Electron–hole pairs binding energies in quantum wires and quantum dots

In a previous paper, we have calculated the binding energies for excitons in quantum wells [A. Simões Baptista, H. Santos, Microelectron. Eng. 43–44 (1998) 481–487]. This was done by solving simultaneously the Schrödinger and the Poisson equations, which determine the interaction potential, both in a fractional dimensional space [F.H. Stillinger, J. Math. Phys. 18 (6) (1977) 1224–1234]. Using the same mathematical framework, we now analyse the so-called one-dimensional and zero-dimensional structures. The results we obtain are essential for simulations of optical-electronic devices that use the optical absorption and the refractive index dispersion curves.