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Thermal Warping Analysis and Control of Heterogeneous Stepped Double-Layer Plate Structures
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Ruichang Zhu1, Lu Li2, Fei Shen1, Yiming Ge3, Liaoliang Ke1, **
Chinese Journal of Solid Mechanics | 2025, 46(3) : 314 - 328
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Chinese Journal of Solid Mechanics | 2025, 46(3): 314-328
Research Papers
Thermal Warping Analysis and Control of Heterogeneous Stepped Double-Layer Plate Structures
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Ruichang Zhu1, Lu Li2, Fei Shen1, Yiming Ge3, Liaoliang Ke1, **
Affiliations
  • 1Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin, 300350
  • 2Xi'an Microelectronics Technology Research Institute, Xi'an, 710054
  • 3Beijing Microelectronics Technology Research Institute, Beijing, 100076
Published: 2025-06-26 doi: 10.19636/j.cnki.cjsm42-1250/o3.2025.011
Outline
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The chip packaging structure is commonly considered to be composed of different material layers stacked together. Due to the inconsistent thermal expansion coefficients of materials, the structure is prone to thermal warping deformation when subjected to significant changes in ambient temperature. At present, thermal warping is a typical failure mode in the field of microelectronic packaging. With the development of ultra-thin packaging components, thermal warping will become more pronounced. However, excessive warping deformation can lead to problems such as chip cracking, interface delamination, and solder joint failure. First, this paper considers the actual size differences between bare chips and substrates, and establishes a heterogeneous stepped double-layer plate model. Second, a thermal warpage experiment platform was constructed using a VIC-3D non-contact full-field strain gauge based on 3D digital image correlation, an infrared thermal imager, and a high-temperature heating stage. Then, the thermal warping deformation of the double-layer plate structure was observed during the heating process, and an equivalent finite element model was established to verify the experimental results. Subsequently, the thermal warpage control of the stepped double-layer board was achieved by attaching a frame sub-structure to the edge of the bottom plate, with its effectiveness verified through both simulations and experiments. Finally, the effects of the geometric and material parameters of the frame sub-structure on the thermal warpage control of the stepped double-layer plate structure are also discussed in detail. It is found that the thermal warping deformation obtained through experimental methods is in good agreement with the simulation results. Moreover, the warping control method using the frame sub-structure can significantly reduce the thermal warping deformation of the heterogeneous stepped double-layer plate structure. The width of the frame structure is the primary factor, and increasing the width can reduce thermal warping deformation effectively. The coefficient of thermal expansion and thickness also have a significant impact on the thermal warping control. As the coefficient of thermal expansion and thickness increase, the thermal warping deformation decreases. The research findings of this paper can provide theoretical guidance for solving thermal warping issues in multi-material laminated structures in microelectronic packaging.

heterogeneous stepped double-layer plate structures  /  thermal warping  /  warping control  /  digital image correlation
Ruichang Zhu, Lu Li, Fei Shen, Yiming Ge, Liaoliang Ke. Thermal Warping Analysis and Control of Heterogeneous Stepped Double-Layer Plate Structures[J]. Chinese Journal of Solid Mechanics, 2025 , 46 (3) : 314 -328 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2025.011
Year 2025 volume 46 Issue 3
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doi: 10.19636/j.cnki.cjsm42-1250/o3.2025.011
  • Receive Date:2025-04-30
  • Online Date:2026-03-20
  • Published:2025-06-26
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  • Received:2025-04-30
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    1Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin, 300350
    2Xi'an Microelectronics Technology Research Institute, Xi'an, 710054
    3Beijing Microelectronics Technology Research Institute, Beijing, 100076
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表12种不同金属材料的力学参数

Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)

Genus
种数
Number of
species
占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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