抛物量子阱中束缚极化子的极化势和结合能

利用改进的Lee-Low-Pines(LLP)方法,用变分法计算了无限深抛物量子阱中同时考虑与体纵光学声子和界面纵光学声子相互作用的束缚极化子的极化势和结合能.数值计算得出:阱宽较大时极化势很小,阱宽较小时极化势较大,所以对于较窄的抛物阱必须考虑极化势.对于给定阱宽的抛物阱,随着远离阱中心极化势迅速减小,当到达阱的界面附近极化势又开始增大.阱宽较小时,束缚极化子的结合能随着阱宽L的增大而急剧减小;阱宽较大时,结合能减小的非常缓慢,最后接近体材料中的三维值.

Polarization Potential and the Binding Energy of a Bound Polaron in a Parabolic Quantum Well

The effect of the electron-phonon interaction on an electron bound to an impurity in a parabolic quantum well(PQW) has been studied theoretically in the past,but similar studies calculating the pola-rization potential in a PQW have not been reported.In this paper,the polarization potential and the binding energy of the bound polaron in the PQW are investigated.The study has taken the effect of bulk longitudinal optical(LO) phonons and the interface longitudinal optical(IO) phonons into account.By using the method of modified Lee-Low-Pines(LLP) variational method,the polarization potential and the binding energy of the bound polaron in the GaAs/Al_xGa_1-xAs PQW are obtained.The contribution of the impurity-phonon interaction to the total electron energy can be eliminated by the first canonical transformation,and the effect of this displacement on the lattice polarization leads to the polarization potential which partially compensates the electron-impurity Coulomb interaction.By the second canonical transformation,the ground state energy of the bound polaron in the infinite parabolic quantum well is worked out,and then the binding energy of the bound polaron can be gained by further calculations.The research results indicate that,the polarization potential is much smaller in the wider wells,but it is larger in the narrow wells,therefore,the polarization potential should not be neglected in the very narrow wells.For a given well width,the polarization potential decreases rapidly with increasing |z| and gets a minimum,then it increases with increasing |z| near the interface of the well.The contribution of the polarization potential to the ground state energy of the bound polaron decreases rapidly with increasing the well width(L) at first,and then decreases slowly with increasing L and approaches zero at large L.The binding energy of the bound polaron decreases rapidly with increasing L at the beginning,then decreases very slowly with increasing L and finally closes to the value of three-dimensional GaAs.In summary,the polarization potential should not be eliminated in a narrow PQW.