Computer simulations of the early-stage growth of Ge clusters at elevated temperatures on patterned Si substrate using the kinetic Monte Carlo method

In this work we investigate the formation of Ge clusters on stepped Si substrate at elevated temperatures (≤ 300 C) with the help of the kinetic Monte-Carlo (kMC) method. The modeling was performed for the case of low surface coverage in order to examine the process of Ge cluster growth at early stages. The temperature dependence of the development of Ge structures was explored and the transition from the growth in the middle of the steps to the growth at step edges was traced. Modeling shows that the formation of Ge clusters at the step edges begins at temperatures higher than 60 C, whereas at temperatures below 60 C clusters grow at the middle of the steps, and at 300 C all Ge atoms are gathered at the bottom of the Si step edges. Results of the kMC simulations were compared to experiments and analytical evaluations. A cluster formation diagram linking deposition rate, terrace width, and transition temperature between different cluster formation modes is presented.