Taking into account the interaction of an electron with bulk longitudinal-optical (LO) and surface longitudinal-optical (SO) phonons

we study the ground state energy and self-trapping energy of the bound polaron in a polar slab by using the Huybrecht's linear combination operator method. The ground state energy and the self-trapping energy are all derived as function of slab thickness. Etre-ph includes two parts

one is

E

e-LO

tr

the other is

E

e-SO

tr

and

E

e-SO

tr

also includes two parts

E

e-SO

tr

(+) and

E

e-SO

tr

(-);taking KCl as an example

E

e-LO

tr

increases with the increase of the slab thickness

but

E

e-SO

tr

E

e-ph

tr

and λ all reduce with the increase of the slab thickness

and when the slab thickness d is more than 5 nm

E

e-ph

tr

is about to a stable number. Especially

vibration frequency (λ) increases when there is the Coulomb potential

because of the interactions are strengthened between the electrons and phonons.