Speaker
Description
Persistence probability is an interesting quantity used in the study of stochastic processes. According to J. Krug [1], persistence probability of height fluctuation is the probability that the height fluctuation does not return to its initial value throughout a time interval. The persistence probability exhibits power law decay with time with the exponent $\theta$. 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 [2-4]. In the first half of this work, we study the effects of temperature on the growth exponent ($\beta$) and persistence exponent ($\theta$). For the relatively low temperature (associated with nearest neighboring site diffusion length), we obtain $\beta \approx 0.16$ and dynamic exponent (z) $\approx 3.30$. When the temperature increases, $\beta$ decreases while $\theta$ increases. In the second half, we study the dependence of persistence probability on initial height fluctuation ($h_0$), system size (L), and discrete sampling time ($\delta t$) and investigate the scaling relation. Our findings show that the steady state persistence probabilities are a function of three parameters: $f(t/L^z ,δt/L^z ,|h_0| /w_{sat} )$ which is the same as what was previously found in linear growth models [5]. We also find that the positive persistence probability of negative initial height does not show power law decay unless the initial height is much greater than the saturated interface width ($w_{sat}$), similar to the Das Sarma–Tamborenea model in [6].
References
[1] Krug, J., et al. "Persistence exponents for fluctuating interfaces." Physical Review E 56.3 (1997): 2702.
[2] Barabási, A-L., and Harry Eugene Stanley. Fractal concepts in surface growth. Cambridge university press, 1995.
[3] Chanyawadee, Soontorn. Modeling of molecular beam epitaxy growth under ehrlich-schwoebel potential barrier effects. Diss. Chulalongkorn University, 2004.
[4] Potepanit, Somjintana. Effects of annealing process on film surfaces grown by molecular beam epitaxy growth model with arrhenius law. Diss. Chulalongkorn University, 2012.
[5] Chanphana, R., P. Chatraphorn, and C. Dasgupta. "Effects of initial height on the steady-state persistence probability of linear growth models." Physical Review E 88.6 (2013): 062402.
[6] Chanphana, R., and P. Chatraphorn. "Persistence probabilities of height fluctuation in thin film growth of the Das Sarma–Tamborenea model." Indian Journal of Physics 95.1 (2021): 187-193.vx
