Analysis of temperature effect on isothermal solidification completion time during transient liquid phase bonding

ABSTRACT

The occurrence of the anomalous behaviour of increased isothermal solidification completion time, $t_f$ with increasing temperature in transient liquid phase (TLP) bonding, is investigated for cases of one-dimensional and multi-dimensional migration of solid–liquid boundary, using a numerical model. The analysis shows that the anomalous behaviour is not restricted to the generally reported one-dimensional case but also occurs during multi-dimensional displacements of the solid–liquid interface. It is found that it is possible for isothermal solidification rate constant $(\mathrm{\varnothing })$ to increase with increasing temperature and yet $t_f$ increase. Instead of a mere increase in $\mathrm{\varnothing }$ with temperature, it is the extent of the increase that determines if $t_f$ will reduce with an increase in bonding temperature. Increase in $t_f$ with temperature occurs when the increase in $\mathrm{\varnothing }$ is inadequate to overcome the concomitant increase in the volume of liquid produced at a higher bonding temperature. Additionally, the study shows that in contrast to general expectation, an increase in temperature can cause the diffusion-controlled $\mathrm{\varnothing }$ to decrease, notwithstanding a concomitant increase in the solute diffusion coefficient. This unique condition also causes$t_f$ to increase with an increase in bonding temperature. The theoretical findings in this work are corroborated by experimental observations reported in the literature.

KEYWORDS:

• TLP bonding
• isothermal solidification
• bonding temperature
• interface migration
• isothermal solidification completion time
• isothermal solidification rate constant

Acknowledgements

The authors gratefully acknowledge the financial support by NSERC of Canada.

Disclosure statement

The authors declare no conflict of interest.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada.