Shallow-donor states in spherical quantum dots with parabolic confinement
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Shallow-donor states in spherical quantum dots with parabolic confinement C. A. Duque1, N. Porras-Montenegro2, M. de Dios-Leyva3, and L. E. Oliveira4 Instituto de Física, Universidad de Antioquia, AA 1226, Medellín, Colombia 2 Departamento de Física, Universidad del Valle, AA 25360, Cali, Colombia 3 Dept. of Theoretical Physics, Univ. of Havana, San Lazaro y L, Vedado, 10400, Havana, Cuba 4 Instituto de Física, Unicamp, CP 6165, Campinas, São Paulo, 13083-970, Brazil
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ABSTRACT The evidence of a parabolic potential well in quantum wires and dots was reported in the literature, and a parabolic potential is often considered to be a good representation of the “barrier” potential in semiconductor quantum dots. In the present work, the variational and fractionaldimensional space approaches are used in a thorough study of the binding energy of on-center shallow donors in spherical GaAs-Ga1-xAlxAs quantum dots with potential barriers taken either as rectangular [ Vb (eV) = 1.247 x for r > R ] or parabolic [ Vb (r ) = β 2 r 2 ] isotropic barriers. We define the parabolic potential with a β parameter chosen so that it results in the same E 0 groundstate energy as for the spherical quantum dot of radius R and rectangular potential in the absence of the impurity. Calculations using either the variational or fractional-dimensional approaches both for rectangular and parabolic potential result in essentially the same on-center binding energies provided the dot radius is not too small. This indicates that both potentials are alike representations of the quantum-dot barrier potential for a radius R quantum dot provided the parabolic potential is defined with β chosen as mentioned above. INTRODUCTION Quantum-dot heterostructures are most studied both from the theoretical and experimental point of view due to the wide possibility of applications in electronic and optoelectronic devices [1]. Such semiconductor nanostructures show interesting physical properties due to the extreme degree of confinement of electrons and holes, and the presence of impurities of course modify both the optical and transport properties of such nanostructures. For impurities in quantum dots, the ultimate goal is an artificial atom whose properties can be controlled through the material parameters and geometry. Using variational and fractional-dimensional space approaches, Porras-Montenegro and Pérez-Merchancano [2] and Oliveira et al. [3] have calculated the binding energy for shallowdonor impurities in rectangular GaAs-(Ga,Al)As quantum dots for both finite and infinite potential confinement. As a general feature, they have found that the binding energy increases as the radius of the dot is diminished and then decreases to the three dimensional limit of the bulk in the case of finite potential confinement, whereas the binding energy always increases with the diminishing of the radius of the dot when the potential confinement is infinite. The evidence of a parabolic potential well in quantum wires and dots was reported in the literature [4, 5], and a para
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