A generalized alternating direction implicit method for transient thermal simulation of 2-D structures with locally refined grids

References

• A. Rahman and R. Reif, “Thermal analysis of three-dimensional (3-D) integrated circuits (ICs),” presented at the Proc. Interconnect Technol. Conf., Burlingame, CA, pp. 157–159, Jun. 2001.
   Google Scholar
• K. N. Tu, “Reliability challenges in 3D IC packaging technology,” Microelectron. Rel., vol. 51, no. 3, pp. 517–523, 2011. DOI: 10.1016/j.microrel.2010.09.031.
   Web of Science ®Google Scholar
• Y. Shabany, Heat Transfer: Thermal Management of Electronics, New York, NY, USA: Taylor & Francis, 2009, pp. 281–283.
   Google Scholar
• M. P. Gupta, A. K. Vallabhaneni, and S. Kumar, “Self-consistent electrothermal modeling of passive and microchannel cooling in AlGaN/GaN HEMTs,” IEEE Trans. Compon. Packag. Manufact. Technol., vol. 7, no. 8, pp. 1305–1312, Aug. 2017. DOI: 10.1109/TCPMT.2017.2693399.
   Web of Science ®Google Scholar
• D. M. Pozar, Microwave Engineering, vol. 162. New York: Wiley, 1998, pp. 424–427.
   Google Scholar
• T. Lu and J.-M. Jin, “Thermal-aware high-frequency characterization of large-scale through-silicon-via structures,” IEEE Trans. Compon., Packag. Manufact. Technol., vol. 4, no. 6, pp. 1015–1025, Jun. 2014. DOI: 10.1109/TCPMT.2014.2312136.
   Web of Science ®Google Scholar
• J. Xu, X.-Y. Yin, and J. Mao, “Transient thermal analysis of GaN heterojunction transistors (HFETs) for high-power applications,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 1, pp. 55–57, Jan. 2007. DOI: 10.1109/LMWC.2006.887261.
   Web of Science ®Google Scholar
• F. Bertoluzza, N. Delmonte, and R. Menozzi, “Three-dimensional finite-element thermal simulation of GaN-based HEMTs,” Microelectron. Rel., vol. 49, no. 5, pp. 468–473, May 2009. DOI: 10.1016/j.microrel.2009.02.009.
   Web of Science ®Google Scholar
• M. N. Ozisik, Finite Difference Methods in Heat Transfer. New York: CRC, 1994.
   Google Scholar
• Z. Liu, S. Swarup, S. X.-D. Tan, H.-B. Chen, and H. Wang, “Compact lateral thermal resistance model of TSVs for fast finite-difference based thermal analysis of 3-D stacked ICs,” IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 33, no. 10, pp. 1490–1502, Oct. 2014. DOI: 10.1109/TCAD.2014.2334321.
   Web of Science ®Google Scholar
• A. Cebula and D. Taler, “Finite volume method in heat conduction,” in Encyclopedia of Thermal Stresses. Amsterdam, The Netherlands: Springer, 2014, pp. 1645–1658.
   Google Scholar
• D. A. Calhoun, C. Halzel, and R. J. LeVeque, “Logically rectangular grids and finite volume methods for PDEs in circular and spherical domains,” SIAM Rev., vol. 50, no. 4, pp. 723–752, 2008. DOI: 10.1137/060664094.
   Web of Science ®Google Scholar
• Z. Huang and M. Tang, “A finite volume scheme for thermal simulation using locally refined semi-structured grids,” presented at the Photonics & Electromagnetics Res. Symp. (PIERS), Hangzhou, China, pp. 508–512, 2022.
   Google Scholar
• Z. Feng, N. Ma, W. Li, K. Narasaki, and F. Lu, “Efficient analysis of welding thermal conduction using the Newton–Raphson method, implicit method, and their combination,” Int. J. Adv. Manuf. Technol., vol. 111, no. 7–8, pp. 1929–1940, Oct. 2020. DOI: 10.1007/s00170-020-06233-6.
