Finite size and length effects on bandgap of CdSe nanorods

As an important property for designing optoelectronic devices, the bandgap E_g of nanorods is tunable with variety of sizes, D, and lengths, L. Unfortunately, the quantitative description of E_g(D, L) is still unavailable. To understand the underlying mechanism of the size and length effects on the bandgap of nanorods, based on size-dependent melting temperature model, a quantitative thermodynamic model without an adjustable parameter was established by considering the variation of the surface-to-volume ratio. Both the size and length have prominent effects on E_g(D, L), and E_g(D, L) increases with decreasing D and L, where the size confinement is stronger than the length confinement for the blue shift of E_g(D, L) due to the different effects of size or length on the A/V variation. The model prediction agrees well with the experimental results of CdSe nanorods. In addition, as the model expansion, for nanocrystals with different shapes, the size effect on the bandgap can be sequenced as follows: E_g(D, L) > E_g(D)_{nanoparticles} > E_g(D)_nanowires at L < D, while E_g(D)_{nanoparticles} > E_g(D, L) > E_g(D)_nanowires at L > D. The validity of the established model will improve the understanding of the bandgap variations and provide guidelines for designing optoelectronic devices.