Magnetic-field effects on shallow impurities in semiconductor GaAs–(Ga,Al)As quantum wells and superlattices within a fractional-dimensional space approach

We have used the fractional-dimensional space approach to study the effects of applied magnetic fields on shallow-impurity states in GaAs–(Ga,Al)As quantum wells and superlattices. In this scheme, a semiconductor heterostructure is treated as isotropic in an effective fractional-dimensional space, and the value of the fractional dimension is associated to the degree of anisotropy introduced both by the heterostructure barrier potential and applied magnetic field. Theoretical fractional-dimensional calculations for shallow-impurity states in GaAs–(Ga,Al)As semiconductor quantum wells and superlattices, under magnetic fields applied along the growth direction, were shown to be in overall agreement with available experimental measurements and previous variational calculations.