   Web of Science ®Google Scholar
• A. Fourmigue, G. Beltrame, and G. Nicolescu, “Transient thermal simulation of liquid-cooled 3-D circuits,” IEEE Trans. Compon. Packag. Manufact. Technol., vol. 6, no. 9, pp. 1349–1360, Sept. 2016. DOI: 10.1109/TCPMT.2016.2599100.
   Web of Science ®Google Scholar
• J. Douglas Jr. and J. E. Gunn, “A general formulation of alternating direction methods—Part I: Parabolic and hyperbolic problems,” Numer. Math., vol. 6, no. 1, pp. 428–453, 1964. DOI: 10.1007/BF01386093.
   Google Scholar
• T.-Y. Wang and C. C.-P. Chen, “3-D thermal-ADI: A linear-time chip level transient thermal simulator,” IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 21, no. 12, pp. 1434–1445, Dec. 2002.
   Web of Science ®Google Scholar
• D. Y. Heh, E. L. Tan, and W. C. Tay, “Fast alternating direction implicit method for efficient transient thermal simulation of integrated circuits,” Int. J. Numer. Model., vol. 29, no. 1, pp. 93–108, 2016. DOI: 10.1002/jnm.2049.
   Web of Science ®Google Scholar
• J. Li, M. Tang, and J. F. Mao, “An efficient ADI method for transient thermal simulation of liquid-cooled 3-D ICs,” IEEE Trans. Compon. Packag. Manufact. Technol., vol. 12, no. 9, pp. 1484–1491, Sept. 2022. DOI: 10.1109/TCPMT.2022.3206613.
   Web of Science ®Google Scholar
• L. Sun, Y. Li, Q. Yuan, and W. Hong, “An innovative sub-gridding method for Helmholtz equation,” presented at the Int. Symp. Antennas and Propagation, Xi-an, China, Oct. 2019.
   Google Scholar
• A. H. Ngo, T. Sekine, and H. Asai, “Subgrid-based equivalent circuit for transient thermal analysis using latency insertion method,” presented at the IEEE Int. Symp. Electromagnetic Compatibility & Signal/Power Integrity, Washington, DC, USA, Aug. 2017.
   Google Scholar
• S. Zivanovic, K. Yee, and K. Mei, “A subgridding method for the time-domain finite-difference method to solve Maxwell’s equations,” IEEE Trans. Microwave Theory Tech., vol. 39, no. 3, pp. 471–479, 1991. DOI: 10.1109/22.75289.
   Web of Science ®Google Scholar
• A. Tabarraei and N. Sukumar, “Adaptive computations on conforming quadtree meshes,” Finite Elem. Anal. Des., vol. 41, no. 7–8, pp. 686–702, Apr. 2005. DOI: 10.1016/j.finel.2004.08.002.
   Web of Science ®Google Scholar
• R. Hu, S. Pang, X. Chen, L. Liang, and X. Shao, “An octree-based adaptive mesh refinement method for three-dimensional modeling of keyhole mode laser welding,” Int. J. Heat Mass Tran., vol. 115, pp. 258–263, Dec. 2017. DOI: 10.1016/j.ijheatmasstransfer.2017.07.061.
   Web of Science ®Google Scholar
• H. Huang and H. Murakawa, “Thermo-mechanical analysis of line heating process by an efficient and accurate multi-level mesh refining method,” Mar. Struct., vol. 49, pp. 239–255, Sept. 2016. DOI: 10.1016/j.marstruc.2016.09.001.
   Web of Science ®Google Scholar
• T.-Y. Wang and C. C. P. Chen, “Thermal-ADI—A linear-time chip-level dynamic thermal-simulation algorithm based on alternating-direction-implicit (ADI) method,” IEEE Trans. VLSI Syst., vol. 11, no. 4, pp. 691–700, Aug. 2003. DOI: 10.1109/TVLSI.2003.812372.
   Web of Science ®Google Scholar
• COMSOL Multiphysics® v. 5.4. Stockholm, Sweden: COMSOL AB, 2018.
   Google Scholar