Coherent resonant tunnelling in an impurity quantum well in the presence of electric and strong magnetic fields

Abstract

A further development is described of an analytical approach to the problem of an impurity electron (or hole) in a quantum well (QW) subject to electric and strong magnetic external fields both directed perpendicular to the hetero-planes. Previous results for an impurity centre at the edge of a QW are extended to the case in which the impurity is located at any position in the QW. It is shown that, as in the edge case, the combined potential acting on the electron (or hole) resembles that of a double quantum well. One effective well is formed by the Coulomb potential and the QW boundary closest to the impurity. A second effective well is formed by the electric field potential and the other boundary of the QW. Analytical expressions for the energy levels of the impurity are obtained. When the levels associated with the two effective QWs anti-cross, the impurity single QW can be treated as a resonant structure. The explicit dependencies of the resonant splitting upon the width of the QW, the magnitudes of the electric and magnetic fields and the position of the impurity centre are obtained. Estimates of the expected splitting and frequency of the emitted radiation relevant to the inter-well oscillations of the electron are made using typical values associated with GaAs QWs.