Modeling and Simulation of Microstructural Changes in Composite Sn-Ag-Cu Solder Alloys with Cu Nanoparticles Yuanyuan Guan, A.Durga, Nele Moelans Dept. Metallurgy and Materials Engineering, K.U. Leuven, Belgium LOGO TC user meeting, Aachen, Germany September 8, 2011
Outline 1 General introduction 2 Validation of the phase-field model 3 Simulation Experiments 4 Results and comparison 5 Generalconclusions
Outline 1 General introduction 2 Validation of the phase-field model 3 Simulation Experiments 4 Results and comparison 5 General conclusions
4 Solder alloy Solder: a fusible metal with a melting point or melting range from 90-450 Sn-Pb solder Sn-Ag-Cu (SAC) solder Composite solder Intermetallic Compounds (IMCs) metallurgical bonding between solder/substrate morphology and thickness Tsao et al, 11th ICEPT-HDP 2010
5 Molar fraction field x Order parameter field η Local phase fraction φ: Diffuse interface description: Domains: constant φ (1 or 0) Interface: φ gradually vary between their values in the neighboring grains (1 0, 0 1)
Phase-field Model 6 Total Gibbs energy F of a heterogeneous system: Interfacial energy parameter: Bulk free energy density:
7 Phase-field model Diffusion equation: Evolution of non-conserved order parameter field:
Phase-field model 8
9 Goals of the thesis Calculation of phase stabilities with Software Pandat Microstructure simulations using a phase-field code on Grain size Diffusion and phase transitions Spatial distribution on the growth and coarsening of IMCs Experimental data from EMPA to validate the modeling
Outline 1 General introduction 2 Validation of the phase-field model. 3 Simulation Experiments 4 Results and comparison 5 General conclusions
x(ag) BCT_A5+CU6SN5+BCT_A5 BCT_A5+CU6SN5 11 Cu 6 + Bct (Sn-rich phase) at 450K 0.9 AG 1 BCT_A5+BCT_A5 0.7 0.8 0.5 x(ag) 0.6 0.3 0.4 0.2 0.2 0 BCT_A5+CU6SN5 0.0 0 0.2 0.4 0.6 0.8 1.0 1 CU x(sn) x(sn) 11 SN 0.0 BCT_A5+CU6SN5
12 1D simulation for Cu 6 and Bct system Equilibrium composition: x(cu) x(sn) x(ag) Cu 6 0.544783 0.455012 2.05e-4 Bct 5.09257e-5 0.999545 4.040743e-4 Non-equilibrium composition: x(cu) x(sn) x(ag) Cu 6 0.544783 0.455012 2.05e-4 Bct 1.6e-3 0.998 4.0e-4
Molar fraction 13 1D simulation for Cu 6 and Bct system 1 0.8 0.6 0.4 X: 24 Y: 0.9995 Molar fraction of Cu after 1s Molar fraction of Sn after 1s Molar fraction of Cu after 1e5s Molar fraction of Sn after 1e5s Molar fraction of Cu after 1e6s Molar fraction of Sn after 1e6s Molar fraction of Cu after 1e8s Molar fraction of Sn after 1e8s X: 92 Y: 0.545 X: 92 Y: 0.455 0.2 X: 24 Y: 5.835e-005 0 0 10 20 30 40 50 60 70 80 90 100 Distance (100nm)
Molar fraction 14 1D simulation for Cu 6 and Bct system 1 0.9995 X: 24 Y: 0.9995 0.999 0.9985 X: 24 Y: 0.998 0.998 0 10 20 30 40 50 60 70 Distance (100nm)
