Optical and X-Ray Metrology for Random Semiconductor Patterns
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Solution Overview
Problem
Current metrology methods struggle to accurately measure and model semiconductor structures with arbitrary randomness and aperiodicity in geometric and material parameters, leading to limited accuracy and applicability to complex structures.
Innovation Solution
A system and method utilizing a computer subsystem with an output acquisition subsystem to generate and analyze optical and x-ray signals, incorporating machine learning models to determine random variations in semiconductor structures, enabling accurate modeling of geometric and material parameters with arbitrary randomness.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional metrology methods are used to measure semiconductor structures with randomness, then measurement simplicity is maintained, but measurement precision deteriorates due to inability to accurately model arbitrary randomness and aperiodicity
Solution Approach 1:
The patent transforms the complex problem of measuring structures with arbitrary randomness into a parameter estimation problem. By defining a statistical model with parameters (mean, standard deviation, correlation length) that characterize the randomness, the system can estimate these parameters from measured data using optimization techniques, thereby achieving accurate measurement without requiring complex direct modeling of every random variation.
Solution Approach 2:
The patent creates a simplified statistical copy or representation of the complex random structures. Instead of directly measuring and modeling every detail of the aperiodic structures, the system uses statistical parameters to create a representative model that captures the essential characteristics of the randomness, enabling accurate measurement through parameter estimation rather than direct complex structure analysis.
2Measurement precision
If current metrology models are applied to structures with aperiodicity, then ease of operation is maintained, but measurement precision deteriorates due to limited accuracy for complex structures
Solution Approach 1:
The patent simplifies the operation by transforming the measurement problem into parameter estimation. Instead of requiring complex direct modeling of aperiodic structures, the system estimates statistical parameters (mean, standard deviation, correlation length) that characterize the aperiodicity. This approach maintains ease of operation while significantly improving measurement precision for complex structures.
Solution Approach 2:
The patent introduces statistical parameters as intermediaries between the measured signal and the underlying structure characteristics. These parameters serve as a bridge that simplifies the relationship between the complex aperiodic structures and the measurement system, enabling accurate characterization without requiring direct complex modeling.
3Measurement precision
If Debye-Waller factors are used to model randomness in x-ray diffraction, then ease of manufacture is maintained, but measurement precision deteriorates due to inability to associate DW factor values directly to complex geometry randomness values
Solution Approach 1:
The patent extends the Debye-Waller factor concept by introducing additional parameters (correlation length, geometric parameters) that directly link the diffraction signal to the physical geometry of the random structures. This transformation allows the model to associate DW factor values with specific geometric randomness characteristics, improving measurement precision while maintaining relatively simple implementation.
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
Enhances the accuracy of semiconductor metrology by effectively modeling the randomness and aperiodicity in semiconductor structures, improving simulation capabilities and measurement predictions.
Implementation Method 1
an output acquisition subsystem to generate output for one or more structures formed on a specimen
Implementation Method 2
optical and x-ray metrology methods for patterned semiconductor structures
Data Source
AI summary
Methods and systems for determining random variation in one or more structures on a specimen are provided. One method includes determining characteristic(s) of output generated by an output acquisition subsystem for structure(s) formed on a specimen and simulating the characteristic(s) of the output with initial parameter values for the structure(s). The method also includes determining parameter values of the structure(s) formed on the specimen as the initial parameter values that resulted in the simulated characteristic(s) that best match the determined characteristic(s). The determined parameter values are responsive to random variation in parameter(s) of the structure(s) on the specimen.