对于离散在本底介质中的纳米晶体量子点,考虑表面极化效应,通过像电荷法建立极化势能项,应用微扰法求解激子的薛定谔方程,得到了与本底介电系数直接相关的量子点带隙解析表达式.对不同本底中尺寸依赖的量子点带隙、第一吸收峰波长、第一吸收峰波长移动进行的计算表明,表面极化效应对量子点的带隙和第一吸收峰波长有明显的影响.随着本底介电系数的增大,量子点的带隙减小,第一吸收峰波长红移.量子点在不同本底中的第一吸收峰波长移动会在某个固定粒径达到最大值,最大值对应的粒径取决于量子点种类.%The surface polarization energy that arises from the difference in dielectric coefficient between the quantum dot (QD) and the background medium is investigated by the equivalent image charge method. A general expression for the bandgap of QD depending on the dielectric coefficient of background medium is presented by solving the exciton Schr?dinger equation with the perturbation method. As examples, the sizedependent bandgaps, bandgap shifts, absorption-peak wavelengths and absorption-peakwavelength shifts of PbSe, PbS and CdSe QDs doped in different background media are determined in detail. There is evidence to show that the effects of surface polarization on the bandgap and the first absorption-peak wavelength of QD are considerable. The bandgap decreases with the increase of dielectric coefficient of background medium, which causes the absorption-peak wavelength to be red shifted. The effect of surface polarization on the bandgap depends substantially on the sign and value of image charge. When the dielectric coefficient of QD is greater than that of background medium, the absorption-peak wavelength comes to blue shift due to surface polarization of QD. On the contrary, the absorption-peak wavelength comes to redshift. The absorption-peak wavelength shifts of QDs doped in different background media will reach a maximum in a certain diameter depending on the kind of QD.
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