平面波展开法计算电子态的影响因素

The influence factors of the plane wave method on calculating electron state

基于有效质量包络函数近似理论,利用平面波展开法计算了InGaN/GaN方形量子阱、圆柱形量子线、球形量子点3种纳米结构中的电子态,分析了纳米结构的尺寸、势垒宽度和平面波数量对计算结果的影响.结果表明:(1)电子和杂质的基态能随纳米结构尺寸的增加而减小.(2)势垒宽度取值太小时,不能很好的把电子和杂质的波函数限制在纳米结构中,基态能会随势垒宽度的变化而快速的变化;当势垒宽度太大时,纳米结构的尺寸相对较小,计算结果不准确;势垒宽度的取值在2 a和4a之间时,基态能稳定,计算结果精确.(3)电子和杂质的前3个能级随平面波数量的增加而趋于稳定,当平面波数量不小于133时,能级稳定.因此,利用平面波展开法计算低维纳米结构中的电子态时,势垒宽度和平面波数量可以分别取为2.5 a和153.

Within the framework of effective mass envelope function approximation,the plane wave method was used to calculate the electron state in InGaN/GaN nanostructures——square quantum well,cylindrical quantum wire,spherical quantum dots.The influences of nanostructure size,barrier width and plane wave number on calculation result were analyzed.The results show that ground state energies of electron and impurity decrease with the increase of nanostructure size.When the barrier width is too small,the wave function of electron or impurity can leak out of the nanostructure,so the ground state energy drops rapidly with the increase of barrier width.When the barrier width is too large,the size of the effective nanostructure is relatively small,the calculation results are inaccurate.When the barrier width is between 2 a and 4 a,the ground state energy remains stable.In addition,the first three energy levels of electron and impurity tend to be stable with the increase of plane wave number.When the plane wave number is no less than 133,they remain stable.Therefore,using the plane wave expansion method to calculate the electron state in the low-dimensional nanostructure,the barrier width and the plane wave number should be 2.5 a and 153,respectively.