Size and surface-dependent phase transition temperature in Cu2Se nanobridges

The critical phase transition temperature (Tc) of Cu₂Se thermoelectric nanomaterials has been a focal point of extensive research, yet the quantification of surface energy on Tc is frequently ignored. In this paper, we systematically investigate the impact of both the width/thickness and surface configuration of Cu₂Se nanobridges (NBs) on Tc. We find that the Tc decreases with size reduction, which becomes particularly accelerated when the size decreases to a few nanometers. Additionally, the NBs with higher energy surfaces exhibit lower Tc. Then we propose an optimized thermodynamic model to quantify the combined effect of size and surface energy on Tc in Cu₂Se NBs, which provides an approach to predict Tc in Cu₂Se and other thermoelectric nanomaterials. Our study facilitates the understanding of the dependence of Tc on size and surface in Cu₂Se, with an eye towards the stable room temperature thermoelectric applications of Cu₂Se nanomaterials.