Recently

with the quick development of nanofabrication technology to material

the physical cha-racteristics of low dimensional material have aroused great interest.The electron energy spectrum of such quantum dot is fully quantized.Such systems are of great interest in fundamental studies

as well as in practical application for microelectronic devices.Electron-phonon interaction

which plays an important role in electronic and optical properties of polar crystalline materials in three dimensions

will have pronounced effects in low-dimensional systems as well.The properties of polaron in quantum dot have been studied by many theoretical and experiment methods.Zhu and Gu studied the ground state and self-energy of the weak-coupling polaron in a quantum dot by using the second order Rayleigh-Sch rdinger perturbation theory.Using the Fock approximation of Matz and Burkey

Lepine and Bruneau discussed the effect of an anisotropic confinement on the ground state energy of a polaron in a parabolic quantum dot.Mukhopadhyay and Chatterjee investigated the polaronic corrections to the first excited state energy of an electron in a parabolic quantum dot using a canonical transformation method based on the L.L.P.G formation.Li and Zhu investigated the strong coupling polaron in a parabolic quantum dot by the Landau-Pekar variational treatment.It is shown that both the polaron binding energy and the average number of virtual phonons around the electron decrease with increasing the effective confinement length.The results indicate that the polaronic effects are more pronounced in quantum dots than those in two-dimensional and three-dimensional cases.With the use of variational approach

the effects of the bulk-LO phonon on the impurity binding energy in a GaAs quantum dot are studied by Es-sbai

et al

.Upon using a curvilinear coordinates system

Cantele

et al

.calculated the effective mass for a particle confined in an ellipsoidal quantum dot.Xie proposed a procedure to calculate the polaron effect of

D

-

centers in quantum dots with a parabolic laternal confining potential by using the method of few-body physics.The properties of the polaron in a parabolic quantum dot are investigated by using a linear combination operator method by the present author and co-workers.However

so far research of the polaron in a quantum dot only was restricted to the approximation and calculation where the interaction between phonons of different wave vectors in the recoil process is neglected.The ground state energy of the polaron in parabolic quantum dot is derived by using a linear combination operator and perturbation methods.Considering interaction between phonons of different wave vectors in the recoil process

the influence on the ground state energy of polaron in quantum dot is discussed.Numerical calculations shown that the ground state energy of polaron in quantum dot will increase strongly with decreasing the effective confinement length and ground state energy will decrease with increasing the electron-LO phonon coupling strength.When

l

0

＜1.4

the interaction between phonons can not be ignored in a parabolic quantum dot.