The Bound Polaron In A Polar Slab

With the further development of the epitaxial technique and the the manufacture of the semiconductor materials, considerable interest has been shown in the investigation of the quantum well and semiconductor superlattice because of their wide application as techniques. consequently, understanding the role of impurities in a polar slab is of particular importance.In this article ,we studied some qualities of the bound polaron in a polar slab with two methods. One is Huybrecht,s linear combination operator method ,the other is Green,s function method.First, we studied the ground state energy of the system when there is a bounding potential and strong coupling with electron-surface optical phonons and weak coupling with electron-bulk longitudinal optical phonons in a slab of polar crystal by using the Huybrecht,s linear combination operator method. We deduced the variation law of the ground state energy ,the variation frequent contactsλ,the self-trapping energy with the slab thickness. And the numerical calculations for KCl crystal show that the variation frequent contactsλand the self-trapping energy are all reduce with the increase of the slab thickness. And the contributions of the interactions between the electron and the different branchs of phonons to the self-trapping energy are greatly difference.Next, we studied the same system by using the improved linear combination operator and the Lagrange multiplier method. We deduced the variation of the effective mass with the slab thickness. And the numerical calculations for KCl crystal show that the effective mass is reduced with the increase of the slab thickness. And the contributions of the interactions between the electron and the different branchs of phonons to the effective mass are greatly difference.At last, we studied the system when there is a coulomb , at the same time we consider the interaction between the electron-SO and the electron-LO by using the method of the Green,s function. We deduced the variation law of the self-trapping energy and the effective mass with the slab thickness. And the numerical calculations for KCl crystal show that the self-trapping energy and the effective mass are all reduced with the increase of the slab thickness.We also find that the effective mass andλall increased but the self-trapping energy decreased when there is a bounding potential.