Excitonic complexes in one dimensional nanostructures

Author: Nino Zurashvili
Keywords: exciton, nanostructures, nanotube, nanowire, biexciton
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Over the last few decades, the optical properties of nanoscale objects have been intensively investigated. The reason for this is the size dependence of electronic structure and connected to this the possibility of engineering optical parameters in a wide range. The excitons are main intrinsic emitters in short wavelength region in semiconductors and therefore, optimization of excitonic emission is very important for emitting device fabrication. Gallium oxide is very promising for optical-electronics material due to its ultra-high band gap. We present a theoretical approach to calculate the electronic state of excitons and biexciton in gallium oxide nanowires (NW) and nanotubes in the framework of the effective-mass model using the Born-Oppenheimer approximation. We consider the formation of excitons and biexcitons under the action of both the lateral confinement and the Coulomb potential. The analytical expressions for the binding energy and eigenfunctions of the excitons and biexciton are obtained in dependence on system geometry. The approach is based on the fact that the confinement effect is stronger than the Coulomb term. The Coulomb term is significant only along nanowire/nanotube axes (z-axes). That is why to calculate exciton states in the presence of space confinement we averaged the Coulomb potential over the lateral (perpendicular to nanowire/nanotube axes) wave functions of electrons and holes. This procedure reduces the dimensionality of Coulomb potential to one, and the 1D Schrödinger equation is solved in the frame of variational technique. Having known single exciton states biexciton states are calculated using Born-Oppenheimer approximation. The calculations reveal strong dependence of binding energy of excitons and biexcitons on geometrical size for nanowires as well as for nanotubes.