1.College of Big Data and Information Engineering, Guizhou University, Guiyang 550025, China 2.School of Education Administrations, Guizhou University of Finance and Economics, Guiyang 550025, China 3.Power Semiconductor Device Reliability Center of the Ministry of Education, Guiyang 550025, China 4.Key Laboratory of Micro-Nano-Electronics and Software Technology of Guizhou Province, Guiyang 550025, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 61564002, 11664005), the Guizhou Provincial Science and Technology Foundation, China (Grant No.QKH-[2017]1055), and the Guizhou University Talent Foundation, China (Grant No. GDJHZ-[2015]23).
Received Date:25 April 2019
Accepted Date:02 July 2019
Available Online:01 September 2019
Published Online:20 September 2019
Abstract: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. Keywords:concentric quantum double rings/ diffusion dynamics of cluster/ atomic force microscope
其中, $\upsilon $表示Ga原子振动频率; P是决定于Ga原子临界成核原子数目的特征值; E是Ga原子成核能, 关于E在不同条件下的表达式, 文献[21]中有详细叙述, 这里不做讨论. 在本实验中, 其他参量可以认为是不变的, 所以CQDRs的密度${n_{{x}}}$和Ga液滴沉积R应该满足幂指函数关系; 图2所示为CQDRs的密度${n_{{x}}}$和Ga液滴沉积速率R的双对数关系曲线$\ln {n_{{x}}} \propto P\ln R - P\ln \upsilon + \left( {E/kT} \right)$, 实线为最佳线性拟合直线, 该直线的斜率为$P = 0.663$. 图 2 GaAs 的CQDRs密度与Ga液滴沉积速率ln-ln图像 Figure2. Density of GaAs CQDRs plotted as a function of Ga droplet deposition rate in logarithm scale.
Ga液滴为3D岛, 根据成核过程的原子数目i与特征值P之间的依赖关系[21], 将游离态、初始凝聚态和完全凝聚态中的原子数目i与特征值P之间的关系式绘制为图3, 其中: 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) Figure3.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.
$P = \frac{2}{3}i,\; \text{完全不凝聚态或游离态}, $
$P = \frac{2}{5}i, \;\text{初始凝聚态}, $
$P = \frac{i}{{i + 2.5}},\; \text{完全凝聚态}.$
图3所示的P-i三支函数线将该图像分成四个区域, 将这四个区域定义为: I区为游离区; II区为初始凝聚区; III区为过渡区; IV区为成核区. 我们已由CQDRs密度和Ga液滴沉积速率间的关系拟合出P = 0.663. 图3中所示的水平虚线为P = 0.663, 可以看出该虚线与完全凝聚态的曲线的交点横坐标为4.9184 $\approx $ 5. 这对理解本实验的Ga液滴成核过程是至关重要的. 当Ga原子沉积到GaAs衬底表面时, 这时候的Ga原子是游离的单个原子; 接下来, 两个Ga原子相遇形成二聚体, 但这些二聚体还不是最稳定的结构, 部分二聚体在衬底温度及应力的作用下可能还会再次离解, 一部分二聚体不断吸附Ga原子形成二聚体团簇直到形成含有5个Ga原子的稳定的“小晶胚”; 含有5个Ga原子的“小晶胚”边扩散边吸附其他Ga原子, 不断地汇聚形成较大的Ga液滴. 由于Ga原子在[110]上的扩散比较明显, 为进一步探讨Ga液滴沉积速率对第一次晶化(实验第二步)和第二次晶化过程(实验第三步)的影响, 本文测量并统计CQDRs在[110]方向的内环平均半径${W'_{\rm{Inner}}}$、外环平均半径${W'_{\rm{Outer}}}$; 为保证测量的准确性, 直接测量量为内环直径${W_{\rm{Inner}}}$、外环直径${W_{\rm{Outer}}}$. 图4(a)为测量示意图, 不难看出: ${W'_{\rm{Inner}}} = $$ {W_{\rm{Inner}}}/2$, ${W'_{\rm{Outer}}} = {W_{\rm{Outer}}}/2$. 图4(b)为内环平均半径${W'_{\rm{Inner}}}$随Ga液滴沉积速率变化的拟合曲线, 图4(c)为外环平均半径${W'_{\rm{Outer}}}$随Ga液滴沉积速率变化的拟合曲线. 图4(b)中, 当Ga液滴沉积速率由0.09 ML/s增加到0.43 ML/s时, 内环半径从83.30 nm逐渐降低到53.33 nm; 同时, 图4(c)中的外环半径从119.56 nm减少到93.65 nm. 这是因为随着沉积速率的增加, Ga原子扩散、汇聚的时间变短, 统计平均而言, 形成的Ga液滴所包含的Ga原子数目减少, 晶化前的Ga液滴较小, 从而内环半径和外环半径在相同的晶化条件下均逐渐减小. 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 Figure4. 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所示的CQDRs形成过程, 可以更加直观地理解CQDRs的形成, 图5(a)为Ga液滴的形成过程, 在该过程中Ga原子通过成核、扩散、汇聚成较大的类似半椭球体形状的Ga液滴以减少表面能而达到稳定状态. 图5(b)为第一次晶化过程, 在浓度梯度和温度的共同驱动下, Ga原子向外扩散, 在As氛围中, As原子会优先在Ga液滴边缘处和As原子结合而快速晶化形成一定高度的Ga—As单层. 由于形成的Ga—As单层有一定高度, 且晶化时间有限, 这会阻碍部分Ga原子的进一步向外扩散. 同时, 由于Ga液滴和衬底的浸润区域为富Ga区域, 即使在提供As束流的条件下, 在Ga液滴中央也会发生衬底表面的Ga—As键的断裂, 也即是液滴的刻蚀过程. 图5(c)为第二次晶化过程, 部分Ga原子继续扩散, 在As束流的晶化作用下, 形成了外环, Ga液滴的刻蚀过程继续进行. 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 Figure5. Schematic diagrams of CQDRs formation process: (a) The formation process of Ga droplet; (b) first crystallization process; (c) second crystallization process.
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
图 2 GaAs 的CQDRs密度与Ga液滴沉积速率ln-ln图像
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)
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
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