Warpage variation analysis of Si/Solder/Cu layered plates subjected to cyclic thermal loading

Abstract

In cyclic thermal tests of Si/solder/OFHC-Cu (silicon/solder/oxygen-free high conductivity copper)-layered plates, the authors observed either the cyclic growth or cyclic recovery of warpage to occur depending on the heat treatment of the copper before soldering. In this study, the test results are numerically analyzed by assuming three material models for the solder and two material models for the copper. It is shown that the test results are reproduced well if proper material models are used in finite element analysis. It is revealed that the so-called multiaxial ratcheting was induced in the solder, while the uniaxial type of ratcheting or cyclic strain recovery occurred in the copper. As a result, the Armstrong and Frederick model is suggested to be valid for the multiaxial ratcheting in the solder at such low strain rates as in the cyclic thermal tests, whereas the Ohno and Wang model is shown to be appropriate for the copper. To confirm this unexpected result for the solder, the Armstrong and Frederick model is applied to the multiaxial ratcheting of another solder at three strain rates.