Library-Based OCD (Optical Critical Dimension)

Keywords: library-based ocd, metrology

Library-Based OCD (Optical Critical Dimension) metrology is a technique that matches measured optical spectra to pre-calculated theoretical spectra libraries — enabling fast, accurate measurement of multiple structure parameters simultaneously by comparing experimental diffraction patterns against simulated reference database, the standard approach for inline semiconductor process control.

What Is Library-Based OCD?

• Definition: Optical metrology using pre-computed spectral libraries for parameter extraction.
• Method: Match measured spectrum to best-fit library entry.
• Output: Multiple parameters (CD, height, sidewall angle) from single measurement.
• Speed: Fast measurement via library lookup vs. real-time fitting.

Why Library-Based OCD Matters

• Inline Capability: Fast enough for production monitoring (seconds per site).
• Multi-Parameter: Measures CD, height, sidewall angle simultaneously.
• Non-Destructive: Optical measurement preserves wafer.
• High Throughput: Enables 100% wafer sampling if needed.
• Cost Effective: Lower cost per measurement than electron microscopy.

How It Works

Step 1: Build Parametric Model:

• Structure Definition: Define geometry (trapezoid, rectangle, complex shapes).
• Parameters: CD (critical dimension), height, sidewall angle, material properties.
• Parameter Ranges: Define min/max values for each parameter.
• Material Stack: Specify all layers and optical properties.

Step 2: Generate Spectral Library:

• Simulation: Use RCWA (Rigorous Coupled-Wave Analysis) to compute spectra.
• Parameter Space: Calculate spectra for combinations of parameter values.
• Grid Sampling: Typically 5-10 points per parameter dimension.
• Computation Time: Hours to days depending on complexity.
• One-Time Cost: Library generated once per structure type.

Step 3: Measure Sample Spectrum:

• Illumination: Broadband light at specific angle(s).
• Detection: Measure reflected/diffracted spectrum.
• Wavelength Range: Typically 200-1000nm.
• Polarization: Multiple polarizations for more information.
• Measurement Time: 1-5 seconds per site.

Step 4: Library Matching:

• Search: Find library entry with best spectral match.
• Metric: Minimize χ² or other goodness-of-fit measure.
• Interpolation: Interpolate between library points for precision.
• Output: Best-fit parameter values.
• Speed: Milliseconds for library lookup.

Advantages

Speed:

• Library Lookup: Much faster than real-time regression.
• Throughput: Enables high-sampling density.
• Inline Use: Fast enough for production monitoring.

Multi-Parameter Measurement:

• Simultaneous: All parameters from single measurement.
• Correlation: Captures parameter correlations.
• Efficiency: No need for multiple metrology tools.

Robustness:

• Pre-Validated: Library entries are pre-computed and validated.
• Convergence: No optimization convergence issues.
• Repeatability: Consistent results, no fitting variability.

Limitations

Model Accuracy:

• Assumption: Model must accurately represent real structure.
• Simplifications: Real structures more complex than models.
• Impact: Model errors propagate to measurements.
• Mitigation: Validate with reference metrology (SEM, TEM, AFM).

Library Coverage:

• Parameter Space: Library must cover actual parameter range.
• Out-of-Range: Extrapolation unreliable if parameters outside library.
• Grid Density: Trade-off between accuracy and library size.
• Solution: Adaptive libraries, expand as needed.

Interpolation Accuracy:

• Between Points: Must interpolate between library grid points.
• Nonlinearity: Spectral response may be nonlinear.
• Error: Interpolation introduces uncertainty.
• Mitigation: Denser grids in sensitive regions.

Computational Cost:

• Library Generation: Days of computation for complex structures.
• Storage: Large libraries require significant storage.
• Updates: New library needed for process changes.
• Solution: Efficient simulation, library compression.

Alternative: Real-Time Regression

Method:

• On-the-Fly: Optimize parameters to fit measured spectrum in real-time.
• No Library: No pre-computation required.
• Flexibility: Handles any parameter combination.

Trade-Offs:

• Slower: Minutes per measurement vs. seconds for library.
• Convergence: May fail to converge or find local minima.
• Flexibility: Better for R&D, process development.
• Use Case: When library impractical or parameters unknown.

Applications

Lithography Process Control:

• After Develop: Measure resist CD, height, profile.
• Feedback: Adjust exposure, focus based on measurements.
• Sampling: Multiple sites per wafer, every wafer.

Etch Process Control:

• After Etch: Measure final feature dimensions.
• Endpoint: Verify etch depth, profile.
• Uniformity: Map CD and height across wafer.

CMP Monitoring:

• Remaining Thickness: Measure film thickness after polish.
• Uniformity: Ensure uniform removal across wafer.
• Endpoint: Verify target thickness achieved.

Advanced Patterning:

• Multi-Patterning: Measure each patterning step.
• Overlay: Combined with overlay metrology.
• 3D Structures: FinFETs, GAA, complex 3D geometries.

Library Optimization

Adaptive Sampling:

• Dense Sampling: More points in sensitive parameter regions.
• Sparse Sampling: Fewer points where response is smooth.
• Benefit: Smaller library with maintained accuracy.

Dimensionality Reduction:

• PCA: Principal component analysis of parameter space.
• Sensitivity: Focus on parameters with high spectral sensitivity.
• Benefit: Reduce library size, faster generation.

Incremental Updates:

• Add Points: Expand library as new parameter ranges encountered.
• Refinement: Add points where interpolation error high.
• Benefit: Start with coarse library, refine over time.

Validation & Calibration

Reference Metrology:

• CD-SEM: Validate CD measurements.
• AFM: Validate height and sidewall angle.
• TEM: Cross-section for complex 3D structures.
• Correlation: Establish correlation between OCD and reference.

Model Validation:

• Goodness of Fit: Check χ² values for library matches.
• Residuals: Analyze spectral residuals for systematic errors.
• Outliers: Identify measurements with poor fits.

Periodic Recalibration:

• Drift: Optical properties may drift over time.
• Process Changes: Update library for process modifications.
• Frequency: Quarterly or after significant process changes.

Tools & Vendors

• KLA-Tencor: SpectraShape, SpectraCD OCD systems.
• Nova Measuring Instruments: Integrated metrology solutions.
• Nanometrics (Onto Innovation): Atlas OCD systems.
• ASML: Integrated metrology in lithography scanners.

Library-Based OCD is the workhorse of semiconductor metrology — by pre-computing spectral libraries, it enables fast, accurate, multi-parameter measurements that make inline process control practical, providing the measurement speed and throughput required for high-volume manufacturing at advanced nodes.

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