B样条函数基在半导体微晶量子尺寸效应研究中的应用

Application of B-spline Function Bases in the Investigation of Quantum Size Effects of the Semiconductor Crystallites Quantum Dots

用有效质量近似模型来描述微晶CdS和CdSe系统中激子的行为,考虑到介电常数在量子点内外的不同,展示B样条函数基在构成激子波函数中的优越性,讨论激子的基态能量随量子点半径变化的量子尺寸效应.将计算结果与实验结果及其他理论计算结果进行比较,计算结果表明:用B样条函数基构成激子波函数是十分成功的,计算激子的能量与实验符合得很好;当同种量子点处在不同环境时,不仅势垒高度和库仑相互作用能不同,而且激子的有效质量也不同;有效质量近似模型可以很好地描述激子的基态能量的量子尺寸效应.

The Bspline function bases is used in the calculation of the exciton ground state energy based on the effective mass approximation (EMA) model. The difference of the dielectric constant between the inside and the outside of the dots is taken into account. Exciton energies as a function of the dots radii are calculated and compared with experimental and other theoretical data. The comparison shows:This method with Bsplines bases leads to good results of the excition energy which are in good agreement with experimental data in the all the regions than others.It is found that the different material surrounding of dots affects both potential energy and Coulomb interaction energy of the system,and the effective messes.The effective mass approximation model can very well describe the behaviors of the excitons confined in the dots.