Numerical Simulation Study of Temperature Gradient Transient Liquid Phase Bonding with Concentration-Dependent Diffusivity

Abstract

A new numerical model is developed to study the kinetics of temperature gradient transient liquid phase (TG-TLP) bonding under concentration-dependent diffusivity by using a first-order implicit–explicit finite-difference numerical method and Landau coordinate transformation with adaptable spatial discretization. The model is validated with experimental data reported in the literature. The results of computational analysis by the new model show that the presence of solute concentration gradient in the liquid is the major factor that enables shorter solidification completion time in TG-TLP bonding compared to the conventional transient liquid phase bonding (C-TLP bonding). In contrast to the common assumption that solid-state diffusion can be ignored during the modeling of TG-TLP bonding, this work shows that solid-state diffusion plays a significant role, not only in controlling the transition in solidification behavior from bidirectional to unidirectional, but also affects the kinetics of the bonding process. Moreover, it is found that the anomalous increase in solidification completion time with increase in temperature that occurs during C-TLP bonding can be avoided by TG-TLP bonding. This is possible if the solute concentration gradient in the liquid is sufficiently high to enable adequate solidification kinetics to overcome increased volume of liquid that accompanies increase in bonding temperature.