1. Structured Calibration Wafer Architecture

On a 300-mm wafer, four circular regions (R1-R4) were defined for particle sizes of 150, 250, 350, and 450 nm. Using a Particle Deposition System (PDS), 1,000 ± 3% monodisperse silica spheres were uniformly deposited ^[18] per region (≈4,000 total), with inter-region spacing to avoid optical cross-talk. This structured artifact enables quantitative, repeatable tool-to-tool comparison under identical scan paths, including robust evaluation in the ultra-low-sensitivity regime (Laser Power: 0.05-1%). Fig. 1 shows the particle-size deposition map and spatial layout ^[14].

Fig. 1. Structured calibration wafer design and deposition map. Four zones on a 300-mm wafer; 1,000 particles per zone (150/250/350/450 nm) uniformly spaced.

2. Selection of Matching Control Parameters: Laser Power and TDI Gain

In this study, laser power and time delay integration (TDI) gain were selected as the key control parameters for achieving sensitivity alignment across optical inspection systems. These two variables are independent within the optical signal chain yet significantly influence defect detection sensitivity, making them ideal candidates for performance matching between tools.

Laser power controls the intensity of the illumination projected onto the wafer. If set too low, the resulting scattering signal from particles may be insufficient, leading to missed defects. Conversely, excessive laser power can cause image saturation and amplified noise, thereby increasing the false detection rate. TDI gain is a sensor amplification technique that improves the signal-to-noise ratio (SNR) by temporally integrating multiple image signals acquired during stage movement ^[16]. When optimally configured, it enhances sensitivity to subtle defects; however, if set too high, it may cause image distortion or contrast loss, ultimately degrading detection accuracy.

These two parameters exert orthogonal influence on the optical system and, when explored jointly, provide a multidimensional space in which sensitivity characteristics can be optimized. Accordingly, this study utilizes the two-dimensional parameter space of laser power and TDI gain to identify the optimal configuration for each tool, enabling precision matching across the equipment set.

3. Quantification and Visualization of Sensitivity Deviation

To quantitatively characterize the sensitivity deviation between semiconductor inspection systems and provide a structured visual representation, we introduce a residual matrix–based analysis framework. This approach evaluates the relative difference in particle detection response between each system and a reference tool under identical operating conditions, mapping the results across a two-dimensional parameter space defined by Laser Power and Time Delay Integration (TDI) Gain.

In this paper, “detection rate” denotes the proportion of planted particle sites on the PDS calibration wafer that are correctly reported by the tool for a given (Laser Power, TDI Gain) setting, using one-to-one positional matching to the deposition map; duplicate calls at a site are counted once, and off-map calls are excluded from the metric. Terminology notes. In this paper, we use “sensitivity deviation” (instead of “residual”) to mean the difference in detection rate between the test tool and the reference at the same (Laser Power, TDI Gain) operating point; values are summarized in a 5 × 5 grid and visualized as heatmaps. The experiment was conducted using 25 combinations derived from five incremental levels of Laser Power and TDI Gain. Tool–reference differences in detection rate at each (Laser Power, TDI Gain) grid point were summarized as a 5 × 5 sensitivity-deviation table and visualized as heatmaps for before/after matching. Calibration workflow (non-iterative). Each tool acquires a single 5 × 5 grid over predefined levels of Laser Power and TDI Gain. Detection rate at each grid point is computed against the PDS deposition map, producing a 5 × 5 sensitivity-deviation table. A software fine-grid search (up-sampling of the 5 × 5 surface) identifies the operating point that minimizes the absolute tool–reference deviation. The selected settings are applied once, and a single verification scan confirms alignment. To facilitate interpretation, we visualized the complete sensitivity-deviation using a heatmap, where the color gradient encodes the magnitude of residual values. As shown in Fig. 2, the heatmap presents both the pre- and post-optimization results side by side, enabling direct visual comparison of sensitivity alignment performance. This unified visualization allows intuitive evaluation of improvements across the full Laser Power–TDI Gain space.

