Shallow-impurity states of semiconductor Fibonacci superlattices

A theoretical study of shallow-donor states of GaAs-(Ga,Al)As semiconducting quasiperiodic Fibonacci superlattices is presented. The impurity states are calculated using different variational methods within the parabolic-band model and effective-mass approximation. We deal with periodic superlattices having a Fibonacci sequence of GaAs and (Ga,Al)As layers as unit cells, the size of these sequences being of increasing order. The binding energy and effective mass associated with the Is-like shallow-impurity states of these systems show a dependence on the donor position in the superlattices, which reflects the self-similarity and quasiperiodicity of the Fibonacci superlattices. We present a detailed explanation of the Fibonacci structures of the binding energies as a function of the impurity position in the superlattice and introduce a one-dimensional effective Coulomb potential that should be useful in the study of shallow-impurity states of Fibonacci superlattices, and other quasiperiodic semiconducting heterostructures, under the action of external electric and/or magnetic fields.