Heyn Christian, Feddersen Stefan
Center for Hybrid Nanostructures (CHyN), University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany.
Nanomaterials (Basel). 2021 Feb 12;11(2):468. doi: 10.3390/nano11020468.
The temperature dependent density of Al and Ga droplets deposited on AlGaAs with molecular beam epitaxy is studied theoretically. Such droplets are important for applications in quantum information technology and can be functionalized e.g., by droplet epitaxy or droplet etching for the self-assembled generation of quantum emitters. After an estimation based on a scaling analysis, the droplet densities are simulated using first a mean-field rate model and second a kinetic Monte Carlo (KMC) simulation basing on an atomistic representation of the mobile adatoms. The modeling of droplet nucleation with a very high surface activity of the adatoms and ultra-low droplet densities down to 5 × 106 cm-2 is highly demanding in particular for the KMC simulation. Both models consider two material related model parameters, the energy barrier ES for surface diffusion of free adatoms and the energy barrier EE for escape of atoms from droplets. The rate model quantitatively reproduces the droplet densities with ES = 0.19 eV, EE = 1.71 eV for Al droplets and ES = 0.115 eV for Ga droplets. For Ga, the values of EE are temperature dependent indicating the relevance of additional processes. Interestingly, the critical nucleus size depends on deposition time, which conflicts with the assumptions of the scaling model. Using a multiscale KMC algorithm to substantially shorten the computation times, Al droplets up to 460 °C on a 7500 × 7500 simulation field and Ga droplets up to 550 °C are simulated. The results show a very good agreement with the experiments using ES = 0.19 eV, EE = 1.44 eV for Al, and ES = 0.115 eV, EE = 1.24 eV (T≤ 300 °C) or EE = 1.24 + 0.06 ([°C] - 300)/100 eV (T>300 °C) for Ga. The deviating EE is attributed to a re-nucleation effect that is not considered in the mean-field assumption of the rate model.
从理论上研究了通过分子束外延沉积在AlGaAs上的铝（Al）和镓（Ga）液滴的温度依赖性密度。此类液滴对于量子信息技术的应用很重要，并且可以通过例如液滴外延或液滴蚀刻进行功能化，以自组装方式生成量子发射器。在基于标度分析进行估计之后，首先使用平均场速率模型，其次基于移动吸附原子的原子表示进行动力学蒙特卡罗（KMC）模拟，对液滴密度进行了模拟。对于具有非常高表面活性的吸附原子和低至5×10⁶ cm⁻²的超低液滴密度的液滴成核建模，对KMC模拟来说要求特别高。这两种模型都考虑了两个与材料相关的模型参数，即自由吸附原子表面扩散的能垒ES和原子从液滴中逸出的能垒EE。速率模型定量地再现了液滴密度，对于Al液滴，ES = 0.19 eV，EE = 1.71 eV，对于Ga液滴，ES = 0.115 eV。对于Ga，EE的值与温度有关，这表明存在其他相关过程。有趣的是，临界核尺寸取决于沉积时间，这与标度模型的假设相矛盾。使用多尺度KMC算法大幅缩短计算时间，在7500×7500的模拟场中对高达460°C的Al液滴和高达550°C的Ga液滴进行了模拟。结果表明，对于Al，使用ES = 0.19 eV，EE = 1.44 eV，对于Ga，使用ES = 0.115 eV，EE = 1.24 eV（T≤300°C）或EE = 1.24 + 0.06（[°C] - 300）/100 eV（T>300°C）时，与实验结果非常吻合。EE的偏差归因于速率模型的平均场假设中未考虑的再成核效应。
