Analysis of concentration dependent interdiffusion coefficient during TLP bonding of copper with germanium powder
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Date
2022-04-24
Authors
Sada, Hassan
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Abstract
Transient liquid phase (TLP) bonding has evolved to be an attractive technique for joining difficult-to-weld structural materials. In this study, copper (Cu) substrates are TLP bonded with germanium (Ge) powder to examine the effects of holding time and bonding temperature on the process kinetics. Deviation from parabolic behavior is observed when the width of the isothermal solidification (ISW) is plotted against √t, which is in contrast to what is generally expected. To explain this deviation, a newly developed analytical method is used to calculate the concentration-dependent interdiffusion coefficient, D=F(C) at different holding times and bonding temperatures. In contrast to the common assumption that D=F(C) is an isothermally constant material parameter, the results show that it changes with time, which is attributable to diffusion-induced stress/strain, and this can explain the observed deviation from parabolic behavior.
Furthermore, it is observed that for all time durations, the rate of isothermal solidification as well as the concentration-averaged diffusivity, D_ave, reduces as temperature increases from 960ºC to 1040ºC. This observation contradicts what is expected based on the classical Arrhenius relationship where diffusivity increases with temperature. The anomalous behavior observed in this work is attributable to the fact that diffusion coefficient largely increases with concentration and, the concentration range of Ge in Cu reduces with increases in temperature above the Cu-Ge eutectic temperature. In contrast, Arrhenius relationship does not consider the dependence of diffusivity on solute concentration at a given temperature and how the concentration range changes with temperature. Therefore, contrary to general expectations, this study shows that diffusivity can indeed decrease with an increase in temperature during TLP bonding and this can cause prolongation of the time required to complete the process. The experimentally observed reduction in the calculated diffusivity values with increases in temperature during TLP bonding is being reported for the first time in the present work.
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Keywords
TLP bonding, Deviation, Parabolic behavior, Concentration dependent interdiffusion coefficient, Concentration averaged diffusivity, Isothermal solidification rate