutions by preventing it from starting in regions that would lead to local minima
Data Source
AI summary
Methods and systems for improved regularization associated with tomographically resolved image based measurements of semiconductor structures are presented herein. The regularizations described herein are based on measurement data and parameterization of a constrained voxel model that captures known process variations. The constrained voxel model is determined based on simplified geometric models, process models, or both, characterizing the structure under measurement. A constrained voxel model has dramatically fewer degrees of freedom compared to an unconstrained voxel model. The value associated with each voxel of the constrained voxel model depends on a relatively small number of independent variables. Selection of the independent variables is informed by knowledge of the structure and the underlying fabrication process. Regularization based on a constrained voxel model enables faster convergence and a more accurate reconstruction of the measured structure with less computational effort. This enables semiconductor measurements with reduced data acquisition requirements, and reduced measurement time.