LOGO. Modeling and Simulation of Microstructural Changes in Composite Sn-Ag-Cu Solder Alloys with Cu Nanoparticles

Transcription

1 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

2 Outline 1 General introduction 2 Validation of the phase-field model 3 Simulation Experiments 4 Results and comparison 5 Generalconclusions

3 Outline 1 General introduction 2 Validation of the phase-field model 3 Simulation Experiments 4 Results and comparison 5 General conclusions

4 4 Solder alloy Solder: a fusible metal with a melting point or melting range from 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 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)

6 Phase-field Model 6 Total Gibbs energy F of a heterogeneous system: Interfacial energy parameter: Bulk free energy density:

7 7 Phase-field model Diffusion equation: Evolution of non-conserved order parameter field:

8 Phase-field model 8

9 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

10 Outline 1 General introduction 2 Validation of the phase-field model. 3 Simulation Experiments 4 Results and comparison 5 General conclusions

11 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_A x(ag) BCT_A5+CU6SN CU x(sn) x(sn) 11 SN 0.0 BCT_A5+CU6SN5

12 12 1D simulation for Cu 6 and Bct system Equilibrium composition: x(cu) x(sn) x(ag) Cu e-4 Bct e e-4 Non-equilibrium composition: x(cu) x(sn) x(ag) Cu e-4 Bct 1.6e e-4

13 Molar fraction 13 1D simulation for Cu 6 and Bct system X: 24 Y: 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: X: 92 Y: X: 24 Y: 5.835e Distance (100nm)

14 Molar fraction 14 1D simulation for Cu 6 and Bct system X: 24 Y: X: 24 Y: Distance (100nm)

15 Local phase fraction 15 1D simulation for Cu 6 and Bct system 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 Distance (100nm)

16 Outline 1 General introduction 2 Validation of the phase-field model 3 Simulation Experiments 4 Results and comparison 5 General conclusions

17 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 x(ag) FCC_A1+FCC_A1 CU3SN+FCC_A1+FCC_A1 CU3SN+CU6SN5+AGSB_ORTHO FCC_A1+CU3SN CU3SN+FCC_A1+HCP_A HCP_A3+CU3SN AG 1 AGSB_ORTHO+CU3SN+HCP FCC_Al+CU3SN CU x(sn) SN x(sn) BCT_A5+CU6SN5

18 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 e-5 Cu 3 Sn e-5 Cu e-6 Bct e e-4

19 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

20 Outline 1 General introduction 2 Validation of the phase-field model 3 Simulation Experiments 4 Results and comparison 5 General conclusions

21 Local phase fraction and Molar fraction 21 1D simulation for IMCs at Cu/SAC solder joint 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 Distance (100nm)

22 Local phase fraction 22 1D simulation for IMCs at Cu/SAC solder joint 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 Distance (100nm)

23 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 Width of Cu 6 from 5.5e7 to 8.7e7s x 10-6 Width of Cu 3 Sn from 1.4e6 to 5.5e7s Width of Cu 3 Sn from 5.5e7 to 8.7e7s 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 Simulation time (s 1/2 ) y = 3.6e-012*x + 2.5e Simulation time (s 1/2 )

24 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 e e e-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 e-18 Fcc/Bct 1.67e-13 Cu 3 Sn/Cu e-18 Cu 3 Sn/Bct 1.67e-13 Cu 6 /Bct 1.67e-13

25 Width of Intermetallic Layer Width of Intermetallic Layer 25 1D simulation for IMCs at Cu/SAC solder joint 2.5 x Width of Cu 3 Sn Linear fitting of Cu 3 Sn Width of Cu x y = - 2.8e-012*x + 2.5e Simulation time (s 1/2 ) y = 5.6e-012*x + 2.5e-006 Width of Cu 3 Sn Width of Cu 6 Linear fitting of Cu Simulation time (s 1/2 )

26 Comparison with thermodynamic calculations 26 Point calculation: the stable phase equlibrium at a single point in a multicomponent system Input: average composition x(cu): x(sn): x(ag): Result: T(K) Phase Name f(cu 6 ) f(bct) f(fcc) 450 Cu 6 +Bct+Fcc

27 x(cu 3 Sn), m x(cu 6 ), m 27 Comparison with Experimental Data 6 Cu SAC o C 180 o C o C 10 Cu SAC o C 180 o C o C t 0.5, s 0.5 t 0.5, s 0.5 Prof. J.Janczak-Rusch at EMPA,

28 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 e e e-19 Cu 6 3.6e e e e-19 Sample K (Cu 3 Sn,cm 2 /s) K (Cu 6,cm 2 /s) T ( ) Cu SAC e e e e e e-14

29 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

30 Order parameter and Molar fraction 2D simulation for Cu 6 growth at interface between Fcc-Cu particle and Bct-Sn matrix x Sn after 1e7s Fcc after 1e7s Cu 6 Sn 5 after 1e7s Bct after 1e7s Distance (100nm)

31 Area of Cu 6 (m 2 ) 2D simulation for Cu 6 growth at interface between Fcc-Cu particle and Bct-Sn matrix x Area of Cu 6 Linear fitting of Cu y = 1.9e-019*x + 4.4e Simulation time (s) x 10 6

32 Outline 1 General introduction 2 Validation of the phase-field model 3 Simulation Experiments 4 Results and comparison 5 General conclusions

33 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

34 LOGO