Journal of the Microelectronics and Packaging Society (마이크로전자및패키징학회지)

The Korean Microelectronics and Packaging Society (한국마이크로전자및패키징학회)
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Development of Warpage Simulation Method according to Thermal Stress based on Equivalent Anisotropic Viscoelastic Model

등가 이방성 점탄성 모델 기반 열 응력에 따른 휨 해석 기법 개발

  • Kim, Heon-Su (Department of Mechanical Convergence Engineering, Hanyang University) ;
  • Kim, Hak-Sung (Department of Mechanical Convergence Engineering, Hanyang University)
  • 김헌수 (한양대학교 융합기계공학과) ;
  • 김학성 (한양대학교 융합기계공학과)
  • Received : 2022.09.08
  • Accepted : 2022.09.30
  • Published : 2022.09.30
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Abstract

In this study, simulation method was developed to improve the accuracy of the warpage simulation based on the equivalent anisotropic viscoelastic model. First, a package with copper traces and bumps was modeled to implement anisotropic viscoelastic behavior. Then, equivalent anisotropic viscoelastic properties and thermal expansion coefficient for the bump region were derived through the representative volume element model. A thermal cycle of 0 to 125 degrees was applied to the package based on the derived mechanical properties, and the warpage according to the thermal cycle was simulated. To verify the simulation results, the actual package was manufactured, and the warpage with respect to the thermal cycle was measured through shadow moiré interferometer. As a result, by applying the equivalent anisotropic viscoelastic model, it was possible to calculate the warpage of the package within 5 ㎛ error and predict the shape of the warpage.

본 연구에서는 재료의 이방성 점탄성 거동을 고려한 해석 기법을 개발하여 휨(Warpage) 해석의 정합성을 개선하고자 하였다. 먼저, 이방성 점탄성 거동 구현을 위해 구리 패턴(Cu trace) 및 범프(Bump)가 존재하는 패키지를 모델링 하였다. 복잡한 형상의 범프 영역은 대표체적요소 모델을 기반으로 등가 이방성 점탄성 물성 및 열 팽창계수를 도출하였다. 도출된 물성을 기반으로 패키지에 0~125도의 열 주기(Thermal cycle)를 가하였으며, 열 주기에 따른 패키지의 휨 경향을 확인하였다. 해석 결과의 검증을 위해 해석 모델과 동일한 패키지를 제작하였고, 쉐도우 모아레 간섭계(Shadow Moire interferometer)를 통해 열 주기에 따른 실제 패키지의 휨 정도를 측정하였다. 결과적으로 구리 패턴, 범프 등의 요소가 고려된 등가 이방성 점탄성 해석 기법의 적용으로 5 ㎛ 이내의 오차로 패키지의 휨 정도를 계산하고 휨의 형태를 예측할 수 있었다.

Keywords

Acknowledgement

This work was supported by Korea Institute of Energy Technology Evaluation and Planning(KETEP) grant funded by the Korea government(MOTIE)(20202020800360, Innovative Energy Remodeling Total Technologies(M&V, Design, Package Solutions, and Testing & Verifications Technologies) for the Aging Public Buildings). This research was also supported by a National Research Foundation of Korea (NRF) grant funded by the Korean Government (MEST) (2021M2E6A1084690).

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