An exciton in a quantum well in the presence of crossed electric and magnetic fields

An analytical approach to the problem of the Wannier-Mott exciton in a semi conductor quantum well (QW) in the presence of external magnetic and electr ic fields is developed. The magnetic field is taken to lie in the heteropla nes while the electric field is directed perpendicular to the heteroplanes. Explicit dependencies of the energy levels and wavefunctions of the excito n on the magnitudes of the fields for a wide range of the width of the QW a re obtained. For the narrow QW, the results are valid for arbitrary electro n and hole effective masses. In the case of intermediate and wide QWs, the adiabatic approximation implying the extreme difference of the electron and hole masses is used. In the intermediate QW, the states of the relative mo tion are the standard Coulomb states affected by the external fields while the states of the centre of mass are the size-quantized states in the QW. W e focus particularly on the delocalized states caused by the external elect ric field and the motion of the excitons centre of mass in the magnetic fie ld. These states are localized far away from the Coulomb centre, A strong i nfluence of the boundaries of the wide QW on the delocalized exciton states is found to occur. Estimates of the expected values are made using-typical parameters associated with GaAs QW. (C) 1999 Academic Press.