Size effect model on kinetics of interfacial reaction between Sn-xAg-yCu solders and Cu substrate

The downsizing of solder balls results in larger interfacial intermetallic compound (IMC) grains and less Cu substrate consumption in lead-free soldering on Cu substrates. This size effect on the interfacial reaction is experimentally demonstrated and theoretically analyzed using Sn-3.0Ag-0.5Cu and Sn-3.5Ag solder balls. The interfacial reaction between the Sn-xAg-yCu solders and Cu substrates is a dynamic response to a combination of effects of interfacial IMC growth, Cu substrate consumption and composition variation in the interface zone. A concentration gradient controlled (CGC) kinetics model is proposed to explain the combined effects. The concentration gradient of Cu at the interface, which is a function of solder volume, initial Cu concentration and reaction time, is the root cause of the size effect. We found that a larger Cu concentration gradient results in smaller Cu6Sn5 grains and more consumption of Cu substrate. According to our model, the growth kinetics of interfacial Cu6Sn5 obeys a t(1/3) law when the molten solder has approached the solution saturation, and will be slower otherwise due to the interfering dissolution mechanism. The size effect introduced in this model is supported by a good agreement between theoretical and experimental results. Finally, the scope of application of this model is discussed.