1. Limitations of Conventional Measurement

Conventional metrology and inspection tools deployed in DRAM fabs are inadequate for the intricate 3D geometry of stacked dies in HBM. Wafer-level critical dimension (CD) and thickness measurements, as well as 2D photo resist (PR) overlay inspections, frequently fail due to absence of surface patterns and limited die edge visibility. Furthermore, traditional overlay techniques cannot detect critical post-bonding defects such as die shift and tilt in stacked HBM. In HBM, precise alignment between through silicon via (TSV) core dies and front/back bumps is essential. Unlike planar wafers with fixed reference points, stacked dies exhibit positional variability, complicating accurate alignment measurement. This work presents a novel metrology methodology tailored to reliably quantify die-to-die alignment in stacked HBM assemblies.

Fig. 1. Conventional metrology and inspection tools.

2. Infrared Imaging for Non-Destructive Inspection in Semiconductor Manufacturing

Infrared (IR) optical imaging has emerged as a practical approach for non-destructive inspection in semiconductor manufacturing, particularly for applications involving silicon-based structures ^[4]. Due to silicon's partial transparency at near-infrared (NIR) wavelengths (typically longer than 1,100 nm), IR imaging enables internal observation of buried patterns (Fig. 2) ^[5], die-to-die alignment markers, and TSVs without physical cross-sectioning. This capability is especially critical for HBM packaging, where stacked die configurations require accurate assessment of die alignment, tilt, and bonding integrity beneath the top layers.

Fig. 2. Schematic diagram of an NIR confocal scanner ^[1].

In a recent study, IR-based optical systems were employed to visualize and inspect the internal structures of silicon dies through non-invasive imaging techniques, demonstrating applicability in defect detection and alignment verification in multi-layer semiconductor devices ^[6].

3. Stack Die Measurement Solution

In this study, we propose a novel metrology methodology based on recognizing silicon-transmitted patterns by leveraging the intrinsic optical properties of silicon wafers. This approach enables detection of patterns that are otherwise unobservable through conventional 2D inspection techniques. Specifically, it facilitates the recognition of internal structures within the top die of HBM by using silicon-transmitted patterns as metrology keys, rather than relying solely on traditional pattern recognition. Consequently, the method integrates both metrology and inspection characteristics, overcoming the limitations of existing single-purpose approaches. This solution employs IR optics to penetrate silicon layers and reveal the internal structures of the top die in stacked HBM. A dual-scan method is used: Scan 1 locates the fixed fiducial on the base wafer, and Scan 2 detects the top die position via pattern recognition. The positional difference between fiducial and die patterns enables accurate quantification of die shift and tilt. To overcome IR resolution limits, advanced image processing algorithms are applied, enhancing detection accuracy. In semiconductor manufacturing, metrology tools require both high resolution and throughput; the proposed method addresses these demands, ensuring reliable and efficient die alignment measurement.

Fig. 3. IR imaging enables internal observation.

1. Edge Detection

In computer vision and image processing, edge detection involves localizing significant variations in gray-level intensity and identifying the underlying physical phenomena that cause them. Such information is essential for various applications, including 3D reconstruction, motion analysis, object recognition, image enhancement and restoration, image registration, and image compression ^[7]. In this context, the concept of edge detection is introduced, and numerous filtering techniques have been explored in the literature to improve the performance of edge detection algorithms. For example, Ranjan et al. ^[8] proposed a method that combines guided image filtering with the Sobel operator, which significantly improves both accuracy and processing speed. By applying a weighted guided filter prior to edge detection, their method preserves detailed edge structures while suppressing noise. The results demonstrated superior performance compared to traditional Sobel-based approaches, particularly in images with complex textures or low contrast regions.

2. Implementation of Sobel Filters for Image Analysis

In this study, various edge detection filters---including Sobel, Laplacian, Resize, and Robert operators---were implemented and compared using custom image processing scripts. The raw images employed were selectively extracted regions of the HBM die, to which each filter was applied via Python coding. The transformed images were then analyzed to evaluate the effectiveness of each filter. The primary objective of applying these image filters was to optimize the clarity of characteristic features in IR-transmitted die patterns. As demonstrated in Fig. 4, Sobel filtering provided the most distinct visualization of active chip patterns, particularly in scans of the top die. The Sobel operator is a first-order edge detection operator widely used to calculate the gradient magnitude of an image. It emphasizes edges by measuring the rate of change in pixel intensity values. Specifically, the Sobel operator employs two 3?3 convolution kernels---one detecting horizontal changes ($G_x$) and the other detecting vertical changes ($G_y$)---defined as follows ^[9]:

The gradient magnitude $G$ at each pixel is then computed as the Euclidean norm of these components:

This calculation effectively highlights regions with significant intensity variations, corresponding to edges within the image. By applying the Sobel operator, the study was able to enhance the edge clarity in IR images, facilitating more accurate recognition of die patterns critical for stacked die alignment and inspection.

Fig. 4. Edge enhancement effect of Sobel filter on weak IR patterns.

3. Cross-correlation

Following edge enhancement, normalized cross-correlation (NCC) was applied to perform sub-pixel alignment ^[10]. Cross-correlation is an established method in semiconductor metrology that identifies the displacement between two images by locating the maximum similarity over spatial shifts. This displacement vector enables accurate correction of die shift and tilt, improving the overall repeatability of inspection. The NCC value ranges from $-1$ to $1$, with a value of $1$ indicating a perfect match. The peak location of the NCC map provides the displacement vector $(\Delta x$, $\Delta y)$, which is used to determine die shift and tilt angles. This approach is inherently robust against uniform variations in brightness and sensor noise, making it particularly suitable for infrared (IR) image environments where contrast can be low and illumination inconsistent. Marušic et al. ^[11] further improved computational efficiency by developing a segmented NCC algorithm for template matching, which demonstrated higher speed and alignment precision.

where

• $T(x, y)$ is the grayscale intensity of the template image,

• $I(x + u, y + v)$ is the target image shifted by $(u, v)$,

• $\bar{T}$ and $\overline{I_{u,v}}$ are the mean intensities of the template and the corresponding search region in the target image ^[10].