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Different growth orientations influence the mechanical properties and behavior of quantum dots, due to the anisotropy of elasticity and surface energy of the material. In this paper, the relations of the strain energy, strain relaxation energy and free energy to growth orientation are analyzed for the self-assembled InAs/GaAs semiconductor quantum dots, based on finite element method of cubic elasticity theory. The results show that the strain relaxation of the (211) quantum dots is biggest, and that of the (100) quantum dots is smallest. These can provide the theoretical basis for the growth of quantum dots in a controlled fashion.
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Keywords:
- quantum dots /
- growth orientation /
- equilibrium morphology /
- strain relaxation
[1] Romanov A E, Petroff P M, Speck J S 1999 Appl. Phys. Lett. 74 2280
[2] Klimov V I 2003 Los Alamos Science 28 214
[3] Shchukin V A, Bimberg D 1998 J. Phys. Lett. A 67 687
[4] Wang Z G 2000 Acta Phys. Sin. 45 643 (in Chinese) [王占国 2000 物理学报 49 643]
[5] Wu Z Q,Wang B 2001 Growth of Thin Films (1st Ed.) (Beijing: Science Press) (in Chinese) [吴自勤, 王兵 2001 薄膜生长(第一版) (北京: 科学出版社)]
[6] Zhao F A, Zhang C L, Wang Z G 2004 Acta Phys. Sin. 53 249 (in Chinese) [赵凤嫒, 张春玲, 王占国 2004 物理学报 53 249]
[7] Wang W Q, Shen Z Y, Bai Y J Y, Hou S M, Zhao X Y, Liu W M, Xue Z Q 2003 Vacuum Science And Technology (China) 23 231 (in Chinese) [万维强, 申自勇, 柏亚军, 侯士敏, 赵兴钰, 刘维敏, 薛增泉 2003 真空科学与技术 23 231]
[8] Niu Z H, Ren Z W, HE Z H 2008 Acta Photonica Sinica 37 1107
[9] Ulloa J M, Koenraad P M, Gapihan E, Létoublon A, Bertru N 2007 Appl. Phys. Lett. 91 3106
[10] Makeev M A, Yu W B, Madhukar A 2004 J. Phys. Lett. 96 4429
[11] Glas F 2003 Phys. Solid State B 237 599
[12] Ni Y, He L H, Song J 2004 Surf. Sci. 553 189
[13] Benabbas T, Androussi Y 1999 J. Phys. Lett. 86 1945
[14] Zhou W M, Cai C Y, Yin S Y, Wang C Y 2008 Appl. Surf. Sci. 10 1016
[15] Grundmann M, Christen J, Ledentsov N N, Böhrer J, Bimberg D 1995 Phys. Rev. Lett. 74 4043
[16] Liu H Y, Xu B, Chen Y H 2000 J. Phys. Lett. 88 5433
[17] Freund L B, Suresh S 2003 Thin film materials: stress, defect formation, and surface evolution (1st Ed.) (UK: Cambridge University Press)
[18] Chen G, Liao L J 2007 Crystal Physics (2nd Ed.) (Beijing: Science Press) p27 (in Chinese)[陈纲, 廖理几 2007 晶体物理学基础(第二版) (北京: 科学出版社)第27页]
[19] Liu P, Zhang Y W, Lu C 2003 Phys. Rev. B 68 195341
[20] Zhang C H 2008 ANSYS12.0 (3nd Ed.) (Beijing: China Machine Press) (in Chinese) [张朝晖 2008 ANSYS12.0 (第三版) (北京: 机械工业出版社)]
[21] Budiman R A, Ruda H E 2000 J. Phys. Lett. 88 4586
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[1] Romanov A E, Petroff P M, Speck J S 1999 Appl. Phys. Lett. 74 2280
[2] Klimov V I 2003 Los Alamos Science 28 214
[3] Shchukin V A, Bimberg D 1998 J. Phys. Lett. A 67 687
[4] Wang Z G 2000 Acta Phys. Sin. 45 643 (in Chinese) [王占国 2000 物理学报 49 643]
[5] Wu Z Q,Wang B 2001 Growth of Thin Films (1st Ed.) (Beijing: Science Press) (in Chinese) [吴自勤, 王兵 2001 薄膜生长(第一版) (北京: 科学出版社)]
[6] Zhao F A, Zhang C L, Wang Z G 2004 Acta Phys. Sin. 53 249 (in Chinese) [赵凤嫒, 张春玲, 王占国 2004 物理学报 53 249]
[7] Wang W Q, Shen Z Y, Bai Y J Y, Hou S M, Zhao X Y, Liu W M, Xue Z Q 2003 Vacuum Science And Technology (China) 23 231 (in Chinese) [万维强, 申自勇, 柏亚军, 侯士敏, 赵兴钰, 刘维敏, 薛增泉 2003 真空科学与技术 23 231]
[8] Niu Z H, Ren Z W, HE Z H 2008 Acta Photonica Sinica 37 1107
[9] Ulloa J M, Koenraad P M, Gapihan E, Létoublon A, Bertru N 2007 Appl. Phys. Lett. 91 3106
[10] Makeev M A, Yu W B, Madhukar A 2004 J. Phys. Lett. 96 4429
[11] Glas F 2003 Phys. Solid State B 237 599
[12] Ni Y, He L H, Song J 2004 Surf. Sci. 553 189
[13] Benabbas T, Androussi Y 1999 J. Phys. Lett. 86 1945
[14] Zhou W M, Cai C Y, Yin S Y, Wang C Y 2008 Appl. Surf. Sci. 10 1016
[15] Grundmann M, Christen J, Ledentsov N N, Böhrer J, Bimberg D 1995 Phys. Rev. Lett. 74 4043
[16] Liu H Y, Xu B, Chen Y H 2000 J. Phys. Lett. 88 5433
[17] Freund L B, Suresh S 2003 Thin film materials: stress, defect formation, and surface evolution (1st Ed.) (UK: Cambridge University Press)
[18] Chen G, Liao L J 2007 Crystal Physics (2nd Ed.) (Beijing: Science Press) p27 (in Chinese)[陈纲, 廖理几 2007 晶体物理学基础(第二版) (北京: 科学出版社)第27页]
[19] Liu P, Zhang Y W, Lu C 2003 Phys. Rev. B 68 195341
[20] Zhang C H 2008 ANSYS12.0 (3nd Ed.) (Beijing: China Machine Press) (in Chinese) [张朝晖 2008 ANSYS12.0 (第三版) (北京: 机械工业出版社)]
[21] Budiman R A, Ruda H E 2000 J. Phys. Lett. 88 4586
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