Fig. 1: Screening criterion for barrier layers.

a The schematic model of IRL growth, taking Nb joint as the example. b The activation energy barrier of Sb migration (EMig) to neighboring Sb vacancy. c The correlated map of interfacial reaction energy (EIR) and activation energy barrier (EMig). Values of EIR and EMig are shown in Supplementary Table 1. The elements in the area (called sweet spot) with negative EIR and larger EMig (similar to or larger than Ti) are believed potential barrier layer candidates.