umD transition data from A Fokker–Planck reaction model for the epitaxial growth and shape transition of quantum dots

We construct a Fokker–Planck reaction (FPR) model to investigate the dynamics of the coupled epitaxial growth and shape transition process of an array of quantum dots (QDs). The FPR model is based on a coupled system of Fokker–Planck equations wherein the distribution of each island type is governed by its own Fokker–Planck equation for growth, with reaction terms describing the shape transitions between islands of different types including asymmetric shapes. The reaction terms for the shape transitions depend on the island size and are determined from explicit calculations of the lowest barrier pathway for each shape transition. This mean-field model enables us to consider the kinetics of asymmetric shape transitions and study the evolution of island shape distributions during the coupled growth and transition process. Asymmetric metastable shapes play a crucial role in the dynamics, with asymmetric QDs comprising up to 10% of the population, and with up to 100% of the shape transitions passing through asymmetric shapes. Moreover, we find that the multimodal distribution characteristic of pyramid/dome QD coarsening can be eliminated at sufficiently high temperature and deposition rate.

我们构建了福克-普朗克反应（Fokker–Planck reaction, FPR）模型，以研究量子点（quantum dots, QDs）阵列的耦合外延生长与形貌转变动力学过程。该FPR模型基于一套耦合的福克-普朗克方程组，其中每种晶岛类型的分布由其自身的生长福克-普朗克方程支配，反应项则用于描述不同类型（包括非对称形貌）晶岛之间的形貌转变。形貌转变的反应项依赖于晶岛尺寸，且通过对每种形貌转变的最低势垒路径进行显式计算确定。该平均场模型使得我们能够研究非对称形貌转变的动力学特性，并探究耦合生长与转变过程中晶岛形貌分布的演化规律。非对称亚稳形貌在该动力学过程中扮演关键角色：非对称量子点的种群占比最高可达10%，且最高有100%的形貌转变过程会经由非对称形貌完成。此外，我们发现金字塔/穹顶状量子岛粗化的多峰分布特征，可在足够高的温度与沉积速率下被消除。