Grating Rayleigh Manifold for Scatterometry Precision
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Solution Overview
Problem
Existing scatterometry techniques for semiconductor wafers often fail to maximize precision and sensitivity due to limitations in identifying optimal wavelength and incidence angle combinations, as most methods rely on conventional Rayleigh manifolds that do not account for the grating's geometric parameterization, leading to suboptimal measurement accuracy.
Innovation Solution
The introduction of a novel 'grating Rayleigh manifold' based on k-vectors computed within the grating itself, allowing for the computation of grating Rayleigh angles that optimize precision by considering the geometric parameterization of the grating structure, enabling more accurate scatterometric measurements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional Rayleigh manifolds are used for scatterometric measurement, then the measurement setup is simpler, but measurement precision and sensitivity are insufficient
Solution Approach 1:
The patent applies parameter changes by computing grating Rayleigh angles based on the actual geometric parameterization of the grating structure (including pitch, depth, and profile) rather than using conventional fixed Rayleigh manifolds. This involves calculating k-vectors within the grating and determining incidence angles that satisfy the grating Rayleigh condition, thereby optimizing measurement precision for specific grating geometries
Solution Approach 2:
The patent implements preliminary action by pre-computing the grating Rayleigh manifold and identifying optimal wavelength and incidence angle combinations before performing the actual scatterometric measurement. This preliminary characterization of the grating structure enables selection of optimal measurement parameters in advance, maximizing precision without adding complexity to the measurement process itself
2Measurement precision
If conventional Rayleigh manifolds are used, then the computational approach is simpler, but sensitivity to grating geometric parameters is reduced
Solution Approach 1:
The patent transforms the computational approach by changing from conventional Rayleigh manifold calculations to grating Rayleigh manifold calculations that incorporate grating-specific geometric parameters. This involves solving for k-vectors within the grating structure and determining incidence angles that satisfy the grating Rayleigh condition, thereby enhancing sensitivity to geometric parameters like pitch, depth, and profile
Solution Approach 2:
The patent uses computational modeling to create a virtual representation of the grating structure and its Rayleigh manifold characteristics. By copying the grating geometry into a computational model, the system can predict optimal measurement parameters without physical trial-and-error, enhancing sensitivity while managing computational complexity through efficient algorithms
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 enhances measurement precision and sensitivity by identifying regions of high parametric sensitivity within the grating Rayleigh manifold, surpassing the limitations of conventional reflection or transmission Rayleigh manifolds, leading to more accurate characterization of semiconductor wafers.
Implementation Method 1
Scatterometry refers to an optical technique that analyzes diffracted light to deduce structural details of a diffracting sample. The diffracting sample is generally a periodic structure, that is, a 'grating.'
Data Source
AI summary
The present application discloses a method for selecting an optical configuration for a high-precision scatterometric measurement. A geometric parameterization of a grating is determined, wherein the grating comprises a periodic structure. The geometric parameterization is used to generate a representative set of model structures. An eigenvalue method is utilized to compute, for each model structure, a set of solutions which satisfy a Rayleigh condition within the grating. The Raleigh condition within the grating is satisfied when a vertical component of a propagating mode within the grating is zero. Other embodiments, features and aspects are also disclosed herein.