Q-BOR–FDTD method for solving Schrodinger equation for rotationally symmetric nanostructures with hydrogenic impurity

An efficient method inspired by the traditional body of revolution finite-difference time-domain (BOR-FDTD) method is developed to solve the Schrodinger equation for rotationally symmetric problems. As test cases, spherical, cylindrical, cone-like quantum dots, harmonic oscillator, and spherical quantum dot with hydrogenic impurity are investigated to check the efficiency of the proposed method which we coin as Quantum BOR-FDTD (Q-BOR-FDTD) method. The obtained results are analysed and compared to the 3-D FDTD method, and the analytical solutions. Q-BOR-FDTD method proves to be very accurate and time and memory efficient by reducing a three-dimensional problem to a two-dimensional one, therefore one can employ very fine meshes to get very precise results. Moreover, it can be exploited to solve problems including hydrogenic impurities which is not an easy task in the traditional FDTD calculation due to singularity problem. To demonstrate its accuracy, we consider spherical and cone-like core-shell QD with hydrogenic impurity. Comparison with analytical solutions confirms that Q-BOR–FDTD method is very efficient and accurate for solving Schrodinger equation for problems with hydrogenic impurity

The Influence of Hydrostatic Pressure on the Binding Energy of Hydrogenic Impurity State in a Wurtzite AlyGa1-yN/AlxGa1-xN Parabolic Quantum Well

The influence of hydrostatic pressure on the binding energy of hydrogenic impurity state in a wurtzite AlyGa1-yN/AlxGa1-xN parabolic quantum well and GaN/AlxGa1-xN square quantum well are studied using the variational method. The ground-state binding energies are presented as the functions of hydrostatic pressure, well width, composition and impurity center position. The anisotropic properties of the parameters in the system, and the changes (dependence) of electron effective mass, the dielectric constant, band gap with pressure and coordinate are considered in the numerical calculations. The results show that the hydrostatic pressure has obvious influence on the binding energy. The binding energy increase slowly with increasing the hydrostatic pressure p and the composition x, while the binding energy decrease significantly with increasing the well width and the position of impurity center. It is seen that the changing trends of the binding energy as a function of well width, pressure and the composition in the AlyGa1-yN/AlxGa1-xN parabolic quantum well are basically the same with that in the GaN/AlxGa1-xN square quantum well, but the changing trends of the binding energy as a function of impurity center position in the AlyGa1-yN/AlxGa1-xN parabolic quantum well are significantly greater than that in the GaN/AlxGa1-xN square quantum well.

First-excited-state energy of hydrogenic impurity bound polaron in an anisotropic quantum dot in an electric field

The first-excited-state (ES) binding energy of hydrogenic impurity bound polaron in an anisotropic quantum dot (QD) is obtained by constructing a variational wavefunction under the action of a uniform external electric field. As for a comparison, the ground-state (GS) binding energy of the system is also included. We apply numerical calculations to KBr QD with stronger electron–phonon (E–P) interaction in which the new variational wavefunction is adopted. We analyzed specifically the effects of electric field and the effects of both the position of the impurity and confinement lengths in the xy-plane and the [Formula: see text] direction on the ground and the first-ES binding energies (BEs). The results show that the selected trial wavefunction in the ES is appropriate and effective for the current research system.