Local phase fraction 15 1D simulation for Cu 6 and Bct system 1 0.8 0.6 Local phase fraction of Cu 6 after 1s Local phase fraction of Bct after 1s Local phase fraction of Cu 6 after 1e5s Local phase fraction of Bct after 1e5s Local phase fraction of Cu 6 after 1e6s Local phase fraction of Bct after 1e6s Local phase fraction of Cu 6 after 1e8s Local phase fraction of Bct after 1e8s 0.4 0.2 0 65 70 75 80 85 90 95 Distance (100nm)
Outline 1 General introduction 2 Validation of the phase-field model 3 Simulation Experiments 4 Results and comparison 5 General conclusions
x(ag) AGSB_ORTHO+CU6SN5+BCT_A5 17 1D simulation for IMCs at Cu/SAC solder joint Isothermal section of SAC ternary system at 450K 0.9 0.7 0.5 0.3 x(ag) FCC_A1+FCC_A1 CU3SN+FCC_A1+FCC_A1 CU3SN+CU6SN5+AGSB_ORTHO FCC_A1+CU3SN CU3SN+FCC_A1+HCP_A3 0.6 0.4 0.8 HCP_A3+CU3SN AG 1 AGSB_ORTHO+CU3SN+HCP 0.2 0.2 FCC_Al+CU3SN 0 0 0.2 0.4 0.6 0.8 1 CU x(sn) SN 0.0 0.0 0.2 0.4 0.6 0.8 1.0 x(sn) BCT_A5+CU6SN5
18 1D simulation for IMCs at Cu/SAC solder joint Initial composition: a point in the 2-phase region Fcc/Cu 3 Sn a point in the 2-phase region Bct/Cu 6 x(cu) x(sn) x(ag) Fcc 0.974224 0.025744 3.15442e-5 Cu 3 Sn 0.749988 0.25 1.17739e-5 Cu 6 0.54497 0.455028 1.92497e-6 Bct 5.19144e-5 0.999578 3.70319e-4
1D simulation for IMCs at Cu/SAC solder joint Molar fraction field x Sn and x Cu Diffusion equation 19 Order parameter field η ρ Order parameter evolution equation Atomic mobilities M ρ of different components in different phases Equal Interface mobilities L for different interfaces Equal
Outline 1 General introduction 2 Validation of the phase-field model 3 Simulation Experiments 4 Results and comparison 5 General conclusions
Local phase fraction and Molar fraction 21 1D simulation for IMCs at Cu/SAC solder joint 1 0.8 of Fcc after 8.7e7s of Cu 3 Sn after 8.7e7s of Cu 6 after 8.7e7s 0.6 of Bct after 8.7e7s x Cu after 8.7e7s x Sn after 8.7e7s 0.4 0.2 0 0 50 100 150 Distance (100nm)
Local phase fraction 22 1D simulation for IMCs at Cu/SAC solder joint 1 0.8 0.6 0.4 of Fcc after 10s of Cu 3 Sn after 10s of Cu 6 after 10s of Bct after 10s of Fcc after 8.7e7s of Cu 3 Sn after 8.7e7s of Cu 6 after 8.7e7s of Bct after 8.7e7s 0.2 0 50 55 60 65 70 75 80 85 90 95 100 105 Distance (100nm)
Width of Intermetallic Layer Width of Intermetallic Layer 23 1D simulation for IMCs at Cu/SAC solder joint 2.56 x 10-6 Width of Cu 3 Sn from 1.4e6 to 5.5e7s 2.55 Width of Cu 3 Sn from 5.5e7 to 8.7e7s 2.54 Fitted line of Cu 3 Sn Width of Cu 6 from 1.4e6 to 5.5e7s y = 5.7e-012*x + 2.5e-006 2.53 Width of Cu 6 from 5.5e7 to 8.7e7s 2.52 2.56 x 10-6 Width of Cu 3 Sn from 1.4e6 to 5.5e7s 2.51 2.55 Width of Cu 3 Sn from 5.5e7 to 8.7e7s 2.5 2.54 Width of Cu 6 from 1.4e6 to 5.5e7s 2.53 Width of Cu 6 from 5.5e7 to 8.7e7s 2.49 Fitted line of Cu 2.52 6 2.48 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 2.51 Simulation time (s 1/2 ) 2.5 2.49 y = 3.6e-012*x + 2.5e-006 2.48 2.47 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Simulation time (s 1/2 )
