Exciton-tunneling-lifetime enhancement by the Coulomb interaction in a quantum well with a perpendicular field

The tunneling lifetime of an exciton in a semiconductor quantum well in the presence of a perpendicular electric field is calculated by using the Wentzel-Kramers-Brillouin method. The confining effect of the electron-hole Coulomb interaction is included for the first time. An effective one-dimensional Schrödinger equation describing the motion of each carrier (electron or hole) relative to the well is constructed from the variational solution of the exciton ground state. For quantum wells with small band offsets, the carrier lifetime against tunneling out of the well is significantly enhanced by the Coulomb interaction. Numerical results are in qualitative agreement with the recent experiment on ZnSe/${\mathrm{Zn}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Se heterostructures.