Stability of D ^– in quantum wells under strong magnetic fields

Abstract

We study the donor position dependence of the ground state binding energy of an off-center D − in a quantum well in the presence of a magnetic field applied in the heterostructure growth direction. In contrast to previous studies, we consider a model in which the correlation in the z direction induced by the Coulomb interaction is not neglected. We suggest that the confinement in the plane perpendicular to the growth axis produced by the strong magnetic field not only decreases the in-plane distance between the electrons, but also increases the effects of electron-electron and electron-ion correlation along the z-axis lowering the system total energy. In the framework of this model the ground state binding energy of an off-center D − within a GaAs-(Ga, Al)As quantum well as a function of the magnetic field is calculated. We have found that the binding energy increases monotonically with increasing magnetic field for any donor position, and consequently the ground state is always bound. Our results shows that the previously predicted D

Charged donors in quantum dots: Finite difference and fractional dimensions results

“…which describes a hydrogenlike atom in a space with an effective fractional dimensionality. 17,19 To obtain the corresponding D 0 energy levels, we solve this equation by using the trigonometric sweep method. 23 The advantage of the procedure explained above lies in the fact that all information about any anisotropy of the system (confinement due to the heterostructure and/ or magnetic field) is contained in the Jacobian J m ͑r͒, which is known analytically.…”

“…13 Such an approach was previously applied to the neutral ͑D 0 ͒ and charged ͑D − ͒ systems in a QW. 19,20 The method of fractional-dimensional space was used to study shallow donor impurities and excitons in quantumconfined semiconductor structures. [16][17][18] In this approach the anisotropic problem in a three-dimensional environment is mapped to an isotropic one in a lower effective fractionaldimensional space, where the dimension is related to the anisotropy introduced both by the heterostructure barrier poten-tial and the magnetic field.…”

“…Recently, a new method was introduced in the study of the ground state of neutral ͑D 0 ͒ and charged donors ͑D − ͒ in QWs and QDs. 19,20 In this procedure, the D 0 and D − systems in semiconductor heterostructures were reduced to similar ones in an isotropic effective space with a nonfixed fractional dimension. Subsequently, a threeparameter Hylleraas trial function was used to solve the renormalized Schrödinger equation for the D − system.…”