Phase Field Modeling of Joint Formation During Isothermal Solidification in 3DIC Micro Packaging

Abstract

In this paper, a computational multi-phase field approach is utilized to study the formation of the Cu/Sn/Cu micro-joint in 3-Dimensional Integrated Circuits (3DICs). The method considers the evolution of the system during isothermal solidification at 250 °C for the case of two different interlayer thicknesses (5 and 10 µm). The Cu/Sn/Cu interconnection structure is important for the micro packaging in the 3DIC systems. The thermodynamics and kinetics of growth of η-Cu₆Sn₅ and ɛ-Cu₃Sn interfacial intermetallics (IMCs) are investigated by coupling the multi-phase field method with CALPHAD approach. The interaction of the phases is addressed by assuming a metastable condition for the Cu/Sn reacting system. The simulations start with the nucleation and rapid growth of the η-Cu₆Sn₅ IMCs at the initial stage, the nucleation and growth of ɛ-Cu₃Sn IMCs at the intermediate stage ending with the full consumption of Sn layer and the domination of ɛ-Cu₃Sn IMCs at the later stages. In addition, comparing different diffusion rates through the grain boundary of η phases show that their morphology is the direct consequence of balance of kinetic forces. This work provides a valuable understanding of the dominant mechanisms for mass transport in the Cu/Sn/Cu low volume interconnections. The results show that the phase field modeling is successful in addressing the morphological evolution and growth of IMC layers in the 3DIC joint formation.

Appendix

The free energy densities per unit molar volume of individual phases are:

$$f_{L} = \left( { 1 - c} \right)G_{\text{Cu}}^{0L} + cG_{\text{Sn}}^{0L} + RT\left[ {\left( { 1 - c} \right) { \ln } \left( { 1 - c} \right) + c\ln c} \right] + c\left( { 1 - c} \right)[L_{0}^{L} + L_{ 1}^{L} \left( { 1 - 2c} \right) + L_{ 2}^{L} \left( { 1 - 4c + 4c^{ 2} } \right]$$

(11)

$$f_{\eta } = 2.0 \times 10^{ 5} \left( {c - 0. 4 3 5} \right)^{ 2} + 0. 5 4 5G_{\text{Cu}}^{\alpha } + 0. 4 5 5G_{\text{Sn}}^{\text{SER}} - 6 8 6 9. 5 - 0. 1 5 8 9T$$

(12)

$$f_{\varepsilon } = 2.0 \times 10^{ 5} \left( {c - 0. 2 4 9} \right)^{ 2} + 0. 7 5G_{\text{Sn}}^{\alpha } + 0. 2 5G_{\text{Sn}}^{\text{SER}} - 8 1 9 4. 2 - 0. 20 4 3T$$

(13)

$$f_{Cu} = \left( { 1 - c} \right)G_{\text{Cu}}^{\alpha } + cG_{\text{Sn}}^{\alpha } + RT\left[ {\left( { 1 - c} \right) { \ln } \left( { 1 - c} \right) + c\ln c} \right] + c\left( { 1 - c} \right)[L_{0}^{\alpha } + L_{ 1}^{\alpha } \left( { 1 - 2c} \right)]$$

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where $G_{\text{Cu}}^{\alpha }$ =  −19073, $G_{\text{Sn}}^{\alpha }$ = −27280, $G_{\text{Cu}}^{L}$ = −11083, $G_{\text{Sn}}^{\text{SER}}$ = 346160, $G_{\text{Sn}}^{L}$ = −28963, L ^α₀  = −11448, L ^α₁  = −11694, L ^L₀  = −10487, L ^L₁  = −18198, L ^L₂  = 10528.4.