## 2 Size Effects on Microstructure in Solder Joints  
### IMC Formation and Growth  
IMCs form during the reflow or thermal aging process in solder materials. Cu and Ni substrates are the most commonly used substrates in lead-free solder joints. For Cu-substrate solder joints, Cu\({}_{6}\)Sn\({}_{5}\) and Cu\({}_{3}\)Sn are the major types of IMCs. As for Ni-substrate solder joints, Ni\({}_{6}\)Sn\({}_{5}\) and Ni\({}_{3}\)Sn IMCs commonly occur at the Ni/Solder interface. Other types of substrate, such as Au/Ni-P/Cu (ENIG), Ag, Pa/Ti/Si, Co, Au, Fe, Cu-Mn, and Cu-Zn were summarized in [PERSON] et al. 's study [10], while the IMCs formed during interfacial reactions in Sn-Ag-Cu solder joints of different substrates are listed in Table 1. IMCs act as the mechanical and electrical connections between the solder matrix and substrate. Therefore, the growth and evolution of IMC layers have a significant effect on the reliability of the solder joints [11; 12]. The IMC growth corresponds to the Cu dissolution from substrate into the solder matrix, which is found to be greatly affected by the substrate area/solder volume ratio (V/A ratio) [9; 13]. By taking the unilateral solder joints as an example, the size effects on the internal microstructure are shown in Figure 2. In general, the decreasing solder volume leads to the apparent coarsening of interfacial IMCs (i.e., Cu\({}_{6}\)Sn\({}_{5}\) and Ag\({}_{3}\)Sn) and a finer dendritic \(\beta\)-Sn phase. The shapes and amount of precipitation (i.e., Cu\({}_{6}\)Sn\({}_{5}\) and Ag\({}_{3}\)Sn) in the solder matrix formed in solidification are  
Figure 1: Schematic diagram of the specimens of solder balls and joints with different sizes and shapes. also dependent on the joint size. In eutectic structures, Ag\({}_{3}\)Sn dispersion in the solder alloy can increase the ductility. However, excessive thermal aging or multiple reflows can lead to plate-like Ag\({}_{3}\)Sn on the Cu\({}_{6}\)Sn\({}_{5}\)IMCs. This plate-like Ag\({}_{3}\)Sn will increase the strain singularity near the interfacial layers of the solder joints. The solder joint size has significant effect on the eutectic structures in Sn-Ag-Cu solder joints. Dendritic Ag\({}_{3}\)Sn precipitation (see in the dashed lines) in the pseudo-eutectic structures also weaken the mechanical strength of the solder joints. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Substrate** & **IMCs** & **Reference** \\ \hline Cu & Cu\({}_{6}\)Sn\({}_{5}\), Cu\({}_{3}\)Sn & [14] \\ Ni & (Cu,Ni)\({}_{3}\)Sn\({}_{4}\) or (Cu,Ni)\({}_{6}\)Sn\({}_{5}\) & [15; 16] \\  & (Cu,Ni)\({}_{3}\)Sn\({}_{4}\) or (Cu,Ni)\({}_{6}\)Sn\({}_{5}\) & [17; 18] \\  & Ni\({}_{3}\)P, Ni-Sn-P & \\ Ag & Ag\({}_{3}\)Sn & [19] \\ Pt/Ti/Si & PtSn\({}_{4}\) & [20] \\ Co & CoSn\({}_{3}\) & [21; 22] \\ Au & AuSn\({}_{2}\) or AuSn\({}_{4}\) or both & [23] \\ Fe & FeSn\({}_{2}\) & [24] \\ Cu-Mn & Cu\({}_{6}\)Sn\({}_{5}\) and Cu-Mn & [25] \\ Cu-Zn & (Cu,Sn)\({}_{6}\)Sn\({}_{5}\) & \\  & (Cu,Zn)\({}_{3}\)Sn & [26] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Interfacial intermetallic compound (IMC) layers between SAC/Substrate after reflow [10]. (Reused with permission). Figure 2: Schematic diagram of microstructure in the as-reflowed Sn3.0 Ag0.5 Cu/Cu solder joints, with solder diameter ranging from 200 to 760 u\(\overline{7}\). (**a**) Eutectic structure in a 200 u\(\overline{\text{m}}\) diameter solder joint; (**b**) pseudo-eutectic structure in a 500 u\(\overline{\text{m}}\) diameter solder joint; (**c**) pseudo-eutectic structure in a 760 u\(\overline{\text{m}}\) diameter solder joint. The IMC layer in a thinner or smaller solder joint is usually thicker than that in a solder joint with a larger volume. [PERSON] et al. [27] studied the effect of gap size in solder joints on the microstructure at the interfaces of Ni/Sn/Cu and Cu/Sn/Cu using single-lap specimens, and showed that the gap size has a more significant effect on IMC thickness at the Ni/Sn interface than at the Cu/Sn interface. [PERSON] et al.