The binding energies of shallow donor impurities in GaAs-(Ga,Al)As coaxial quantum-well wires

Within the effective-mass approximation a simple method to calculate the spectra of a shallow-donor impurity in GaAs-(Ga, Al)As cylindrical quantum-well wires (QWWs) suitable for any confinement potential shape in radial direction is proposed. A trial function is taken as the product of a hydrogenic part with two envelope functions: the ground state wave function of the uncoupled electron in quantum-well wire f(k)(Q), and a variational function phi(z) that describes the orbit confinement in axial direction. A Schrodinger-type equation for phi(z) corresponding to the best trial function is deduced. The method is applied to analyze the DO ground and first excited states in coaxial cylindrical QWWs. Two peaks in the curve of the 1s-like state binding energy vs. the QWW radius are found.