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For the fabrication of particular nanostructures, Stranski-Krastanov (SK) growth mode driven by strain is most widely used. Meanwhile, another technique that is used to form the complex nanostructures is the droplet epitaxy technique, which is based on the deposition of group III element nanoscale droplets onto substrate and followed by the reaction with group V element for crystallization into III-V compound nanostructures. Droplet epitaxy technique is simple and flexible, and it does not require additional complicated processing and has potential to develop various quantum nanostructures. It, unlike standard MBE growth, exploits the sequential supply of group-III and group-V elements to form quantum nanostructures. Quantum rings are a special class of quantum-confinement structure that can be fabricated by the droplet epitaxy technique and have attracted wide attention due to the Aharonov-Bohm effect, which is specific to the topology of a ring. In this paper, GaAs/GaAs (001) concentric quantum double rings (CQDRs) are prepared by droplet epitaxy technique at different Ga droplet deposition rates in monolayer per second (ML/S). The 2 μm × 2 μm atomic force microscope images are obtained to show the morphologies of CQDRs. We study the effects of Ga droplet deposition rates (0.09 ML/s, 0.154 ML/s, 0.25 ML/s, 0.43 ML/s) on CQDRs. The results show that with the increase of Ga droplet deposition rate, the density of CQDRs increases and the radius of inner ring and the radius of outer ring decrease. According to the nucleation theory, through the relationship between the maximum cluster density and the Ga droplet deposition rate, the critical number of atom nucleations is found to be 5, which suggests that the stable Ga atom crystal nucleus should contain at least 5 Ga atoms in the process of forming Ga droplet, and a nucleation state transformation diagram is drawn in order to obtain an insight into the process of forming Ga droplet according to the nucleation theory and fitting results. The research results could be instructive for preparing the GaAs concentric quantum double rings that the density can be controlled by droplet epitaxy.
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图 1 不同Ga液滴沉积速率下CQDRs的AFM形貌图像(a) 0.09 ML/s; (b) 0.154 ML/s; (c) 0.25 ML/s; (d) 0.43 ML/s
Figure 1. AFM morphologies of CQDRs formed at different Ga droplet deposition rates: (a) 0.09 ML/s; (b) 0.154 ML/s; (c) 0.25 ML/s; (d) 0.43 ML/s.
图 2 GaAs 的CQDRs密度与Ga液滴沉积速率ln-ln图像
Figure 2. Density of GaAs CQDRs plotted as a function of Ga droplet deposition rate in logarithm scale.
图 3 三种状态的P-i图像(I区, 游离区; II区, 初始凝聚区; III区, 过渡区; IV区, 成核区)
Figure 3. P-i graph of three states. Zone I, extreme incomplete condensation state; zone II, initially incomplete condensation state; zone III, transition state; zone IV, nucleation state.
图 4 CQDRs 内、外环半径拟合曲线图及测量示意图 (a) 内外环测量示意图; (b) 内环平均半径拟合曲线图; (c) 外环平均半径拟合曲线图
Figure 4. Fitting curves and the measurement schematic diagram of the radii of inner and outer ring for CQDRs: (a) Schematic diagram of inner and outer ring measurement; (b) fitting curve of the inner ring average radii; (c) fitting curve of the outer ring average radii.
图 5 CQDRs形成过程示意图 (a) Ga液滴形成过程; (b) 第一次晶化过程; (c) 第二次晶化过程
Figure 5. Schematic diagrams of CQDRs formation process: (a) The formation process of Ga droplet; (b) first crystallization process; (c) second crystallization process.
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[1] Lorke A, Luyken R J, Govorov A O, Kotthaus J P 2000 Phys. Rev. Lett. 84 2223
Google Scholar
[2] 吴洪 2009 物理学报 58 8549
Google Scholar
Wu H 2009 Acta Phys. Sin. 58 8549
Google Scholar
[3] Zarenia M, Pereira J M, Peeters F M, Farias G A 2009 Nano Lett. 9 4088
Google Scholar
[4] Bayer M, Korkusinski M, Hawrylak P, Gutbrod T, Michel M, Forchel A 2003 Phys. Rev. Lett. 90 186801
Google Scholar
[5] Ribeiro E, Govorov A O, Carvalho Jr W, Medeiros-Ribeiro G 2004 Phys. Rev. Lett. 92 126402
Google Scholar
[6] 刘高福, 郭光杰, 周筑文 2015 四川大学学报(自然科学版) 52 6
Google Scholar
Liu G F, Guo G J, Zhou Z W 2015 J. Sichuan. Univ: Nat. Sci. Ed. 52 6
Google Scholar
[7] Chakraborty T, PietilInen P 1994 Phys. Rev. B 50 8460
Google Scholar
[8] Teodoro M D, Campo V L, Lopez-Richard V, Marega Jr E, Marques G E, Galvao Gobato Y, Iikawa F, Brasil M J S P, AbuWaar Z Y, Dorogan V G, Mazur Yu I, Benamara M, Salamo G J 2010 Phys. Rev. Lett. 104 086401
Google Scholar
[9] Sellers I R, Whiteside V R, Kuskovsky I L, Govorov A O, McCombe B D 2008 Phys. Rev. Lett. 100 136405
Google Scholar
[10] Kobayashi S, Jiang C, Kawazu T, Sakaki H 2004 Jpn. J. Appl. Phys. 43 L662
Google Scholar
[11] 王一, 杨晨, 郭祥, 王继红, 刘雪飞, 魏节敏, 郎啟智, 罗子江, 丁召 2018 物理学报 67 080503
Google Scholar
Wang Y, Yang C, Guo X, Wang J H, Liu X F, Wei J M, Lang Q Z, Luo Z J, Ding Z 2018 Acta Phys. Sin. 67 080503
Google Scholar
[12] Chikyow T, Koguchi N 1990 Jpn. J. Appl. Phys. 29 L2093
Google Scholar
[13] Kim J S, Song J D, Byeon C C, Kang H, Jeong M S, Cho N K, Park S J,Chol W J, Lee J, Kim J S, Leem J Y, Yim S Y 2009 Phys. Status Solidi C 6 802
Google Scholar
[14] Kim H D, Okuyama R, Kyhm K, Eto M, Taylor R A, Nicolet A L, Potemski M, Nogues G, Dang L S, Je K C, Kim J, Kyhm J H, Yoen K H, Lee E H, Kim J Y, Han II K, Choi W, Song J D 2016 Nano. Lett. 16 27
[15] Kunrugsa M, Tung K H P, Danner A J, Panyakeow S, Ratanathammaphan S 2015 J. Cryst. Growth 425 287
Google Scholar
[16] Mano T, Kuroda T, Sanguinetti S, Ochiai T, Tateno T, Kim J, Noda T, Kawabe M, Sakoda K, Kido G, Koguchi N 2005 Nano Lett. 5 425
Google Scholar
[17] Boonpeng P, Jevasuwan W, Nuntawong N, Thainoi S, Panyakeow S, Ratanathammaphan S 2011 J. Cryst. Growth 323 271
Google Scholar
[18] Li X L 2013 J. Cryst. Growth 377 59
Google Scholar
[19] Kunrugsa M, Kiravittaya S, Panyakeow S, Ratanathammaphan S 2014 J. Cryst. Growth 402 285
Google Scholar
[20] Venables J A, Persaud R, Metcalfe F L, Milne R H, Azim M 1994 J. Phys. Chem. Solids 55 955
Google Scholar
[21] Venables J A, Spiller G D T, Hanbucken M 1984 Rep. Prog. Phys. 47 399
Google Scholar
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