Fig. 2. Heatmap visualization of residual matrix before and after matching.

Notably, significant reductions in deviation were observed in the ultra-low sensitivity region (Laser Power: 0.05-1%), where conventional manual calibration is often unreliable. These results demonstrate the robustness and practical effectiveness of the proposed matching framework in minimizing hardware-induced performance discrepancies across tools. To obtain a denser view of the response surface, the 5 × 5 grid was up-sampled to a finer grid by standard bilinear interpolation, and the setting with the minimum absolute tool–reference deviation was selected. A 3D visualization of the interpolated surface is shown in Fig. 3, Fleet-level dispersion was summarized by the root-mean-square error (RMSE) across tools, computed on detection-rate deviations at matched operating points ^[20].

Fig. 3. Interpolated sensitivity-surface visualization.

We summarize across-tool dispersion using the conventional root-mean-square error (RMSE): where $y_t$ is the observed detection rate (%) of tool $t$ at its matched operating point (Laser Power, TDI Gain), $\hat{y}_t$ is the target detection rate (%) given by the reference tool at the same operating point (thus constant across $t$), and $n$ is the number of non-reference tools (here $n=190$). Detection rates are expressed in percent, so residuals and RMSE are reported in percentage points (pp). RMSE is non-negative (zero only under perfect alignment); for interpretation, RMSE = 2.0 implies an average 2.0-pp difference at the matched operating point. Because errors are squared, RMSE is more sensitive to large mismatches than to small ones ^[21]. For completeness, we also computed a surface-level RMSE across the full 5 × 5 (Laser Power, TDI Gain) grid per tool; conclusions were unchanged.

1. Experimental Configuration and Implementation

To evaluate the sensitivity alignment performance of the proposed framework under actual manufacturing conditions, a structured calibration wafer was custom-fabricated using a 300 mm substrate. The wafer incorporated four distinct particle zones, each populated with 1,000 monodisperse silica particles of varying diameters: 150 nm, 250 nm, 350 nm, and 450 nm. These particle sizes were chosen to represent a realistic range of critical defect dimensions encountered in optical inspection processes. The spatial layout of the particle zones was symmetrically arranged to minimize cross-interference, and deposition uniformity was strictly controlled to ensure high repeatability and metrological consistency across tools. Tooling and deployment stages. The 191 inspection systems used in this study are Hitachi High-Tech IS4100 patterned-wafer defect inspection tools (registered in Korea as a Patterned Wafer Inspection System; a regulatory entry lists IS4100 (DI4200)), deployed in-line at after-develop inspection (ADI/PDI), after-etch inspection (AEI/PEI), and after-CMP (API) checkpoints. These stations provide high-throughput particle and pattern-defect detection on product wafers and gate hold/rework logic in real time. Hitachi’s public documentation for its patterned-wafer platforms (e.g., DI-series) describes sheet-beam optical illumination with spatial filtering for high-sensitivity detection, and its wafer-surface LS-series explicitly documents laser-based illumination, consistent with the optical pipeline used for defect/particle capture in our fleet ^[15,19]. A total of 191 optical inspection systems was subjected to evaluation. Each tool scanned the same calibration wafer using 25 distinct parameter settings defined by a 5×5 matrix of Laser Power and Time Delay Integration (TDI) Gain values. One system was designated as the reference tool, and the remaining 190 systems were compared against it. For each tool, residual matrices were constructed by calculating the deviation in particle detection rates from the reference values at corresponding parameter points. These matrices provided a structured and quantitative representation of hardware-induced sensitivity variation across the toolset. To further refine the alignment precision beyond the discrete resolution of the experimental grid, a bilinear interpolation algorithm was applied to each residual matrix. This technique enabled the generation of a continuous residual surface comprising 1,600 virtual parameter combinations per tool, thereby increasing spatial resolution within the Laser Power–TDI Gain domain. The parameter set corresponding to the minimum interpolated residual value was identified as the optimal configuration for that tool. Once optimal parameters were determined, each tool was rescanned under the new settings to validate the improvement. This closed-loop process—encompassing structured calibration, grid-based sensitivity analysis with fine-grid search, and post-adjustment verification—was fully automated and standardized across all tools. The implementation of this workflow resulted in robust, scalable, and repeatable sensitivity matching, demonstrating significant performance enhancement over traditional manual calibration methods. In particular, the framework reduced reliance on operator experience and iterative tuning, while enabling high-throughput, data-driven optimization suitable for Smart Fab environments.

