Quantum-size effects on the band edge of CdTe clusters in glass

The measurement of quantum-size behavior in semiconductor crystals has been examined through an analysis of the size dependence of the semiconductor’s absorption edge. In past studies, there appeared to be little agreement between theory and experiment for very small crystals. In this paper, the effects of crystal-size distribution and tunneling of the carrier wave functions into the quantum well barrier are considered. An analysis of the microstructure size and absorption edge of CdTe clusters in a glass matrix is conducted with samples ranging from 0.16 to 0.8 times the exciton Bohr diameter at the Γ point and from 1 to 5 times the exciton Bohr diameter at the L point. Results show fully coupled exciton behavior at the L point and a more complex process at the Γ point. In the latter, the band-gap energy increase with decreasing cluster size is significantly smaller than that calculated using a model in which the photoexcited carriers are assumed to be confined to a monosize set of clusters bounded by an infinite potential well. Analysis presented here shows that this discrepancy can be explained in part by inhomogeneous broadening of the absorptive transition and by carrier penetration into the insulator. The quantum-size behavior of CdTe crystals at the Γ point is subsequently found to follow fully decoupled carrier behavior modeled by Efros and Efros [Sov. Phys. Semicond. 16, 772 (1982)] when the inhomogeneous broadening and tunneling effects are taken into account.