Electronic properties of two dimensional semiconducting Nano-systems, by using few numerical approaches: meshless, finite element and finite difference methods
In this paper, we have studied the electronic structure of few two dimensional semiconducting nano-systems by suing three numerical methods meshless, finite element and finite difference. These methods .have been used to solve the two dimensional stationary Schrodinger equation w and the results have been compared. In order to solve the applied problems in the computational semiconducting quantum electronics, it is usually needed to solve the two dimensional stationary Schrodinger equation which have special numerical complexities. Evaluation of the energy eigenvalues is a challenging problem in this field of study. Here, by applying the methods on five applied examples we have shown that the eigenvalues converge to the exact values from lower bound in the finite difference method and converge to the exact values from upper bound in the finite element method. Therefore, in general applied problems under research, that we have not analytic eigenvalues and solutions, we are confidently able to find the upper and lower bounds of the eigenvalues. Finally, we have shown that in the mentioned examples, the meshless method has maximum accuracy among the investigated methods.
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The effect of the geometrical parameters and composing materials type on the bandgap width of two-dimensional phononic crystals
Mehdi Solaimani *, Parisa Mahmoodi
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