EXISTENCE OF AN EXCITON BOUND TO AN IONIZED DONOR IMPURITY IN SEMICONDUCTOR QUANTUM CRYSTALLITES

We study the influence of the quantum confinement on the stability of an exciton bound to an ionized hydrogenic donor impurity placed at the centre of a semiconductor spherical quantum well as a function of the sphere radius R and of the mass ratio sigma of the electron and hole. We assume infinite conduction and valence band offsets and use the envelope function approximation. We compare the ground state energy of the complex, obtained within the variation method, to that of the most stable dissociation product : a hole and a neutral donor. It appears, that in opposition to the 3D-case, where the complex is unstable for sigma > 0.426, it remains stable for R1(sigma) < R < R2(sigma), where R1(sigma)/a(D) congruent-to 2 - 5 and R2(sigma)/a(D) > 20, a(D) being the 3D donor Bohr radius. If sigma < 0.426, it is stable for R > R1(sigma). However the complex is unstable for any value of sigma if R < R1(sigma).