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Q-BOR–FDTD method for solving Schrödinger equation for rotationally symmetric nanostructures with hydrogenic impurity
Type Article
Q-BOR–FDTD method, energy eigenvalue, eigenfunction, low dimensional semiconductor structures, symmetric nanostructures
An efficient method inspired by the traditional body of revolution finite-difference time-domain (BOR-FDTD) method is developed to solve the Schrödinger 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 3D FDTD method, and the analytical solutions. Q-BORFDTD method proves to be very accurate and time and memory efficient by reducing a threedimensional 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-shellQDwith hydrogenic impurity. Comparison with analytical solutions confirms that Q-BOR–FDTD method is very efficient and accurate for solving Schrödinger equation for problems with hydrogenic impurity
Researchers arezoo firoozi (First researcher) , Ahmad Mohammadi (Second researcher) , reza khordad (Third researcher) , Tahmineh Jalali (Fourth researcher)