Modeling thermal stress in thin films produced by photonic curing

Abstract

A thermal stress model is developed to simulate stresses produced in the processing of thin film metal inks due to arbitrary time dependent temperature variations through the film stack. The current model employs and extends the method developed by Hsueh (2002), which models stresses in thin films where the temperature of each layer in the film stack was assumed to be uniform at a temperature different from the initial temperature. The model results in two integrals involving temperature distribution through the film stack. The thermal stress model developed is validated using two cases where analytical temperature solutions are available. The first is a constant surface heat flux on a single layer. The second is a constant surface temperature on a three-layer film stack. Both cases begin from an initial uniform temperature. The integrals appearing in the expressions for stress distributions are computed using the analytical solutions of the temperature distributions and are used to compute the stress distributions through the film stack. The analytical solutions are compared to numerical results produced by solving the transient heat conduction equation using a previously developed finite volume method. In the numerical solutions, the integrals involving temperature are approximated using the midpoint rule. The computed numerical results compare very well with the analytical solutions for both cases studied.