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<p>The accuracy of viscoelastic testing and fitting will directly affect the stress and warpage prediction ability of advanced microelectronic packaging. It is necessary to directly verify and improve the accuracy of the viscoelastic model and the temperature shift factors. This study proposes and validates an improved fitting method for the viscoelastic generalized Maxwell model, guided by stress relaxation curves. The proposed method aims to reduce a priori empirical errors associated with determining temperature shift factors based on the time–temperature superposition principle and to overcome limitations in the fitting accuracy and applicable range of the Williams–Landel–Ferry (WLF) equation. Using experimentally measured stress relaxation curves as benchmarks, improved temperature shift factors are calculated via a characteristic node approach, enabling the construction of an enhanced master curve and refined fitting parameters for the viscoelastic constitutive model. An interpolation method is additionally employed to replace WLF equation fitting for calculating temperature-dependent parameters via shift factors. To validate the accuracy of the proposed method, four finite element methods for viscoelastic parameters were analyzed, and the polyimide stress relaxation process was simulated using the finite element method and compared with experimental results. The findings demonstrate that, compared with traditional fitting approaches, the proposed method significantly improves the accuracy of viscoelastic parameters and enables reliable prediction of stress relaxation behavior across a range of temperatures. It provides an engineering approach for high-precision material testing for semiconductor industry research and development.</p>

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An Integrated Dynamic Mechanical Analysis and Stress Relaxation Approach for the Improved Viscoelastic Characterization of Polyimide Films

  • 期刊论文

  • 发表日期：

    2026年5月7日

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  • Zhuangchao Zhan,
  • Yifan Zhou,
  • Quanzheng Tan,
  • Guixiang Xu,
  • Qiqin Wei,
  • Yupeng Wang,
  • Xiyou Wang,
  • Daoguo Yang,
  • Hongbo Qin

摘要

The accuracy of viscoelastic testing and fitting will directly affect the stress and warpage prediction ability of advanced microelectronic packaging. It is necessary to directly verify and improve the accuracy of the viscoelastic model and the temperature shift factors. This study proposes and validates an improved fitting method for the viscoelastic generalized Maxwell model, guided by stress relaxation curves. The proposed method aims to reduce a priori empirical errors associated with determining temperature shift factors based on the time–temperature superposition principle and to overcome limitations in the fitting accuracy and applicable range of the Williams–Landel–Ferry (WLF) equation. Using experimentally measured stress relaxation curves as benchmarks, improved temperature shift factors are calculated via a characteristic node approach, enabling the construction of an enhanced master curve and refined fitting parameters for the viscoelastic constitutive model. An interpolation method is additionally employed to replace WLF equation fitting for calculating temperature-dependent parameters via shift factors. To validate the accuracy of the proposed method, four finite element methods for viscoelastic parameters were analyzed, and the polyimide stress relaxation process was simulated using the finite element method and compared with experimental results. The findings demonstrate that, compared with traditional fitting approaches, the proposed method significantly improves the accuracy of viscoelastic parameters and enables reliable prediction of stress relaxation behavior across a range of temperatures. It provides an engineering approach for high-precision material testing for semiconductor industry research and development.