Nondestructive monitoring of annealing and chemical-mechanical planarization behavior using ellipsometry and deep learning

Three-dimensional integrated circuits using through-silicon vias (TSVs) enable high-density interconnects and reduced interconnect length but suffer reliability issues such as residual stress, protrusion, cracking, delamination, and Cu leakage, largely due to thermal expansion mismatch between Cu and Si. CMP and annealing, critical steps in TSV fabrication, can induce protrusion and dishing of the Cu fill, degrading bonding strength and electrical/thermal performance. Conventional defect characterization methods are destructive and slow, limiting in-line, real-time process control. The research addresses the challenge of nondestructive, rapid, and nanoscale-sensitive monitoring of TSV-Cu topography in the z-direction across microscale feature dimensions. The study proposes using Mueller matrix spectroscopic ellipsometry combined with deep learning to classify defects and quantify Cu surface height variations with nanometer accuracy, enabling better control of CMP and annealing windows for reliable 3D stacking.

Prior work has examined TSV process-induced issues including Cu protrusion after annealing and CMP-induced dishing, as well as broader reliability problems such as warpage, delamination, and cracking due to coefficient of thermal expansion mismatch. Studies highlight the need to control CMP rate, annealing time, and temperature to avoid leaks, shorts, and weak bonding. However, existing characterization approaches are largely destructive and unsuitable for rapid, in-line monitoring, and there remains a gap in nondestructively quantifying z-direction Cu height variations at nanometer precision within microscale TSV geometries. This motivates the development of optical polarization-based metrology enhanced by modeling and machine learning.

An ellipsometry-based approach was developed to characterize TSV-Cu structures. An optical model reflecting a typical TSV stack was constructed: 20 nm Ta barrier, 200 nm SiO2 insulator, Si substrate, and Cu-filled vias of 3 µm diameter and 8 µm depth with 6 µm pitch. The incident angle was fixed at 45°, with wavelengths from 400 to 1000 nm. Rigorous coupled-wave analysis (RCWA) computed reflected fields for varying Cu top surface heights Hu (z-direction). From these, 4×4 Mueller matrix elements (MMEs) were calculated and normalized by m11. Off-diagonal elements were near zero due to isotropy. Sensitivity analysis identified seven effective MMEs (m12, m21, m22, m33, m34, m43, m44) with strong dependence on Hu in specific wavelength bands. Defect taxonomy was defined relative to the Si surface plane (0 nm): protrusion (defect-P) when Hu > 0 nm or < 4 nm (context-dependent definition around the process window), defect-free when Hu in 4–16 nm, and overdishing (defect-OD) when Hu > 16 nm. For classification, datasets were generated using effective MMEs over structures representing defect-free (Hu = 4–16 nm, 1 nm steps), defect-OD (Hu = 17–29 nm, 1 nm steps), and defect-P (Hu = 3–9 nm, 1 nm steps), with 300 noisy samples per structure (e.g., 10% random noise) to emulate measurement variability. A single-channel deep learning classifier (one MME as input) was trained and evaluated across MMEs. Lu–Chipman polar decomposition was used to interpret sensitivity, linking diattenuation D ≈ m12. For quantitative sizing, a multichannel artificial neural network used seven MMEs as independent input channels to regress or classify Hu at 1 nm resolution. Training labels spanned Hu from −30 to 30 nm in 1 nm increments (61 labels). Robustness was assessed under varying random noise levels (10–30%), TSV aspect ratios (0.5–10 with 3 µm diameter), top–bottom diameter differences ΔTop–Bottom (2.0 to 0 µm at aspect ratio 1), and azimuthal incidence angles (0°–180°). t-SNE visualizations assessed class/size separability. Complementary experiments measured Cu grain size evolution via EBSD at different annealing temperatures and times to relate processing to Hu sensitivity and to define practical quantization needs.

- Single-channel classification using individual MMEs accurately distinguished defect types: m12 (99.53%), m21 (99.75%), m22 (98.69%), m33 (99.80%), m34 (99.94%), m43 (99.77%), m44 (99.66%). m12 also reached 99.80% validation accuracy by epoch 7 with cross-entropy loss 0.00043. - Multichannel deep learning with seven MMEs enabled quantitative discrimination of Hu with 1 nm resolution. Under 30% random noise, test accuracy reached 98.92%, and accuracy decreased by only ~1.01% when noise increased from 10% to 30%. - Robustness to TSV morphology and measurement variations was demonstrated: changes in aspect ratio (0.5–10), ΔTop–Bottom (2.0–0 µm), and azimuth (0°–180°) altered test accuracies by no more than ~1%, with training converging (cross-entropy → 0, validation accuracy → 1). - EBSD showed annealing-driven Cu grain growth; at 250 °C, average grain size increased by ~60 nm from 9 h to 40 h, underscoring the need to control annealing to manage Hu and indicating the metrology must resolve ~1.2 nm or better within a 12 nm process window. - t-SNE visualizations confirmed clear separability among defect classes and among 1 nm Hu increments when using multichannel inputs.

The proposed ellipsometry-plus-deep-learning framework directly addresses the need for nondestructive, rapid, and nanoscale-sensitive monitoring of TSV-Cu vertical topography caused by CMP and annealing. By leveraging RCWA-modeled Mueller matrices, the approach detects polarization signatures sensitive to subtle Hu variations, enabling reliable classification of protrusion, defect-free, and overdishing conditions with >99% accuracy using even a single MME. Extending to multichannel inputs improves robustness and precision, achieving 1 nm quantization accuracy and maintaining high performance under substantial random noise and across variations in TSV aspect ratio, sidewall taper (ΔTop–Bottom), and incident azimuth. These results demonstrate suitability for in-line monitoring and process control of CMP and annealing to maintain the Hu process window, thereby mitigating risks of cracks, voids, poor bonding, and degraded electrical/thermal performance. The observed dependence of Hu on annealing temperature/time via grain growth further emphasizes the importance of such metrology to optimize thermal budgets and CMP endpoints for reliable 3D integration.

The study introduces a fast, nondestructive metrology for TSV-Cu using Mueller matrix spectroscopic ellipsometry combined with deep learning. A single effective MME enables defect-type classification with accuracies exceeding 99%, while a multichannel approach using seven MMEs quantifies Cu top-surface height Hu with 1 nm resolution. The method remains highly accurate (98.92%) even under 30% random noise and is robust to TSV geometry and measurement condition variations. These capabilities support improved monitoring and control of CMP and annealing to enhance reliability in high-density 3D integration. Future work could extend to experimental validation across diverse TSV designs and process lines, integrate real-time hardware for in-situ monitoring, and explore domain adaptation to bridge simulation-to-measurement gaps.