The binding energies of a hydrogenic impurity located at the center and off-center of a multilayered quantum wire (MLQW) are studied within the framework of the effective-mass approximation. The MLQW consists of a GaAs core wire coated by a Al_(x)Ga_(1-x)As cylindrical shell and embedded in the bulk Al_(y)Ga_(1-y)As. It is found that for a small wire radius, the ground state binding energy of hydrogenic impurity located at the center of a MLQW behaves very differently from that of a single-layered QW. Our calculation shows that the binding energy depends on the potential profiles, potential barrier height, impurity position, shell thickness and the difference between the Al concentration contained in the shell region and bulk regions. Our trial function is also used to reproduce the binding energies of a hydrogenic impurity located at the center of a single-layered QW. Good agreement with the previous results is obtained. Therefore, our trial wave function is suitable for single-layered and multilayered QW systems.
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