With the advance in the nanofabrication technology

there has been a great deal of interest in the investigating of quasi-zero-dimensional electronic systems(quantum dots).Since its newly opto-electric and electron transport characteristics

it is becoming a heat field in the study of quantum fanctional device.Many investigators studied the properties of the polaron in a quantum dots in many aspects by a variety of theoretical and experimental methods.Recently

the properties of strong and weak-coupling of the polaron in an asymme-tric quantum dot have been studied using the linear-combinating operator method by the present authors.However

using improved linear combination operator method

the properties of the polaron in an asymmetric quantum dot has not been investigated so far.In this paper

the properties of the vibrational frequency and the interaction energy of weak-coupling polaron in an asymmetric quantum dot were studied by using a improved linear combination operator and unitary transformation method.The relations of the vibrational frequency and the interaction energy of the weak coupling polaron in an asymmetric quantum dot with the transverse and the longitudinal effective confinement length of the quantum dot and the electron-phonon coupling strength are derived.If the units have been chosen in the usual polaron units(2m=

h

=ω

LO

=1)

we perform a numerical calculation.The results show that the vibrational frequency and the interaction energy of the weak coupling polaron in an asymmetric quantum dot will increase strongly with decreasing the transverse and longitudinal effective confinement length of quantum dot.Those attributed to interesting quantum size effects also appear.The interaction energy of weak coupling polaron in an asymmetric quantum dot will decrease with increacing the electron-phonon coupling strength.