After the optimal settings are applied, each tool completes a single verification scan on the same PDS wafer at the selected operating point. Acceptance is explicit: the tool is deemed “Spec in” if its PDS count matches the reference within ±5%; a ≥10% difference is “Spec out” and triggers immediate readjustment or maintenance. Intermediate gaps are re-checked by an immediate repeat verification scan to rule out transient variation. For every run, the system archives the calibration-wafer ID, recipe/firmware hashes, selected Laser Power and TDI Gain, the tool–reference deviation at the chosen point, and the verification outcome. Using a dedicated structured wafer—rather than production wafers—ensures repeatability, prevents cross-contamination of process lots, and provides a clean audit trail for PM planning and long-term drift monitoring. This single-pass verify-and-log step standardizes acceptance across the fleet and makes subsequent audits straightforward.

Fig. 4. Workflow comparison: manual calibration (iterative trial-and-error) versus proposed single-pass software-assisted matching.

Fig. 4 presents a comparative flowchart illustrating the key differences between the conventional manual calibration procedure and the automated sensitivity matching framework proposed in this study. In typical semiconductor manufacturing environments, optical inspection tools are calibrated during scheduled preventive maintenance using production wafers. This conventional approach depends heavily on manual parameter adjustments by field engineers, with calibration quality varying according to individual technical expertise rather than standardized methodology. Such variability often results in inconsistent sensitivity alignment across tools and necessitates rework—particularly in low-sensitivity regions where precise tuning is essential. Moreover, the manual calibration process is time-consuming and inefficient, often requiring over three hours per tool due to iterative scan–adjust–verify cycles. This prolonged procedure consumes significant engineering resources and reduces fab throughput. In contrast, the proposed framework is fully automated and standardized. It begins with a single scan of a PDS-based structured wafer, followed by grid-based sensitivity analysis and a fine-grid search over 1,600 parameter combinations. The optimal Laser Power and TDI Gain settings are applied automatically, and a verification scan (rescanning) of the same wafer confirms sensitivity alignment—all completed within approximately one hour per tool. By reducing calibration time and eliminating operator-induced variability, the proposed process improves metrology accuracy and establishes a scalable, reproducible methodology suitable for Smart Fab and high-volume manufacturing environments. Spec criterion. In the manual flow, “Spec in” means the tool’s PDS count matches the reference within ±5% at the selected settings; a ≥10% count gap is flagged as Spec out and triggers readjustment.

2. Improvement in Sensitivity Matching Accuracy

The deviation in detection rates among tools was significantly reduced after applying the sensitivity matching algorithm. Initially, an average deviation of ±9.86% (standard deviation: 4.12%) was observed, which was reduced to ±1.73% (standard deviation: 0.58%) after optimization. A one-sided t-test confirmed that this difference was statistically significant with $p < 0.001$. This indicates a more than fivefold improvement in matching accuracy and a substantial contribution to consistent inspection performance across tools.

Beyond the mean shift, dispersion tightens markedly: the across-tool standard deviation contracts from 4.12% to 0.58% (≈86% drop; ≈98% in variance). As Fig. 5 shows, the interquartile range shrinks, outliers largely disappear, and the effect holds across all particle sizes—strongest at low Laser Power (0.05-0.5%). In root-mean-square error (RMSE) terms (Eq. (1)), the fleet is within ±2%, stabilizing excursion thresholds and reducing decision variability, false alarms, and defect escapes.

