Model structure for D- states in GaAs-(Ga,Al)As quantum wells

A simple model in which both electrons of the shallow-negative donor D- are instantaneously localized approximately at the same distance with respect to the ion nucleus is considered. Within this model, the D- Hamiltonian bec omes separable, and the effect of the electron-electron interaction is esse ntially taken into account by the interaction of each of the electrons with a renormalized-nucleus effective charge which depends on the angle between the two electron vector positions. The trial function is taken as a produc t of two three-parameter one-particle wave functions to calculate the groun d state energy as a function of the angle. Theoretical results for the D- e nergy including zero-point energy corrections within the harmonic approxima tion, are obtained for D- states centered in GaAs-(Ga,Al)As quantum wells a s a function of the well width, and for different values of the magnetic fi eld, applied perpendicular to the interfaces of the heterostructure. Our re sults are in good agreement with experimental data and with theoretical cal culations using variational or Monte Carlo techniques.