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分别采用单带重空穴近似和六带Kronig-Penney模型, 对垂直耦合锗量子点在不同耦合距离下的空穴态特性进行了计算, 并探讨了自旋-轨道的相互作用对空穴态对称性的影响. 计算结果表明: 多带耦合的框架下, 随着量子点垂直间距的增大, 空穴基态从成键态转变为反键态, 而且价带基态能级和第一激发态能级发生反交叉现象, 这与单带模型下得到的相应结果存在较大差异. 通过分析六带模型计算得到的成、反键态波函数, 轻、重空穴态和自旋-轨道分裂态对特征空穴态波函数的贡献比例随着量子点垂直间距的增大发生了转变, 并最终导致量子点空穴基态波函数由成键态转变为反键态.The two lowest single-particle hole states in the vertically coupled Ge/Si double layer quantum dots are investigated numerically by using the single-band heavy hole effective mass approximation and six-band Kronig-Penney model, respectively. The calculated results indicate that within the frame of several-band coupled model, the bonding-antibonding ground-state transition and a bonding-antibonding energy anti-crossover phenomenon are observed with interdot distance increasing. These results have not been observed previously in those single-band model calculations. The analysis of the wavefunction component of bonding-antibonding hole state shows that the contribution ratios of light, heavy and spin-orbital-split-off hole states to the characteristic hole wavefunction vary with the increase of the vertical coupled distance, resulting in the ground state wavefunction changing from bonding states to antibonding ones finally.
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Keywords:
- coupled quantum dots /
- hole states /
- bonding-antibonding states /
- spin-orbit
[1] Liu W C, Guo B L, Wu X S, Zhang F M, Mak C L, Wong K H 2013 J. Mater. Chem. A 1 3182
[2] Bimberg D, Grundmann M, Ledentsov N N 1999 Quantum Dot Heterostructures (Vol. 471973882) (Chichester: John Wiley) pp299-302
[3] Coleman J J, Young J D, Garg A 2011 J. Lightwave Technol. 29 499
[4] Hu Y, Kuemmeth F, Lieber C M, Marcus C M 2011 Nat. Nanotechnol. 7 47
[5] Chen K H, Chien C Y, Li P W 2010 P Nanotechnology 21 055302
[6] Cuadra L, Martí A, Luque A 2004 Thin Solid Films 451 593
[7] Kechiantz A M, Kocharyan L M, Kechiyants H M 2007 Nanotechnology 18 405401
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[9] Luque A, Martí A, Stanley C 2012 Nat. Photon. 6 146
[10] Melnik R V N, Willatzen M 2004 Nanotechnology 15 1
[11] Shadi D 2012 M. S. Dissertation (Waterloo: University of Waterloo)
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[14] Yakimov A I, Bloshkin A A, Dvurechenskii A V 2010 Phys. Rev. B 81 115434
[15] Tang N Y 2013 Acta Phys. Sin. 62 57301 (in Chinese) [汤乃云 2013 62 57301]
[16] Planelles J, Climente J I, Rajadell F, Doty M F, Bracker A S, Gammon D 2010 Phys. Rev. B 82 155307
[17] Zhang X G, Wang C, Lu Z Q, Yang J, Li L, Yang Y 2011 Acta Phys. Sin. 60 096101 (in Chinese) [张学贵, 王茺, 鲁植全, 杨杰, 李亮, 杨宇 2011 60 096101]
[18] Yang J, Wang C, Jin Y X, Li L, Tao D P, Yang Y 2012 Acta Phys. Sin. 61 016804 (in Chinese) [杨杰, 王茺, 靳映霞, 李亮, 陶东平, 杨宇 2012 61 016804]
[19] Wang H P, Ke S Y, Yang J, Wang C, Yang Y 2014 Acta Phys. Sin. 63 098104 (in Chinese) [王海澎, 柯少颖, 杨杰, 王茺, 杨宇 2014 63 098104]
[20] Dai X Y, Yang C, Song J J, Zhang H M, Hao Y, Zheng R C 2012 Acta Phys. Sin. 61 137104 (in Chinese) [戴显英, 杨程, 宋建军, 张鹤鸣, 郝跃, 郑若川 2012 61 137104]
