Theoretical prediction for the band gap of semiconductor nanoparticles as function of bond number

Taken bond number as the only parameter, an unified model for the size-dependent band gap Eg(D) of semiconductor nanoparticles is established in this work, with D being the particle size. As expected, the band gap increases with size dropping, and the success of the model is confirmed not only by the results of single elemental Si nanoparticles but also by the II-VI semiconductor compounds nanoparticles even in full size range. Based on the bond number of cubooctahedron which is used to describe the shape of the nanoparticles in this work, a good agreement between the model predictions and experimental, first-principle calculation results is obtained. Since there is no other adjustable parameter, the established model presents a possible way to predict the band gap of other nanostructure as long as its bond number is known.