Analytical model for adhesive die-attaching subjected to thermal loads using second-order beam theory

In this work, an analytical model for adhesive die-attaching under thermal loads is proposed. The second-order beam theory is employed to model the die and substrate, so the shearing deformations can be evaluated more accurately comparing to models based on the Timoshenko beam theory and interface compliance. Then, governing equations are solved by Fourier series with the elastic foundation for the adhesive layer. As such, numerical calculations for eigenvalues are avoided, and explicit closed-form solutions are obtained. Based on the analytical model, effects of material properties and dimensions on the thermal deformation in the die are discussed. In the die, the longitudinal expansion and transverse warpage induced by thermal deformation both decrease with decreasing Young's modulus of adhesive. The longitudinal expansion decreases with increasing die thickness. However, the transverse warpage increases with increasing die thickness.