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.

In the present work, the case of a spherical quantum dot with parabolic confinement subjected to an external electric field with the presence of an impurity, the linear and third-order nonlinear optical absorption coefficients as well as refractive index changes have been calculated. The numerical method we are using for the calculation of the energy levels and the corresponding wave functions is the potential morphing method in the effective mass approximation. As our results indicate an increase of the electric field and/or the position of the impurity and/or the quantum dot radius redshifts the peak positions of the total absorption coefficient and total refractive index changes. Additionally, an increase of the position of the impurity and/or the quantum dot radius decreases the total absorption coefficient and increases the total refractive index changes. An increase also of the electric field decreases the total absorption coefficient but does not significantly affect the peak values of the total refractive index changes. Finally, an increase of the optical intensity considerably changes the total absorption coefficient as well as the total refractive index changes.

The electronic structure of a spherical quantum dot with parabolic confinement that contains a hydrogenic impurity and is subjected to a DC electric field is studied. In our calculations we vary the position of the impurity and the electric field strength. The calculated electronic structure is further used for determining the nonlinear optical rectification coefficient of the quantum dot structure. We show that both the position of the impurity and the strength of the electric field influence the nonlinear optical rectification process.

We study the electronic and optical properties of ZnO quantum dots within the atomistic empirical pseudopotential framework. The highest occupied molecular orbital (HOMO) is found to be of orbital P character for structures larger than 2.6 nm in diameter. We identify the origin of this unconventional situation in the electronic character of the HOMO state, originating from an even mixture of the A- and B-bands of the Wurtzite band structure. This situation, however, does not lead to an orbitally dark exciton ground state, as one might expect. Coulomb interactions lower the bright (electron-S−hole-S) exciton below the orbitally forbidden (electron-S−hole-P) exciton to recover the conventional situation of an orbitally allowed, but spin-forbidden, exciton ground state and a Stoke’s shift originating from electron−hole exchange interactions.

No abstract