  Wannier-Mott excitons in a semiconductor layered superlattice (SL) of period
much smaller than the 2D exciton Bohr radius in the presence of a longitudinal
external dc electric field directed parallel to the SL axis are investigated
analytically. The exciton states and the optical absorption coefficient are
derived in the tight-binding and adiabatic approximations. Strong and weak
electric fields providing spatially localized and extended electron and hole
states, respectively, are studied. The dependencies of the exciton states and
the exciton absorption spectrum on the SL parameters and the electric field
strength are presented in an explicit form. We focus on the fine structure of
the ground quasi-2D exciton level formed by the series of closely spaced energy
levels adjacent for higher frequencies. These levels are related to the
adiabatically slow relative exciton longitudinal motion governed by the
potential formed by the in-plane exciton state. It is shown that the external
electric fields compress the fine structure energy levels, decrease the
intensities of the corresponding optical peaks and increase the exciton binding
energy. A possible experimental study of the fine structure of the exciton
electroabsorption is discussed.
