Field and size dependence of exciton–LO-phonon interaction in a semiconductor quantum dot

We theoretically study the exciton–LO-phonon interaction in a semiconductor quantum dot in the presence of an electric field. The confinement potential of the dot in the direction of the field is assumed to be a quantum well with various barrier heights while that in the direction transverse to the field is modeled by a parabolic form. The adiabatic approximation is employed to treat the effect of LO phonon. A trial wave function with a parameter describing the electron-hole correlation is used in the calculation of the ground-state energy of the exciton by the variational method. The magnitude of the exciton–LO-phonon interaction energy $|E_{\mathrm{e}\mathrm{x}-\mathrm{p}\mathrm{h}}|$ and the corresponding Huang-Rhys factor S are evaluated as functions of field strength and the size of the quantum dot for different barrier heights. With the field strength, the separation between electron and hole is enhanced and thus $|E_{\mathrm{e}\mathrm{x}-\mathrm{p}\mathrm{h}}|$ increases. Moreover, lowering of the barrier height further increases the separation, resulting in greater values of $|E_{\mathrm{e}\mathrm{x}-\mathrm{p}\mathrm{h}}|.$ With a fixed strength of field, the increase of size of the quantum dot leads to both delocalization of wave packets for electrons and holes and an increase of their separation simultaneously. Consequently the size dependence of $|E_{\mathrm{e}\mathrm{x}-\mathrm{p}\mathrm{h}}|$ is complicated. For comparison, an additional calculation is performed for a quantum dot with the shape of a cylindrical disk and barrier of infinite height in all directions and the contrast feature is discussed.