The finite element simulation for the shallow impurity in quantum dots

The finite element method (FEM) has been implemented in this paper to investigate the electronic state of shallow hydrogenic impurities in spherical GaAs (Al,As) quantum dots (SQDs) by taking into account the finite value of realistic potential barrier height. The nonlinear partial differential equations have been discretized by means of Galerkinʹs weighted residue method assuming a uniform partition and using a quadratic Lagrange basis function for each finite element of the physical domain considered. The impurity binding energies have been calculated numerically by solving the governing equations and compared with the variational method. The results we have obtained are in excellent agreement with those published in the literature.