对称与非对称应变双量子阱中电子与空穴的本征态
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摘要
本文考虑自发与压电极化引起的内建电场,基于常微分数值计算方法,求解纤锌矿GaN/Al_(0.2)Ga_(0.8)N对称和非对称应变双量子阱中,电子与空穴的薛定谔方程,得到电子与空穴的本征能量和相应本征波函数。计算结果表明:对比对称及非对称势阱情形时,得到电子(空穴)基态和第一激发态能级均随阱宽的增大而减小;且非对称双量子阱结构中波函数向另一阱中的遂穿效应有所增加,相应能级略高于对称双阱中的计算结果。同时调整左边和右边2个势阱的宽度或者单独调整某一势阱宽度时,电子(空穴)的基态和第一激发态能级均随相应阱宽的增加而减小。
The Schr?dinger equations of electron and hole in the GaN/Al_(0.2)Ga_(0.8)N wurtzite nitride strained symmetry and asymmetry double quantum well are solved to obtain the eigen-states based on the numerical computation of ordinary differential equations. The built-in electric field induced by spontaneous and piezoelectric polarization is considered. The results show that, in both the symmetry and asymmetry double quantum wells, the eigen-state energy levels of electron and hole decrease with increasing of the well width. In the asymmetry double quantum wells, the tunneling effect of the wave functions to the barrier layer is enhanced and then the corresponding eigen energies are lager than the results in the symmetry one. Under the adjustments of the left and right well widths at the same time or the single well thickness alone, all the first and second energy levels decrease with the increasing of the well widths.
The Schr?dinger equations of electron and hole in the GaN/Al_(0.2)Ga_(0.8)N wurtzite nitride strained symmetry and asymmetry double quantum well are solved to obtain the eigen-states based on the numerical computation of ordinary differential equations. The built-in electric field induced by spontaneous and piezoelectric polarization is considered. The results show that, in both the symmetry and asymmetry double quantum wells, the eigen-state energy levels of electron and hole decrease with increasing of the well width. In the asymmetry double quantum wells, the tunneling effect of the wave functions to the barrier layer is enhanced and then the corresponding eigen energies are lager than the results in the symmetry one. Under the adjustments of the left and right well widths at the same time or the single well thickness alone, all the first and second energy levels decrease with the increasing of the well widths.
引文
[1] Salem L D,Montemayor R.Modified ricatti approach to partially solvable quantum Hamiltonians:Finite laurent-type potentials [J].Phys.Rev.A,1991,43:1169-1182.
[2]Barclay D T.New exactly solvable hamiltonians:Shape invariance and self-similarity[J].Phys.Rev.A,1993,48:2786-2797.
[3]李培咸,郝跃,范隆,张进城,张金凤,张晓菊.基于量子微扰的AlGaN/GaN异质结波函数半解析求解[J].物理学报,2003,52 (12):2985-2988.
[4]Kalliakos S,Lefebvre P,Taliercio T.Nonlinear behavior of photo absorption in hexagonal nitride quantum wells due to free carrier screening of the internal fields [J].Phy s.Rev.B,2003,67:205307.
[5]哈斯花,班士良.电子-空穴气屏蔽影响下有限深量子阱中电子与空穴的本征态[J].内蒙古大学学报 (自然科学版),2007,38(3):272-277.
[6]郭海峰,哈斯花,朱骏.应变GaN/AlxGa1-xN量子阱中电子的跃迁能量[J].功能材料,2011,II(42):241-244.
[7]Perlin P,Gorczyca I,Suski T,et al.Influence of pressure on the optical properties of InxGa1-xN epilayers and quantum structures[J].Phys.Rev.B,2001,64(11):115319.
[8]Nardelli M B,Rapcewicz K,Bernholc.Strain effects on the interface properties of nitride semiconductors[J].Phys.Rev.B,1996,55(12):7323-7326.
[2]Barclay D T.New exactly solvable hamiltonians:Shape invariance and self-similarity[J].Phys.Rev.A,1993,48:2786-2797.
[3]李培咸,郝跃,范隆,张进城,张金凤,张晓菊.基于量子微扰的AlGaN/GaN异质结波函数半解析求解[J].物理学报,2003,52 (12):2985-2988.
[4]Kalliakos S,Lefebvre P,Taliercio T.Nonlinear behavior of photo absorption in hexagonal nitride quantum wells due to free carrier screening of the internal fields [J].Phy s.Rev.B,2003,67:205307.
[5]哈斯花,班士良.电子-空穴气屏蔽影响下有限深量子阱中电子与空穴的本征态[J].内蒙古大学学报 (自然科学版),2007,38(3):272-277.
[6]郭海峰,哈斯花,朱骏.应变GaN/AlxGa1-xN量子阱中电子的跃迁能量[J].功能材料,2011,II(42):241-244.
[7]Perlin P,Gorczyca I,Suski T,et al.Influence of pressure on the optical properties of InxGa1-xN epilayers and quantum structures[J].Phys.Rev.B,2001,64(11):115319.
[8]Nardelli M B,Rapcewicz K,Bernholc.Strain effects on the interface properties of nitride semiconductors[J].Phys.Rev.B,1996,55(12):7323-7326.