Calculation Of Exciton In Semi-Conductor Nanostructure

The research work in this dissertation is surpported by National High Technology Research and Development Program of China (Grant No. 2009AA03Z405),the National Natural Science Foundation of China (Grant Nos.60644004,60908028,60971068,10979065 and 10947150).The optical characters of exciton in nanostructure play important role in the fields of optoelectronic device based on nanostructure semiconductor nanostructrue. This thesis is organized with the theories and mathematical methods in the field of semiconductor nanostructure and exciton.The exciton bind energy in quantum dots and quantum wires are analyzed.Firstly, based on effective mass approximation, we establish the geometrical model for InAs/GaAs pyramidal quantum dots,and obtain the electronic structure of quantum dots by using Finite Element Method. The numberical relationship of the energy level of the quantum dots and the geometry size of the quantum dots is quantitatively analyzed.Based on Hartree self-consistent field approximation, we establish the geometrical model of InAs/GaAs cylindrical quantum dots,and calculate the exciton energy in quantum dots.Iterative method is used in the computation of self-consistent effective field.The relationship between the exciton energy of quantum dots and the geometry size of quantum dots and is analyzed.The one-dimension quantum physical model of InAs/InP quantum wires is established.Because of the strong confinement of the 3D(x-y directions) of quantum wires,we are allowed to separate of z motion from that in the xy-plane.The strain effects on the band structure of the quantum wires are considered.We obtain the exciton's binding energy in one-dimension quantum wires by solving the one-dimension Schrodinger equation on Z direction.The behavior of the exciton binding energy in quantum wires with the growing length of the exciton is analyzed.We build a model for coupled double quantum wires,and calculate the energy of the electron and energy of the hole in coupling double quantum wires by using finite element method.The influence of coupling on the energy of the electron and the energy the hole in double quantum wires is analyzed in both vertical and horizontal coupling model.The behavior of the binding energy of the exciton in coupling double quantum wires with growing length is analyzed.Based on the convolution theorem, we could calculate the Coulomb integrals quickly and efficiently by using the method of fast Fourier transformation.