Taking into account the interaction of an electron with bulk longitudinal-optical(LO) and surface longitudinal-optical(SO) phonons
we studied the effective mass of the bound polaron in a polar slab by using the method of Green's function.The effective mass was derived as function of slab thickness
and it reduces with the increase of the slab thickness;for a very thin slab(d<5 nm)
the effective mass was mainly attributed to the electron-SOphonon interaction
oppositely
d>10 nm
the effective mass was mainly attributed to the electron-LO phonon interaction.But when 5nm<d<10 nm
all of them must be consider together.Especially
the effective mass increased when there was the Coulomb potential because the interactions between the electrons and phonons was strengthened.