Abstract
In this paper, numerical experiments are conducted to explore quantum scattering, resonant tunneling, and decay probability along with transmission and reflection coefficients. Finite element method is used with Ben Daniel-Duke boundary conditions which are applied on the interfaces and Dirichlet and Neumann boundary conditions on outer boundaries. We have accomplished a study in which barrier width is changed from 1nm to 6 nm by keeping dot width constant 10nm. Al<sub>x</sub>Ga1-<sub>x</sub>As with concentration of 0.32 and bandgap (E<sub>g</sub> (Γ)) of 1.84 eV is used. GaAs with bandgap (E<sub>g</sub> (Γ)) of 1.42 is used as barrier material. The total width is 40 nm. The wave functions of the electrons penetrate through the quantum wells using time-independent Schrödinger equation are calculated and applied on the GaAs/Al<sub>x</sub>Ga<sub>1-x</sub>As quantum well to see the behaviors of wave functions in resonant tunneling, scattering and their total decay probabilities by changing width of barrier. The Hamiltonian is calculated by effective mass approximation and finite element method is used to find the energies and potential well. Four studies are set up to discuss different aspects related to the proposed structure. First, the eigen energies are solved for the quasi-bound states using an eigenvalue study, with open boundary conditions for outgoing waves at both ends of the modeling domain. Then, the time evolution of one of the quasi-bound states is solved in a time-dependent study. Next, the resonant tunneling condition is solved in an eigenvalue study, with a special type of open boundary condition for incoming waves on one end of the modeling domain. Finally, the transmission and reflection coefficients are computed using a stationary study, with regular open boundary conditions and a prescribed incoming wave from one end of the modeling domain. The eigen energies can be computed analytically using the transfer matrix method. The time evolution of the quasi-bound states wave functions as the initial condition.
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