Abstract
In this paper, a co-optimization design method for thermal-stress coupling 3-dimensional integrated system with through silicon via is proposed based on the finite element method, support vector machine model and modified particle swarm optimization algorithm. In the cause of analyzing the effects of geometrical parameters (radius of through silicon via, oxide thickness and the height of oxide insolation layer) on the thermal-stress distribution, the finite element method based COMSOL software is conducted to simulate the thermal-stress coupling 3-dimensional integrated system. Based on the simulation data obtained by COMSOL, the support vector machine models are adopted to establish the database for describing the relationships between the geometrical parameters and key indexes (peak temperature, peak stress and temperature difference) to improve the design efficiency. Based on the desired key indexes of thermal-stress coupling 3-dimensional integrated system, the multi-objective evaluation function is formulated. Then, the geometrical parameters are optimized by the modified particle swarm optimization algorithm. The finite element simulation is conducted to verify the effectiveness of the proposed strategy. In three cases, the errors between the simulated and desired temperature differences are all less than 0.28 K, and the relative errors between the simulated and desired peak temperature/peak stress are all less than 4.78%, which indicates that the geometrical parameters can be optimized to control the key indexes of thermal-stress coupling 3-dimensional integrated system. Therefore, the developed method can be used in the design and manufacture of 3-dimensional integrated system.
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Abbreviations
- d :
-
Degree of the polynomial kernel function
- c :
-
Offset of polynomial kernel function
- s :
-
Width of Gauss kernel function
- r :
-
Radius of through silicon via unit
- t ox :
-
Oxide thickness
- h 1 :
-
Height of oxide isolation layer
- AARE:
-
Absolute average relative error
- PT:
-
Peak temperature
- PS:
-
Peak stress
- TD:
-
Temperature difference
- α:
-
Weight coefficient of peak temperature
- β:
-
Weight coefficient of peak stress
- γ:
-
Weight coefficient of temperature difference
- v i :
-
Velocity of the ith particle
- x i :
-
Position of the ith particle
- x r , x tox , x hl :
-
Range of particle position
- v r , v tox , v hl :
-
Range of particle velocity
- w :
-
Inertia weight
- p i :
-
Best previous positions of the ith particle
- p g :
-
Best previous positions of all particles
- C 1 , C 2 :
-
Constants to determine the weights of pi and pg
- r 1 , r 2 :
-
Two random values
- iter :
-
Current iteration
- iter max :
-
Maximum of the current iteration
- w max :
-
Maximum of inertia weight
- w min :
-
Minimum of inertia weight
- N :
-
Population size
- M G :
-
Maximum generation
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Acknowledgements
This work was supported by the Fundamental Research Funds for the Central Universities (No: QTZX23022), the Innovation Fund of Xidian University (No: YJSJ23019), Youth Talent Fund of Joint Fund of the Ministry of Education for Equipment Pre-Research (No: 8091B032138), the National Natural Science Foundations of China (No: 62104177), the Equipment Pre-research Project of China (No:80924020307), and the Cooperation Program of XDU-Chongqing IC Innovation Research Institute (No: CQIRI-2022CXY-Z01).
Funding
Fundamental Research Funds for the Central Universities, QTZX23022, Dongdong Chen, the Innovation Fund of Xidian University, YJSJ23019, Xianglong Wang, Youth Talent Fund of Joint Fund of the Ministry of Education for Equipment Pre-Research, 8091B032138, Dongdong Chen, National Natural Science Foundations of China,62104177, Dongdong Chen,Equipment Pre-research Project of China, 80924020307, Dongdong Chen,Cooperation Program of XDU-Chongqing IC Innovation Research Institute, CQIRI-2022CXY-Z01, Di Li
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XW and DC wrote the manuscript with support from DL and YY generated the simulation results. DC (ddchen@xidian.edu.cn) and DL (lidi2004@126.com) supervised the project, and they are co-corresponding authors of this paper.
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Wang, X., Chen, D., Li, D. et al. A co-optimization method of thermal-stress coupling 3D integrated system with through silicon via. Struct Multidisc Optim 66, 251 (2023). https://doi.org/10.1007/s00158-023-03706-6
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DOI: https://doi.org/10.1007/s00158-023-03706-6