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状转变过程的动力学特性。该FPR模型基于一套耦合的福克-普朗克方程组（Fokker–Planck equations），其中每种岛状结构的分布由其自身用于生长的福克-普朗克方程支配，并通过反应项描述不同类型岛状结构（包括非对称形状）之间的形状转变过程。上述形状转变的反应项依赖于岛的尺寸，且可通过对每种形状转变的最低势垒路径进行显式计算确定。这一平均场模型（mean-field model）使得我们能够探究非对称形状转变的动力学过程，并研究耦合生长与转变过程中岛状形状分布的演化规律。非对称亚稳形状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%，且高达100%的形状转变过程均会经由非对称形状完成。此外，我们发现金字塔/穹顶状量子点熟化过程的多峰分布特征，可在足够高的温度与沉积速率下被消除。