Optical transitions in semiconductor quantum dots: Three pseudopotential models

The calculations of this paper try to explain the electronic transitions of semiconductor nanocrystals, also called quantum dots, with three different Hamiltonian approximations. In the first approximation, spectral shifts of the lowest absorption energy were computed for spherical quantum dots with the wurtzite and zinc-blende crystal types; and the wurtzite quantum dot spectral shifts were much closer to the experimental results than the effective mass model. No actual quantum dot wave-functions were computed in that approximation.; For the second model, energy eigenvalues of a quantum dot Hamiltonian, consisting of a plane-wave semiconductor pseudopotential inside the quantum dot and a spherical barrier outside the quantum dot, were computed numerically with a real-space basis. The surface boundary conditions prevented the removal of surface states from the band gap region.; For the third model, excitation energies for wurtzite, spherical ZnS and CdSe quantum dots in the range of 40–4000 atoms were calculated using atom centered empirical pseudopotentials and a real-space basis. The energies are compared to experiments and other pseudopotential models. For ZnS quantum dots, squared transition dipole sums were computed efficiently, without the need for full wavefunctions of the excited states; and some transition dipole calculations include the effects of an approximate electron-hole Coulomb potential. Squared transition dipole sums from the highest energy linear dipole-like valence states to the lowest excited state were computed as a function of dot size. The model predicts that the per atom dipole transition sum decreases with quantum dot size for those transitions. The mixing of even and odd angular components and charge asymmetry of the wavefunctions affect the dipole transition strengths. The total oscillator strength for the lowest energy transition region increases with size at small radii. We examined the role of wavefunction angular momentum for transitions to conduction band surface states.