[21] Liu E K, Zhu B S, Luo J S 2011 The Physics of Semiconductors (Vol. 7) (Beijing: Electronics Industry Press) p385 (in Chinese) [刘恩科, 朱秉升, 罗晋生2011 半导体物理学 (北京: 电子工业出版社) 第385页]
[22] Yuan F, Jiang Z, Lu F 2006 Appl. Phys. Lett. 89 072112
[23] Li X, Xu W, Cao S, Cai Q, Lu F 2007 Phys. Rev. B 76 245304
[24] Nenashev A V, Dvurechenskii A V, Zinovieva A F 2003 Phys. Rev. B 67 205301
[25] Bir G L, Pikus G E 1974 Symmetry and Strain-Induced Effects in Semiconductors (Vol. 624) (New York: Wiley) pp32-54
[26] Luttinger J M, Kohn W 1955 Phys. Rev. 97 869
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[1] Liu W C, Guo B L, Wu X S, Zhang F M, Mak C L, Wong K H 2013 J. Mater. Chem. A 1 3182
[2] Bimberg D, Grundmann M, Ledentsov N N 1999 Quantum Dot Heterostructures (Vol. 471973882) (Chichester: John Wiley) pp299-302
[3] Coleman J J, Young J D, Garg A 2011 J. Lightwave Technol. 29 499
[4] Hu Y, Kuemmeth F, Lieber C M, Marcus C M 2011 Nat. Nanotechnol. 7 47
[5] Chen K H, Chien C Y, Li P W 2010 P Nanotechnology 21 055302
[6] Cuadra L, Martí A, Luque A 2004 Thin Solid Films 451 593
[7] Kechiantz A M, Kocharyan L M, Kechiyants H M 2007 Nanotechnology 18 405401
[8] Luque A, Linares P G, Antolín E, Cánovas E, Farmer C D, Stanley C R, Martí A 2010 Appl. Phys. Lett. 96 013501
[9] Luque A, Martí A, Stanley C 2012 Nat. Photon. 6 146
[10] Melnik R V N, Willatzen M 2004 Nanotechnology 15 1
[11] Shadi D 2012 M. S. Dissertation (Waterloo: University of Waterloo)
[12] Yakimov A I, Bloshkin A A, Dvurechenskii A V 2008 Phys. Rev. B 78 165310
[13] Yakimov A I, Bloshkin A A, Dvurechenskii A V 2009 Semicond. Sci. Technol. 24 095002
[14] Yakimov A I, Bloshkin A A, Dvurechenskii A V 2010 Phys. Rev. B 81 115434
[15] Tang N Y 2013 Acta Phys. Sin. 62 57301 (in Chinese) [汤乃云 2013 62 57301]
[16] Planelles J, Climente J I, Rajadell F, Doty M F, Bracker A S, Gammon D 2010 Phys. Rev. B 82 155307
[17] Zhang X G, Wang C, Lu Z Q, Yang J, Li L, Yang Y 2011 Acta Phys. Sin. 60 096101 (in Chinese) [张学贵, 王茺, 鲁植全, 杨杰, 李亮, 杨宇 2011 60 096101]
[18] Yang J, Wang C, Jin Y X, Li L, Tao D P, Yang Y 2012 Acta Phys. Sin. 61 016804 (in Chinese) [杨杰, 王茺, 靳映霞, 李亮, 陶东平, 杨宇 2012 61 016804]
[19] Wang H P, Ke S Y, Yang J, Wang C, Yang Y 2014 Acta Phys. Sin. 63 098104 (in Chinese) [王海澎, 柯少颖, 杨杰, 王茺, 杨宇 2014 63 098104]
[20] Dai X Y, Yang C, Song J J, Zhang H M, Hao Y, Zheng R C 2012 Acta Phys. Sin. 61 137104 (in Chinese) [戴显英, 杨程, 宋建军, 张鹤鸣, 郝跃, 郑若川 2012 61 137104]
[21] Liu E K, Zhu B S, Luo J S 2011 The Physics of Semiconductors (Vol. 7) (Beijing: Electronics Industry Press) p385 (in Chinese) [刘恩科, 朱秉升, 罗晋生2011 半导体物理学 (北京: 电子工业出版社) 第385页]
[22] Yuan F, Jiang Z, Lu F 2006 Appl. Phys. Lett. 89 072112
[23] Li X, Xu W, Cao S, Cai Q, Lu F 2007 Phys. Rev. B 76 245304
[24] Nenashev A V, Dvurechenskii A V, Zinovieva A F 2003 Phys. Rev. B 67 205301
[25] Bir G L, Pikus G E 1974 Symmetry and Strain-Induced Effects in Semiconductors (Vol. 624) (New York: Wiley) pp32-54
[26] Luttinger J M, Kohn W 1955 Phys. Rev. 97 869
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