Numerical analysis of thermo-mechanical behavior of indium micro-joint at cryogenic temperatures

Microelectronic packaging plays an important role in cryogenic engineering; in particular, a solder joint as interconnection, which offers a mechanical, thermal and electrical support, undergoes much larger and harsher thermal changes during its service compared with conventional customer electronic products. The impact of thermo-mechanical properties of such solder joints under cryogenic service conditions becomes even more significant due to the continuing miniaturization of solder joints. Indium, a solder material with a low melting point and excellent cryogenic properties, has been favorable in various low temperature applications, in particular, to form solder joints for electronics interconnections. In order to understand the fundamental aspects of reliability of indium joints, this paper reports a constitutive model accounting for the effect of temperature change on thermo-mechanical behavior of indium joints. Especially, the model is used and subsequently implemented in a FE analysis to simulate a hybrid pixel detector system, in which indium micro-joints are manufactured to serve at cryogenic conditions. The response of indium joints to low-temperature cycling (300-76 K) was analyzed based on the proposed model, which not only offers a tool to understand the performance and experimental testing of solder joints under cryogenic temperatures, but can also be used for design optimization of the microelectronic package.