Effects of surface diffusion length on steady-state persistence probabilities

Chanphana, R.; Chatraphorn, P.

doi:10.1088/1742-6596/1380/1/012024

Cited by 2 publications

(4 citation statements)

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“…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].…”

Section: The Persistence Probabilities and Exponents In The Steady-statementioning

confidence: 98%

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

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

Chatraphorn,

Chanphana

2023

J. Phys.: Conf. Ser.

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The Wolf-Villain (WV) model, which, in some literature, has shown trait of up-down asymmetry, is investigated through the study of the persistence probability of height fluctuations in simulated film surfaces. The persistence probability is the probability that the height fluctuation of each site does not cross its initial value (h 0) along a time interval. When averaged over all possible values of h 0, the probability is known to exhibit a power law decay behavior with the exponent called persistence exponent. In this work, instead of averaging over all h 0, we consider a fixed value of h 0 and find that the persistence probability of the WV model still decreases with time as a power law if the fixed value meets a necessary condition, i.e. h 0 is roughly equal to or larger than the saturated roughness of the film. The persistence exponent for each h 0 is measured and found to decrease as the value of h 0 increases. Scaling form of the persistence probability at a specific h 0 is also studied. Notably, all results obtained here are in agreement with those of the up-down symmetric models appeared in literatures despite the fact that the WV model is an asymmetric model. These results support the idea from other studies that the asymmetry in the WV is very weak.

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Section: The Persistence Probabilities and Exponents In The Steady-statementioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Chatraphorn,

Chanphana

2023

J. Phys.: Conf. Ser.

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“…Chanphana & Chatraphorn (Chanphana and Chatraphorn, 2019a) demonstrated that the diffusion length (l) affects the value of the persistence exponents. In our work, l can be varied by adjusting the growth parameters i.e., the substrate temperature, and the deposition rate.…”

Section: P Smentioning

confidence: 99%

Persistence of height fluctuation in molecular-beam epitaxy model

Sanseeha

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Persistence probability is an interesting quantity in stochastic process which is the dynamics of surface growth in this study. Persistence probability of height f luctuation is the probability that the height fluctuation does not return to its initial value throughout a time interval. In this work, we use a numerical simulation approach to investigate the persistence probability in Molecular-Beam Epitaxy (MBE) model which is associated with Molecular-Beam Epitaxy technique. First half, we study the effects of temperature and deposition rate on the growth exponent () and persistence exponent (). For the temperature corresponds to 1 diffusion length, we get 017 and positive steady-state persistence exponent, S+ 078. When the temperature increases, the growth exponent value decreases while the persistence exponent rises. The same results happen when the deposition rate is decreased. On the second half, we investigate how the persistence probabilities change with a particular initial value of height fluctuation. The negative persistence probability of positive initial height shows power lawwhentheinitial height is slightly greater than sat. The positive persistence probability of negative initial height does not show power law decay unless the initial height is much greater than sat. We measure the relationship of persistence probability on initial height fluctuation (0), system size, and discreate sampling time to investigate the scaling relation. The persistence probability is a function of three parameters.

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Effects of surface diffusion length on steady-state persistence probabilities

Cited by 2 publications

References 12 publications

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

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

Persistence of height fluctuation in molecular-beam epitaxy model

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