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Zhen Zhang, Zhigang Suo Division of Engineering and Applied Sciences Harvard University Jean H. Prévost Department Civil and Environmental Engineering Princeton University Cracking in Interconnects due to Thermal Ratcheting MRSEC
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Time Temperature 150 0 C 125 0 C -55 0 C Packaging temperature Loading range Cyclic loading test Silicon Lower level interconnects (10-15 mm thick) Al-Cu 2 m thick Underfill Polyimide (4 mm thick) SiN (0.45 m thick) underfill Flip-chip structure Plan view of SiN Silicon die Organic substrate What is the origin of high stress?
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Ratcheting Plastic Deformation Huang, Suo, Ma, Fujimoto, J. Mater. Res., 15, 1239 (2000) Biased Shear Stress Al or Cu Silicon 10~100 µm 2 µm 0.5 µm SiN Silica and low level interconnects (10~15µm thick) Polymeric underfill underfill Silicon die Organic Substrate Time Temperature 150 0 C 125 0 C -55 0 C Packaging temperature Loading range Packaging and loading
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First cycle mm SiN film What is the crack behavior? membrane stress due to CTE mismatch Metal yields every cycle ! Many cycles mm Al / Cu pad Stress builds up in SiN mm m biased shear stress Al / Cu pad Ratcheting Plastic Deformation p
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2D Shear Lag Model stress Y E strain Two challenges for simulation Crack growth Plasticity 00 Elastic substrate x y z x0x0 y0y0 Elastic film Elastic-plastic sublayer X-FEM Linear creep analogy Gradual loss of constraint Stress relaxes in crack wake, but intensifies at crack tip.
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Extended Finite Element Method (X-FEM) Nodal Enrichment functions: Moës, Dolbow, Belytschko, Int. J. Num Math. Eng, 46, 131 (1999). –Displacement jumps –Singular crack tip field –Relative coarse mesh –No remeshing required for crack growth simulations Benefits: Time-saving
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Linear Ratcheting-Creep Analogy Strain per cycle Uni-directional shear stress metal film cyclic membrane stress substrate Cycle Temperature 125 °C -55 °C Cyclic loading 1 cycle Y strain stress E Linear approximation Ratcheting-Creep analogy Time-saving Huang, Suo, Ma, Acta Materialia, 49, 3039-3049 (2001) p
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Semi-infinite Stationary Crack in Blanket Film Comparison of time cost: Creep: 1hr 20min Ratchet: 22 hr Creep Ratchet Length scale Both creep and ratcheting calculation show the same trend. K l(N) K
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Finite Stationary Crack in Blanket Film Normalized cycles Creep Ratchet Final stage l>>a Griffith crack limit Early stage l<<a Infinite crack limit 2a2a Early stage l 2a2a Final stage l>>a 2a2a Evolving l ~ a
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Crack Propagation in a Blanket Film aa Normalized cycles Preparation Initiation Transient Propagation Steady-state Length scale Cycle scale K ss
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Simulation of Cracks Propagation in Interconnects Initial state After 100 cycles Time Temperature 150 °C 125 °C -55 °C Packaging temperature Loading range Cyclic loading Tensile stress Compressive region
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Summary Ratcheting deformation in metal layer High stress in SiN passivation film X-FEM + Linear creep analogy Simulation of cracking in interconnects becomes feasible High temperature packaging Thermal cyclic loading Cracking in interconnects
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