Direct Observation of Energy-Gap Scaling Law in CdSe Quantum Dots with Positrons

CdSe quantum dot samples with sizes in the range of 1.8-∼6 nm in diameter were examined by positron annihilation spectroscopy. The results were compared to data obtained for single-crystal bulk CdSe. Evidence is provided that the positrons annihilate within the nanospheres. The annihilation line shape shows a smearing at the boundary of the Jones zone proportional to the widening of the band gap due to a reduction in the size of the quantum dots. The data confirm that the change in the band gap is inversely proportional to the square of the quantum dot diameter