多原子极性晶体中表面激子的自陷条件

SELF-TRAPPING CONDITION OF SURFACE EXCITON IN POLYATOMIC POLAR CRYSTALS

本文研究多原子极性晶体中表面激子的性质,采用微扰法导出表面激子的有效哈密顿量.在计及反冲效应中不同波矢的声子之间的相互作用时,讨论对电子、空穴间的相互作用势、表面激子的自陷能和自陷条件的影响.

The properties of exciton in the surface layer of crystals influence the optical properties of the crystals very remarkably. In recent years, many scholars [1-2] discussed the properties of the surface exciton. Most polar crystals are diatomic. In these crystals there is one mode of the longitudinal optical (LO) phonon . However, a large number of polar crystals, with several atoms per unit cell, have more than one LO phonon branch. In recent years the polar on problem with many LO phonon branches has been studied [3-4] . However, the exciton in polyatomic polar crystals has not been investigated so far. The ground state energy of a weak, intermediate and strong coupling exciton in polyatomic polar crystals has been obtained by means of perturbation and linear -combination-operator method by one of authors [5-6] . Recently the effective Hamiltonian of the surface exciton in polyatomic polar crystals was derived by using perturbation method by author[7] . When we consider the interaction between phonons of different wave vector in the recoil process, the influence on effective potential between the electron and the hole, the self-trapping energy and the self -trapping condition are discussed.The Hamiltonian of a polyatomic surface exciton -phonon system isWe introduce two unitary transformations U1 and U2. In the Hamil-tomian (?),(?)0 and (?)ex are the unperturbed parts and ((?)1+(?)2+(?)ex1+ (?)ex2)is a perturbing term in the perturbation calculations. We calculated the effective Hamiltonian of the surface excitonThe results are represented as follows 1. Screening potential energyThe interaction potential betwean electron and hole, which is induced by the interaction of them with surface optical phonon acted as screen. The interaction potential isTo explain more crearly the relationship of V1(pppppppppppppp) and V2,(pppppppp), we discuss only shows the variation of the functions f1 and Ti(p) with distance p between electron and hole. From the figure one can see that the functions f1 and Ti(ppppppppppp) decrease with incre-asing distance is proportional to p-1 approximately,when This indicates that interaction potential of a Wannier exciton is Coulombic.2. Self-trapping energy and self -trapping condition The self-trapping energy of the surface exciton isThe self -trapping ranges of the exciton are when . The exciton is self-trapped for arbitrary value