Online proceedings - EDA Publishing Association

24-26 September 2008, Rome, ItalyS 4Ω 3Ω 4DΩ 1Ω 2S 3C0.3 PrototypeDefect0.250.20.15S 1 S 20.10.05Fig. 5. Localization of a defect D.00 2 4 6 8 10 12 14 16R0.30.25PrototypeDefectFig. 7.Structure functions for the second heat source0.2PrototypeDefectC0.150.250.10.20.05C0.150 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5R0.10.05Fig. 6.Structure functions for the first heat sourceby the standard finite difference method. Structure functionsare computed from the discretized models by the algorithmproposed by the authors in [9]. The eikonal equation for reconstructingwave fronts have been solved by the Fast MarchingAlgorithm [4], which has been implemented in a code. In thisway an accurate localization of the defect is achieved, as inFig. 5 the wave fronts having been determined with less thena 1% error. The comparison between the structure functionsfor the four heat sources, with and without defect is shown inFigs. 6-9VII. CONCLUSIONSIn this paper previous results proposed by the authors forlocalizing defects in components and packages by means ofstructure functions in three-dimensional heat diffusion problemshave been generalized. To this aim a novel triangulationapproach has been presented. Such method is based on the useof structure functions corresponding to dinstinct heat sources.Both analytical and numerical results have shown that accuratelocalizations of defects can be achieved in this way.00 2 4 6 8 10 12 14Fig. 8.RStructure functions for the third heat sourceREFERENCES[1] V. Székely, T. Van Bien, “Fine Structure of Heat Flow Path in SemiconductorDevices: a Measurement and Identification Method,” Solid-State Electronics, Vol. 21, pp. 1363-1368, 1988.[2] L. Codecasa, “Canonical Forms of One-Port Passive Distributed ThermalNetworks,” IEEE Trans. Components and Packaging Technologies, Vol.28, No. 1, pp. 5-13, 2005.[3] L. Codecasa, “Structure Function Representation of MultidirectionalHeat-Flows,” IEEE Trans. Components and Packaging Technologies, Vol.30, No. 4, pp. 643 - 652, 2007.[4] J. A. Sethian, “Level Set Methods and Fast Marching Methods,” CambridgeUniversity Press, 1999.[5] L. Codecasa, D. D’Amore, P. Maffezzoni, “Compact Modeling of ElectronDevices for Electro-thermal Analysis,” IEEE Trans. on Circuits andSystems I, Vol. 50, No. 4, pp. 465–476, 2003.[6] L. Codecasa, D. D’Amore, P. Maffezzoni, “Compact Thermal Networksfor Modeling Packages,” IEEE Trans. Components and Packaging Technologies,Vol. 27, No. 1, pp. 96-103, 2004.©EDA Publishing/THERMINIC 2008 12ISBN: 978-2-35500-008-9