Size-dependent band gap of colloidal quantum dots

The size-dependent band gap of semiconductor quantum dots is a well-known and widely studied quantum confinement effect. In order to understand the size-dependent band gap, different theoretical approaches have been adopted, including the effective-mass approximation with infinite or finite confinement potentials, the tight-binding method, the linear combination of atomic orbitals method, and the empirical pseudopotential method. In the present work we calculate the size-dependent band gap of colloidal quantum dots using a recently developed method that predicts accurately the eigenstates and eigenenergies of nanostructures by utilizing the adiabatic theorem of quantum mechanics. We have studied various semiconductor (CdS, CdSe, CdTe, PbSe, InP, and InAs) quantum dots in different matrices. The theoretical predictions are, in most cases, in good agreement with the corresponding experimental data. In addition, our results indicate that the height of the finite-depth well confining potential is independent of the specific semiconductor of the quantum dot and exclusively depends on the matrix energy-band gap by a simple linear relation.