Identification of shallow-donor impurity states in GaAs/GaAlAs multi-quantum wells in moderate magnetic fields

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Abstract
Far infrared photoconductivity experiments have recently been reported on silicon-doped GaAs/GaAlAs multi-quantum well structures in magnetic fields of up to 8 T. The resulting spectra contain peaks which can be identified with transitions from the ground state to several higher excited states of a confined Si impurity. In this paper, details of a theoretical model are given which allow these transition energies to be predicted. The model is firstly used to determine transitions to states which are truly bound in the weak field limit. A set of hydrogen-like basis states is constructed in which the exponentials are expanded in terms of Gaussian-type functions in order to introduce some of the Landau-like behaviour required for large fields. Approximate eigenstates are then determined using a numerical diagonalization procedure. The possibility of transitions to states with m=2 is investigated, and mixing between basis states of different parity is allowed for in the case of impurities which are not located at the centre of a quantum well. These results are then used to determine the energies of so-called metastable state, which do not have a low-field counterpart. Transitions to these states are identified in the observed experimental data.