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

Time Temperature C C C Packaging temperature Loading range Cyclic loading test Silicon Lower level interconnects (10-15 mm thick) Al-Cu 2  m thick Underfill Polyimide (4 mm 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?

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 C C C Packaging temperature Loading range Packaging and loading

First cycle    mm SiN film What is the crack behavior? membrane stress due to CTE mismatch   Metal yields every cycle ! Many cycles    mm Al / Cu pad Stress builds up in SiN    mm  m biased shear stress Al / Cu pad Ratcheting Plastic Deformation  p

2D Shear Lag Model stress Y E strain Two challenges for simulation Crack growth Plasticity 00 Elastic substrate x y z x0x0 y0y0 Elastic film Elastic-plastic sublayer X-FEM Linear creep analogy Gradual loss of constraint Stress relaxes in crack wake, but intensifies at crack tip.

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

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, (2001)  p

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

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

Crack Propagation in a Blanket Film   aa Normalized cycles Preparation Initiation Transient Propagation Steady-state Length scale Cycle scale K ss 

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

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