论文标题
同伴薄膜生长的高度波动：数值研究
Height fluctuations in homoepitaxial thin film growth: A numerical study
论文作者
论文摘要
我们报告了从著名的Clarke-Vvedensky（CV）模型的高度数值模拟获得的二维表面的高度分布（HDS）和空间协方差的研究。在此模型中，温度，沉积通量和原子 - 原子相互作用的强度的效果以两个参数进行编码：扩散比率$ r = d/f $和$ \ varepsilon $，这与Adatom“打破”横向键的概率有关。我们证明，HDS对$ r $和$ \ Varepsilon $都非常依赖，即使在沉积$ 10^5 $单层（MLS）之后，它们在某些情况下仍然远离渐近性。例如，HDS的偏度（峰度）的时间演变显示出明显的最小值（最大值），对于小$ r $和$ \ varepsilon $，并且只有很长时间才能通过（减小）向其无关值增加（减少）。但是，很难确定它们是收敛到单个值还是不同的非普通价值。另一方面，对于大型$ r $和/或$ \ varepsilon $，这些数量显然汇合到Villain-lai-das Sarma（VLDS）通用类别的预期价值。在空间协方差中观察到了类似的行为，但有限的时间效应较弱，因此它们的曲线在长期很长一段时间内与VLDS类别的曲线崩溃了。模拟粒子迁移率有限的模型，该模型以不可逆的聚合极限（$ \ varepsilon = 0 $）捕获了CV模型的一些基本特征，显示出类似的情况。总体而言，这些结果指出，同性恋薄膜表面的波动的研究可能是一项非常困难的任务，并且一旦典型的实验膜具有$ \ lyssim 10^4 $ mls，因此应非常谨慎地进行，因此它们的HDS和协方差可以在暂时性的领域中。
We report on the investigation of height distributions (HDs) and spatial covariances of two-dimensional surfaces obtained from extensive numerical simulations of the celebrated Clarke-Vvedensky (CV) model for homoepitaxial thin film growth. In this model, the effect of temperature, deposition flux, and strengths of atom-atom interactions are encoded in two parameters: the diffusion to deposition ratio $R=D/F$ and $\varepsilon$, which is related to the probability of an adatom "breaking" a lateral bond. We demonstrate that the HDs present a strong dependence on both $R$ and $\varepsilon$, and even after the deposition of $10^5$ monolayers (MLs) they are still far from the asymptotics in some cases. For instance, the temporal evolution of the HDs' skewness (kurtosis) displays a pronounced minimum (maximum), for small $R$ and $\varepsilon$, and only at long times it passes to increase (decrease) toward its asymptotic value. However, it is hard to determine whether they converge to a single value or different nonuniversal ones. For large $R$ and/or $\varepsilon$, on the other hand, these quantities clearly converge to the values expected for the Villain-Lai-Das Sarma (VLDS) universality class. A similar behavior is observed in the spatial covariances, but with weaker finite-time effects, so that rescaled curves of them collapse quite well with the one for the VLDS class at long times. Simulations of a model with limited mobility of particles, which captures some essential features of the CV model in the limit of irreversible aggregation ($\varepsilon=0$), reveal a similar scenario. Overall, these results point out that the study of fluctuations in homoepitaxial thin films' surfaces can be a very difficult task and shall be performed very carefully, once typical experimental films have $\lesssim 10^4$ MLs, so that their HDs and covariances can be in the realm of transient regimes.
