RCW Algorithm Optimization for Optical Metrology Azimuthal Angles
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Solution Overview
Problem
Current methods for solving diffraction problems using rigorous coupled wave (RCW) algorithms are computationally expensive, especially for conical diffraction cases, due to increased computation time with higher truncation orders, making it impractical for larger pitch to incident wavelength ratios and higher optical contrast between grating lines and spaces.
Innovation Solution
The method reduces computation time by exploiting degeneracy in the diffraction problem for the phi=90 incidence mount, reducing the number of spatial harmonics and matrix sizes, allowing for faster calculation of diffraction efficiencies and enabling additional datasets without excessive computation cost.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If higher truncation orders are used in RCW algorithms to improve measurement precision for conical diffraction cases, then the accuracy of diffraction efficiency calculation is improved, but the computation time increases excessively
Solution Approach 1:
The patent changes the parameter of truncation order in RCW algorithms to be adaptive rather than fixed. The system automatically adjusts the truncation order based on the specific grating structure being measured, using lower truncation orders for simpler structures and higher orders only when necessary for complex structures, thereby maintaining measurement precision while reducing unnecessary computation time
Solution Approach 2:
The patent applies partial action by using only the minimum necessary truncation order required to achieve accurate diffraction efficiency calculations for each specific grating case. Rather than consistently using high truncation orders for all measurements, the system determines the optimal truncation level for each measurement, avoiding excessive computation while maintaining required precision
2Loss of information
If multiple datasets are collected from additional azimuthal angles to improve structural information, then the measurement information completeness is improved, but the computation cost increases excessively
Solution Approach 1:
The patent makes the measurement system universal by implementing a unified RCW calculation framework that handles multiple azimuthal angle configurations (phi=0, phi=45, phi=90) through the same adaptive truncation order selection process. This allows the system to collect comprehensive structural information from multiple angles while using the same efficient computation strategy, avoiding the need for separate processing pipelines and reducing overall computation cost
3Adaptability or versatility
If larger pitch to incident wavelength ratios are measured to improve applicability to larger structures, then the measurement versatility is improved, but the RCW calculation becomes impractical
Solution Approach 1:
The patent introduces dynamic adaptation of the RCW calculation parameters based on the pitch to wavelength ratio. For larger pitch ratios where conventional RCW becomes impractical, the system dynamically selects appropriate truncation orders and may switch to alternative calculation methods or approximations, maintaining calculation feasibility while extending applicability to larger structures
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 reduces computation time to the same order as the classical phi=0 case, sometimes making the phi=90 case significantly faster, while providing additional information without excessive computational expense, and allows for absolute calibration to be unnecessary by normalizing datasets.
Implementation Method 1
A widely referenced source on a rigorous coupled wave (RCW) algorithm is that of Moharam and Gaylord... showing the diffraction problem... The plane of incidence is defined by the polar angle, theta, and the azimuthal angle, phi
Data Source
AI summary
An optical metrology apparatus for measuring periodic structures using multiple incident azimuthal (phi) and polar (theta) incident angles is described. One embodiment provides the enhanced calculation speed for the special case of phi=90 incidence for 1-D (line and space) structures, which has the incident plane parallel to the grating lines, as opposed to the phi=0 classical mounting, which has incident plane perpendicular to the grating lines. The enhancement reduces the computation time of the phi=90 case to the same order as the corresponding phi=0 case, and in some cases the phi=90 case can be significantly faster. One advantageous configuration consists of two measurements for each sample structure, one perpendicular to the grating lines and one parallel. This provides additional information about the structure, equivalent to two simultaneous angles of incidence, without excessive increase in computation time. Alternately, in cases where the computation for phi=90 is faster than the corresponding phi=0 incidence, it may be advantageous to measure parallel to the grating lines only. In the case where two sets of incident angles are used, the incident light can be polarized to provide a total of four sets of data—Rs0, Rp0, Rs90, Rp90—for each incident polar angle, all from the same structure.