Persistence probabilities of height fluctuation in thin film growth using discrete models with up-down symmetry

The problem of persistence of height fluctuations in non-equilibrium surface growth and interface dynamics has been widely studied in recent years. The persistence concept is interesting theoretically and also has practical applications in many areas. The persistence probability is the probability that the height fluctuation of a growing film does not return to its initial value over a specified time interval. For several models of surface growth, the persistence probability decreases in time as a power law. The persistence probability and the corresponding exponents appear to change when the initial height changes. The persistence probability also depends on the discrete sampling time (discrete time interval between two measurements used to calculate the persistence probability). The main purpose of this study is to understand how the persistence probability of up-down symmetric models change as the initial height and the discrete sampling time are varied and determine a scaling description for it. Another goal is to study effects of patterned substrate. The healing times of thin films simulated by Family and Das Sarma-Tamborenea models grown on the smooth triangular substrate, and the rough pillar and groove substrate are studied. The healing time is the time when influences of the initial pattern in the substrate disappear and characteristics of the growing interface are healed to those obtained by a film grown on a flat substrate. The healing time is determined via the study of the nearest-neighbor height difference correlation function. The theoretical solution of the correlation function describing dynamics of film surface of the Family model grown on both patterns is also investigated.

非平衡表面生长与界面动力学中的高度涨落持续性问题，近年来已得到广泛研究。持续性概念兼具重要理论价值与广泛实际应用场景。持续性概率（persistence probability）指在指定时间区间内，生长薄膜的高度涨落始终未回归初始值的概率。针对多种表面生长模型，持续性概率随时间呈幂律衰减。研究表明，当初始高度改变时，持续性概率及其对应指数会发生变化；此外，持续性概率还取决于离散采样时间，即两次用于计算持续性概率的测量之间的离散时间间隔。本研究的核心目标在于厘清上下对称模型的持续性概率如何随初始高度与离散采样时间的变化而改变，并为其确立标度描述。另一研究目标为探究图案化衬底（patterned substrate）的影响效应。本文针对在光滑三角衬底、粗糙柱形与沟槽衬底上生长的Family模型以及Das Sarma-Tamborenea模型所模拟的薄膜愈合时间（healing time）展开研究。愈合时间指衬底初始图案的影响完全消失，生长界面的特性恢复至平坦衬底上生长薄膜所获特性的时刻。我们通过近邻高度差关联函数（nearest-neighbor height difference correlation function）的分析确定愈合时间。此外，本文还对两种图案衬底上生长的Family模型薄膜表面动力学的关联函数理论解进行了研究。