Correlation between the band gap expansion and melting temperature depression of nanostructured semiconductors

The band gap and melting temperature of a semiconductor are tunable with the size and shape of the specimen at the nanometer scale, and related mechanisms remain as yet unclear. In order to understand the common origin of the size and shape effect on these two seemingly irrelevant properties, we clarify, correlate, formulate, and quantify these two properties of GaAs, GaN, InP, and InN nanocrystals from the perspectives of bond order-length-strength correlation using the core-shell configuration. The consistency in the theoretical predictions, experimental observations, and numerical calculations verify that the broken-bond-induced local bond contraction and strength gain dictates the band gap expansion, while the atomic cohesive energy loss due to bond number reduction depresses the melting point. The fraction of the under-coordinated atoms in the skin shell quantitatively determines the shape and size dependency. The atomic under-coordination in the skin down to a depth of two atomic layers inducing a change in the local chemical bond is the common physical origin