Fig. 5. Box-plot comparison of detection-rate alignment across tools before and after matching.

Fig. 5 illustrates a comparative box plot showing the distribution of sensitivity alignment across 191 optical inspection tools, evaluated before and after the implementation of the proposed matching framework. Prior to optimization, the detection rates exhibited a broad distribution, characterized by a wide interquartile range and a number of statistical outliers—indicating significant variability in defect detection performance among tools. Following the application of the automated matching algorithm, the distribution converged markedly toward the median, with a pronounced reduction in interquartile range. This narrowing of the distribution reflects improved consistency and alignment in sensitivity responses across the entire toolset. Additionally, the substantial decrease in outlier occurrence signifies a meaningful enhancement in uniformity, even among tools that previously showed large deviations from the reference. These results visually and quantitatively demonstrate the effectiveness of the proposed framework in achieving stable and repeatable tool-to-tool calibration. Unlike conventional manual approaches—which often rely on iterative trial-and-error procedures and are prone to operator variability—this improvement was realized through a fully automated process, driven by residual matrix analysis and bilinear interpolation-based parameter optimization. The enhanced alignment contributes directly to increased measurement reliability, reduced false detection rates, and improved predictive quality control. As semiconductor manufacturing continues to push toward higher density and complexity, such consistency is critical to sustaining yield and ensuring robust defect detection across process layers. The results in Figure 5 underscore the value of adopting data-driven, algorithmic calibration methods as a core component of modern Smart Fab environments.

3. Yield Calculation Protocol and Dataset

Yield metric and aggregation. Overall production yield was computed from electrical die-sort (EDS) results as Yield = (Npass/Ntested) × 100%, aggregated at the lot level and summarized per product family. Manufacturing scope. The study covered 300-mm high-volume manufacturing for 10-nm-class second-generation DRAM (1y, a.k.a. D1y), consistent with industry nomenclature that maps “1x/1y/1z” to successive generations of 10-nm-class DRAM; here, 1y (D1y) denotes the second generation. Inspection control points included post-develop inspection (PDI/ADI), post-etch inspection (PEI/AEI), and CMP defect-control checkpoints. Observation window and population. Pre- and post-deployment windows were defined around the fleet-wide rollout of the matching framework; products and layers were selected to ensure comparable layer mix and stable fab conditions across the windows. Controls and exclusions. To isolate the matching effect, periods with mask revisions, recipe retargets, or equipment retrofits were excluded, and we verified that no concurrent changes were made to SPC guard bands; product mix and layer distribution were held comparable between the two windows. Statistics. Paired analyses were performed on lot-level yields per product × layer cell. The fleet-level improvement of +0.41 percentage points remained statistically significant ($p = 0.012$, paired t-test), with a confirmatory Wilcoxon signed-rank test showing consistent directionality. Usage frequency of matched optical tools. In production, the matched patterned-wafer optical inspectors were executed per lot at after-develop inspection (ADI/PDI) on the critical lithography layers analyzed, consistent with industry-standard high-frequency ADI sampling (every lot or every few lots). Given the standard lot size of 25 wafers, each per-lot invocation corresponds to 25 wafers scanned at that checkpoint. These in-line inspections also operate at AEI/PEI and API (post-CMP) control points as part of excursion gating; because the matched tools drive hold/rework decisions at these stations, their per-lot usage establishes a direct causal pathway from improved sensitivity alignment to the measured yield gain ^[17].

4. Improvement in Maintenance Efficiency

The proposed automatic matching algorithm yielded substantial improvements in efficiency during Preventive Maintenance (PM) operations, particularly in the context of tool calibration workflows.