24 1D simulation for IMCs at Cu/SAC solder joint Atomic mobilities M ρ for different phases Nonequal Phase Fcc Cu 3 Sn Cu 6 Bct M ρ (m 2 molj -1 s -1 ) 1.64e-29 5.34e-23 4.04e-21 2.84e-16 Interface mobilities L for different interfaces Nonequal Interface L (m 3 J -1 s -1 ) Fcc/Cu 3 Sn 1.67e-19 Fcc/Cu 6 1.67e-18 Fcc/Bct 1.67e-13 Cu 3 Sn/Cu 6 1.67e-18 Cu 3 Sn/Bct 1.67e-13 Cu 6 /Bct 1.67e-13
Width of Intermetallic Layer Width of Intermetallic Layer 25 1D simulation for IMCs at Cu/SAC solder joint 2.5 x 10-6 2.495 Width of Cu 3 Sn Linear fitting of Cu 3 Sn Width of Cu 6 2.49 2.5 x 10-6 2.485 y = - 2.8e-012*x + 2.5e-006 2.495 2.48 260 270 280 290 300 310 320 330 Simulation time (s 1/2 ) 2.485 2.49 y = 5.6e-012*x + 2.5e-006 Width of Cu 3 Sn Width of Cu 6 Linear fitting of Cu 6 2.48 260 270 280 290 300 310 320 330 Simulation time (s 1/2 )
Comparison with thermodynamic calculations 26 Point calculation: the stable phase equlibrium at a single point in a multicomponent system Input: average composition x(cu): 0.453834 x(sn): 0.463975 x(ag): 0.083191 Result: T(K) Phase Name f(cu 6 ) f(bct) f(fcc) 450 Cu 6 +Bct+Fcc 0.832757 0.056106 0.111136
x(cu 3 Sn), m x(cu 6 ), m 27 Comparison with Experimental Data 6 Cu SAC405 150 o C 180 o C 4 200 o C 10 Cu SAC405 150 o C 180 o C 8 200 o C 6 2 4 0 0 0 300 600 900 1200 0 300 600 900 1200 t 0.5, s 0.5 t 0.5, s 0.5 Prof. J.Janczak-Rusch at EMPA, 2011 2
28 Comparison with Experimental Data Diffusion controlled phase transition: d the thickness of the IMC layer, K the growth rate coefficient, t the aging time, d 0 the initial thickness Simulation at 450K (177 ): Equal M ρ Experiment data from EMPA: Non-equal M ρ Phase K 1/2 (m/s 1/2 ) K (cm 2 /s) K 1/2 (m /s 1/2 ) K (cm 2 /s) Cu 3.7e-12 3.249e-19-2.8e-12-0.784e-19 Cu 6 3.6e-12 1.296e-19 5.6e-12 3.136e-19 Sample K (Cu 3 Sn,cm 2 /s) K (Cu 6,cm 2 /s) T ( ) 150 180 200 150 180 200 Cu SAC405 2.01 e-14 4.91e-14 1.63 e-14 1.08 e-14 4.29 e-14 4.6 e-14
2D simulation for Cu 6 growth at interface between Fcc-Cu particle and Bct-Sn matrix Configuration of Fcc+Cu 6 +Bct phases in Cu-Sn binary system at 450K: 29
Order parameter and Molar fraction 2D simulation for Cu 6 growth at interface between Fcc-Cu particle and Bct-Sn matrix 30 1 0.8 0.6 x Sn after 1e7s Fcc after 1e7s Cu 6 Sn 5 after 1e7s Bct after 1e7s 0.4 0.2 0 0 50 100 150 Distance (100nm)
Area of Cu 6 (m 2 ) 2D simulation for Cu 6 growth at interface between Fcc-Cu particle and Bct-Sn matrix 31 4.75 x 10-11 4.7 Area of Cu 6 Linear fitting of Cu 6 4.65 4.6 4.55 4.5 y = 1.9e-019*x + 4.4e-011 4.45 4.4 0 2 4 6 8 10 12 14 Simulation time (s) x 10 6
Outline 1 General introduction 2 Validation of the phase-field model 3 Simulation Experiments 4 Results and comparison 5 General conclusions
33 General Conclusions Correct Gibbs energy expression Phase-field method The IMCs at solder joint and IMCs at interface between Cu particle and Sn matrix Accurate diffusion data The complete description of parabolic behavior of the IMCs evolution
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