Based on model of Huybrechts strong-coupling polaron

the ground state energy of the system

in which the excitons interact with both the weak-coupling bulk longitudinal-optical(LO) phonons and strong-coupling interface-optical(IO) phonons in a polar crystal

is studied by using the Lee-Low-Pines variational method

the self-trapping energy and the induced potential of the excitons are derived.The results are shown as following:1.The self-trapping energy of the excitons is composed of two parts.One part is the polaron effects resulting from the exciton-LO phonon interaction

the other part is induced by the exciton-IO phonon interaction.The self-trapping energy E

e

h-LO

tr

which is produced by the interaction between the exciton and LO-phonon

will increase with increasing the coordinate z

it tends to a constant finally.The self-trapping energy E

e

h-IO

tr

which is induced by the interaction between the exciton and IO-phonon

will increase with decreasing the coordinate

especially near the interface

the decrease in z will lead to drastic increase in E

e

h-IO

tr

.It is indicated that near the interface

the contribution of the electron-IO phonon interaction to the self-trapping energy of the excitons is dominant

whereas the exciton in the bulk far from the interface

the contribution of the electron-LO phonon interaction to the self-trapping energy of exciton is dominant.The influence of the distance ρ between the electron and hole on the self-trapping energy E

e

h-IO

tr

is also remarkable.E

e

h-IO

tr

will increase with increasing ρ.With ρ increasing

the decrease in coordinate z will lead to drastic increase in E

e

h-IO

tr

.2.The induced potential of the excitons is also composed of two parts

one part is the polaron effects produced by the interaction between the exciton and LO phonons

the other part is induced by the exciton-IOphonon interaction.The variation law of the induced potential V

e

h-LO

and V

e

h-IO

resulting from the exciton-LO phonon and exciton-IO phonon interaction

respectively

is agreement with the variation law of the induced potential produced by the weak-coupling exciton-LO phonon interaction in 3D polar crystal and the strong-coupling exciton-SO phonon interaction in 2D polar crystal respectively.The influence of the coordinate of the exciton on the induced potential V

e

h-IO

and V

e

h-IO

is notable.V

e

h-LO

increases with increasing the coordinate z.With z increasing

the increase in the distance ρ between the electron and hole will lead to drastic decrease in V

e

h-LO

.The induced potential V

e

h-IO

decreases with increasing z.With z decreasing

the decrease in ρ will lead to drastic increase in induced potential V

e

h-IO

.The results show that the influence of the surface and interface phonon in polar crystal can not be neglected.It is especially important for the polar slab

quantum well and heterostructures

in which the carriers are both strong-coupling with surface or interface optical phonon and weak-coupling with bulk longitudinal optical phonon.