After implementing automation, the average calibration time per optical inspection tool was measured at approximately 3.8 hours, accounting for multiple scan–adjust–verify cycles and manual tuning steps. Following implementation of the automated framework, this time was reduced to 2.1 hours, representing a 44.7% reduction in per-tool calibration time. This decrease was consistently observed across the 191 tools evaluated, underscoring the robustness and repeatability of the proposed method under varied tool conditions. Fig. 6 provides a visual comparison between the manual and automated calibration workflows, highlighting both the procedural differences and time savings.

Fig. 6. Comparative diagram of workflow efficiency between manual and automated matching processes.

While the manual method necessitates repeated iterative adjustments—each susceptible to human variability and misalignment—the automated approach executes sensitivity analysis, parameter optimization, and final validation in a single, continuous calibration cycle. This eliminates the trial-and-error iterations inherent in manual processes and ensures convergence to optimal settings based on quantitative residual minimization rather than subjective assessment. The data further reveal that the automated system not only reduces the time burden but also enhances the stability and standardization of PM routines. As calibration can now be completed within a fixed and predictable window (∼2.1 hours), equipment availability is improved, and production schedules can be more reliably maintained. When extrapolated to the full set of 191 tools, the total annual engineering resource savings are estimated to exceed 1,300 hours, assuming quarterly PM schedules per tool. These savings can be redirected toward higher-value engineering tasks, contributing to both human resource efficiency and process innovation. Additionally, by minimizing operator involvement and increasing process reproducibility, the proposed method strengthens equipment history tracking, improves the fidelity of sensitivity alignment records, and facilitates predictive maintenance planning. This operational advancement aligns well with the goals of Smart Fab initiatives, where automation, data integrity, and resource optimization are critical performance indicators.

5. Yield Improvement and Process Stability Assessment

An analysis of actual production yield before and after applying the matching system showed an improvement from 92.43% to 92.84%, a gain of approximately 0.41 percentage points. A paired-sample t-test confirmed statistical significance ($p = 0.012$). Notably, process layers requiring high-resolution sensitivity (e.g., Layers 7-9) saw improvements of up to 0.63 percentage points, attributed to more accurate defect detection and reduced false positives. Additionally, sensitivity alignment across tools was compared based on Laser Power settings. The results showed significant improvements, particularly under low Laser Power conditions (0.05-0.5%), after applying the automated matching system. This suggests that the proposed method enables reliable sensitivity alignment even in regions where traditional calibration methods struggle. Such improvements are especially valuable in advanced process nodes, where tight control of inspection performance directly affects device reliability and production yield.

Fig. 7. Detection-sensitivity alignment comparison by laser-power setting (before vs. after optimization).

Fig. 7 quantitatively compares detection sensitivity alignment across various Laser Power conditions (0.05%, 0.1%, 0.5%, 1.0%). Tools optimized via the proposed method consistently outperformed those using traditional calibration, particularly in low-sensitivity regions. This demonstrates the effectiveness of the interpolation-based matching algorithm in maintaining robust sensitivity alignment under challenging conditions. The reduced variance and improved convergence in detection rates further validate the algorithm’s ability to ensure consistent inspection performance across all tools.

6. Summary of Key Results

The proposed automatic matching framework addresses the sensitivity alignment challenge in semiconductor optical inspection systems through a combination of structured calibration wafers, residual matrix analysis, and interpolation-based optimization. Large-scale validation across 191 tools confirmed its effectiveness across multiple quality metrics, including alignment accuracy, maintenance efficiency, and production yield. Matching deviations were reduced from ±10% to within ±2%, PM time was cut by 45%, and overall yield improved by more than 0.4 percentage points. These results indicate that the framework is more than a technical enhancement; it represents a new paradigm for quantitative defect sensitivity control. Furthermore, all procedures are fully automated and operator-independent, ensuring high repeatability and reproducibility. As a core technology for Smart Fab realization, this framework offers strong industrial scalability. It is expected to be expanded to other in-line inspection systems, such as CD-SEM, E-Beam inspection, and overlay metrology, evolving into an integrated alignment solution that ensures quality uniformity across diverse semiconductor tools.