Persistence probabilities of height fluctuation in thin film growth of the Das Sarma–Tamborenea model

Analyzing asymmetry in the Wolf-Villain model via the study of the persistence of various initial height fluctuations

“…The persistence probabilities of a specific h 0 , P ± S (h 0 ,t), are investigated when the strength of fluctuations is of interest. Previous researches [10,12] have found that the function of P ± S (h 0 ,t) are not power-law decay when fluctuations are very weak compared to the saturation width i.e. |h 0 |≪W sat .…”

“…For all discrete growth models, P ± S (t)∝ t -θ ± S , where θ ± S is the persistence exponent which indicates how long the fluctuations last. In up-down symmetric models, θ + S = θ -S [9,[12][13]18]; while in asymmetric models, θ + S ≠ θ -S [9][10]14,18].…”

“…From the figures, we can see qualitatively that the two plots are slightly different statistically implying that the WV model may have weak up-down asymmetry. It is unlike other prominent toy models such as the Das Sarma-Tamborenea (DT) model [7][8] which shows clear strong up-down asymmetric properties [9][10] and the Family model [11] which demonstrates definite symmetry properties [9,12]. One common method to study symmetry quantitatively in film morphologies is by measuring the skewness.…”

“…Another method to analyse this asymmetry is the study of persistence probabilities, which is the topic of this work. Persistence probabilities of height fluctuations [9][10][12][13][14][15][16][17][18] are probabilities that indicate how well the height fluctuations can maintain their initial properties. There are two types of persistence probabilities, which are the positive and the negative one.…”

“…The positive (negative) persistence probability is the probability that the height fluctuations h remain larger (smaller) than the initial height fluctuations h 0 . It has been shown that the positive and negative persistent probabilities are the same in symmetric growth models [9,[12][13]18], but they differ in growth model without the up-down symmetry [9][10]14,18].…”