Optical Critical Dimension Measurement Using Linear Parameter Transformation
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Solution Overview
Problem
Conventional methods for measuring the critical dimension of three-dimensional structures in semiconductor devices are inaccurate and inefficient, especially at the nano scale, due to sensitivity to objective function characteristics and high correlation between parameters, leading to incorrect parameter vector estimation.
Innovation Solution
A method involving linear transformation and filtering of candidate parameter vectors using matrix information on hypothesized parameter distributions, combined with heuristic algorithms, to accurately and quickly estimate the critical dimension by minimizing differences between measurement and numerical simulation spectra.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional optical critical dimension measuring method is used to estimate parameter vector through nonlinear parameter estimation, then throughput is improved compared to SEM method, but measurement precision deteriorates due to sensitivity to objective function characteristics and high parameter correlation
Solution Approach 1:
The patent applies preliminary action by performing linear transformation on candidate parameter vectors before evaluating them against the objective function. The transformation uses pre-calculated transformation matrices that are determined based on the specific three-dimensional structure being measured. This preliminary transformation repositions candidate vectors in a transformed parameter space where the objective function landscape is more favorable, reducing sensitivity to objective function characteristics and improving estimation accuracy while maintaining the efficiency of the optical measurement approach
Solution Approach 2:
The patent changes parameters by transforming the candidate parameter vectors from the original parameter space to a transformed parameter space using linear transformation matrices. This parameter transformation modifies the search landscape for the nonlinear parameter estimation, making the objective function less sensitive to variations and reducing the impact of high parameter correlations. The transformation matrices are specifically tailored to the three-dimensional structure being measured, optimizing the estimation process for each case
2Quantity of substance
If conventional numerical simulator is used to estimate parameter vector for nano scale semiconductor devices, then device integration density is increased, but measurement precision deteriorates due to difficulty and inaccuracy in estimating parameter vector
Solution Approach 1:
For nano scale devices with high integration density, the patent applies preliminary linear transformation to candidate parameter vectors before nonlinear parameter estimation. The transformation matrices are determined based on the specific nano scale three-dimensional structure characteristics. This preliminary action repositions the search in parameter space to account for the challenging measurement conditions at nano scale, improving estimation accuracy while enabling the measurement of highly integrated circuits
Solution Approach 2:
The patent transforms parameters by applying linear transformation to candidate parameter vectors, changing the search landscape for parameter estimation. This parameter change adapts the estimation process to nano scale dimensions and high integration density conditions, making the objective function evaluation more reliable and accurate for small scale devices where conventional methods fail
3Measurement precision
If gradient vector estimation or Hessian matrix estimation is performed on each candidate solution to reduce estimation error, then measurement precision is improved, but device complexity and calculation time increase
Solution Approach 1:
The patent applies preliminary linear transformation to candidate parameter vectors before evaluating them with the objective function. This preliminary action improves estimation accuracy by repositioning candidates in a transformed space where the objective function is less sensitive to estimation errors. Importantly, this approach achieves improved precision without requiring additional gradient vector or Hessian matrix calculations, thus avoiding the increase in calculation complexity that would result from such operations
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 enables accurate and rapid calculation of parameter vectors that model measurement spectra, improving precision and efficiency in critical dimension estimation, even for high aspect ratio structures with strong parameter correlations.
Implementation Method 1
obtaining a measurement spectrum for each wavelength of light reflected from the three-dimensional structure
Data Source
AI summary
A method of measuring a critical dimension comprises determining matrix information on a hypothesized parameter distribution on the critical dimension; obtaining a measurement spectrum for each wavelength of a light reflected from the three-dimensional structure; sampling a first candidate parameter vector for determining a numerical simulation spectrum that approximates the measurement spectrum; linearly transforming the first candidate parameter vector by using the matrix information; determining a first candidate parameter which minimizes a difference between the measurement spectrum and the numerical simulation spectrum within the linearly transformed first candidate parameter vector; determining a second candidate parameter vector derived from the first candidate parameter and having the hypothesized parameter distribution by using a heuristic algorithm; determining a second candidate parameter that minimizes a difference between the measurement spectrum and the numerical simulation spectrum within the second candidate parameter vector; and updating the first candidate parameter by using the second candidate parameter.