Deep Clustering based Boundary-Decoder Net for Inter and Intra Layer Stress Prediction of Heterogeneous Integrated IC Chip

Kart Leong Lim; Ji Lin

cs.LGFeb 25, 2026

Deep Clustering based Boundary-Decoder Net for Inter and Intra Layer Stress Prediction of Heterogeneous Integrated IC Chip

Authors: Kart Leong Lim, Ji Lin

Organizations: Institute of Microelectronics (IME), Agency for Science, Technology and Research (A*STAR), 2 Fusionopolis Way, Innovis #08-02, Singapore 138634, Republic of Singapore

Abstract

High stress occurs when 3D heterogeneous IC packages are subjected to thermal cycling at extreme temperatures. Stress mainly occurs at the interface between different materials. We investigate stress image using latent space representation which is based on using deep generative model (DGM). However, most DGM approaches are unsupervised, meaning they resort to image pairing (input and output) to train DGM. Instead, we rely on a recent boundary-decoder (BD) net, which uses boundary condition and image pairing for stress modeling. The boundary net maps material parameters to the latent space co-shared by its image counterpart. Because such a setup is dimensionally wise ill-posed, we further couple BD net with deep clustering. To access the performance of our proposed method, we simulate an IC chip dataset comprising of 1825 stress images. We compare our new approach using variants of BD net as well as a baseline approach. We show that our approach is able to outperform all the comparison in terms of train and test error reduction.

Figures & tables

Figure 1: Two dies IC package geometric representation

Figure 2: 3D representation of stress prediction, using $D_{1...Z,\;1...V}$ where $Z=3$ layers and $V=L^{P}$ cases.

Parameters (P)		Levels (L)
EMC Modulus [GPa]	5~30	5, 11, 17, 23, 30
EMC CTE [ppm/C]	5~20	5, 9, 12, 16, 20
Die Size [mm]	0.5~1.8	0.5, 0.8, 1.2, 1.5, 1.8
Gap between dies [mm]	0.2~1	0.2, 0.4, 0.6, 0.8, 1.0

Table I: DOE for each case using factorial design.

Figure 3: Stress images corresponding to different parameters (column) and at different layers (row).

Figure 4: Min and max range for RDL (top row), UF (middle), Overmold (bottom)

Figure 5: Architecture of Boundary Decoder net

Panel of Figure 6 — Figure 6: Scatter points and regression lines for 1500 train samples.

	train error	test error	train time
AE+KNN(baseline)	-	0.1589 $\pm$ 0.0186	30~40s
BD (proposed)	0.1424 $\pm$ 0.0069	0.1437 $\pm$ 0.0014	8~25s
AE+BD (proposed)	0.1416 $\pm$ 0.0031	0.1409 $\pm$ 0.0074	25~50s
DC+BD (proposed)	0.1441 $\pm$ 0.0056	0.1309 $\pm$ 0.0019	400~600s

Table II: Comparison of Boundary-Decoder (BD) variants vs baseline

Panel of Figure 8 — Figure 8: Large die size for overmold layer

Panel of Figure 11 — Figure 11: Small die size for overmold layer

Neural Surrogate Modeling

Neural surrogate modeling uses learned models to approximate costly simulations, enabling faster prediction, design, control, and inference.

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A Hybrid Conditional Diffusion-DeepONet Framework for High-Fidelity Stress Prediction in Hyperelastic Materials

Purna Vindhya Kota, Meer Mehran Rashid, Somdatta Goswami, Lori Graham-Brady

Department of Civil and Systems Engineering, Johns Hopkins University, 3400 N. Charles Street, Baltimore, 21218, MD, USA

Neural Surrogate Modeling Hyperelasticity Deep Operator Networks Conditional Diffusion Models

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Predicting stress fields in hyperelastic materials with complex microstructures remains challenging for traditional deep learning surrogates, which struggle to capture both sharp stress concentrations and the wide dynamic range of stress magnitudes. Convolutional architectures such as UNet tend to oversmooth high-frequency gradients, while neural operators like DeepONet exhibit spectral bias and underpredict localized extremes. Diffusion models can recover fine-scale structure but often introduce low-frequency amplitude drift, degrading physical scaling. To address these limitations, we propose a hybrid surrogate framework, cDDPM-DeepONet, that decouples stress morphology from magnitude. A conditional denoising diffusion probabilistic model (cDDPM), built on a UNet backbone, generates normalized von Mises stress fields conditioned on geometry and loading. In parallel, a modified DeepONet predicts global scaling parameters (minimum and maximum stress), enabling reconstruction of full-resolution physical stress maps. This separation allows the diffusion model to focus on spatial structure while the operator network corrects global amplitude, mitigating spectral and scaling biases. We evaluate the framework on nonlinear hyperelastic datasets with single and multiple polygonal voids. The proposed model consistently outperforms UNet, DeepONet, and standalone cDDPM baselines by one to two orders of magnitude. Spectral analysis shows strong agreement with finite element solutions across all wavenumbers, preserving both global behavior and localized stress concentrations.

Abstract

Neural Surrogate Modeling

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