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![Page 1: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/1.jpg)
Thermal-aware DC IR-drop co-analysis using non-conformal domain decomposition methods
by Yang Shao, Zhen Peng, and Jin-Fa Lee
Proceedings AVolume 468(2142):1652-1675
June 8, 2012
©2012 by The Royal Society
![Page 2: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/2.jpg)
The geometry of the computational model.
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 3: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/3.jpg)
Electrical–thermal coupling.
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 4: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/4.jpg)
Notations for decomposing the original problem domain into two sub-domains.
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 5: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/5.jpg)
Partitioning of the sub-domain unknowns into interior and boundary unknowns.
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 6: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/6.jpg)
Views of the simulated IBM package geometry: (a) top view and (b) side view.
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 7: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/7.jpg)
PDN geometry that could cause the Swiss cheese effect.
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 8: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/8.jpg)
Convergence study using DDM to compute voltage distribution of a product-level three-dimensional IC package.
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 9: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/9.jpg)
IBM package PDN with boundary conditions and voltage distribution on the top plane (unit: V).
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 10: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/10.jpg)
Voltage distribution on the power planes of layer 1 and layer 7 (unit: V).
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 11: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/11.jpg)
Voltage distribution on the ground planes of layers 3, 4, 5, 6 and 8 (unit: V).
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 12: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/12.jpg)
Notations for partitioning the problem domain into two sub-domains for steady-state thermal analysis.
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 13: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/13.jpg)
Convergence study to compute voltage and temperature distribution of the chip-package-PCB model.
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 14: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/14.jpg)
Chip, memory and thermal TSVs of chip and memory layers: (a) top view and (b) side view.
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 15: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/15.jpg)
Volumetric power densities in chip and memory layers: (a) CPU1, (b) CPU2 and (c) RAM1 and RAM2.
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 16: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/16.jpg)
Non-conformal partitioning and mesh of the PDN of the chip-package-PCB model.
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 17: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/17.jpg)
Boundary conditions and voltage distribution of the PDN. (a) Boundary conditions and (b) computed initial voltage distribution at room temperature (unit: V).
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 18: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/18.jpg)
Boundary conditions and temperature distribution of the chip-package-PCB.
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 19: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/19.jpg)
Detailed thermal-aware voltage distributions on the chip modules (unit: V).
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society
![Page 20: Thermal-aware DC IR-drop co-analysis using non- conformal domain decomposition methods by Yang Shao, Zhen Peng, and Jin-Fa Lee Proceedings A Volume 468(2142):1652-1675.](https://reader035.fdocuments.in/reader035/viewer/2022062409/5697bf791a28abf838c82624/html5/thumbnails/20.jpg)
Maximum thermal-aware IR-drop results with iterations.
Yang Shao et al. Proc. R. Soc. A 2012;468:1652-1675
©2012 by The Royal Society