An Efficient Implementation of Polymer Viscoelastic Behavior Through a Pseudo Viscoelastic Model

Modeling of viscoelastic relaxation of polymer materials is important to understand the thermo-mechanical behavior of organic microelectronic systems. However, incorporation of viscoelastic behavior into numerical models makes the models compute-intensive. This paper presents a different technique to incorporate the polymer viscoelastic behavior into the numerical models such that the computation time is not adversely affected without compromising the accuracy of the results obtained. In the proposed “pseudo viscoelastic” modeling technique, the modulus of the viscoelastic material is computed as a function of time and temperature loading history outside of the finite-element simulation, and is then input into the simulation as a thermo-elastic material incorporating the viscoelastic relaxation of the material. This paper compares the warpage results obtained through the proposed technique against a complete viscoelastic simulation model and experimental data, and it is seen that the maximum warpage predicted using the proposed technique agree within 10% compared with the results obtained from a “full” viscoelastic model. Also, it is shown through some of our simulations that the proposed technique could result in a computational time saving of more than 50% and hard disk space saving of 65%.