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

Abstract

The dependence of the steady-state persistence probability on initial height fluctuation $$\left( {h_{0} } \right)$$ in the (1 + 1)-dimensional Das Sarma–Tamborenea (DT) model, which is up–down asymmetric, is investigated. Our results show that the positive and negative persistence probabilities for fixed $$h_{0}$$ are not equal to each other. The positive persistence probability for negative initial height $$\left( {P_{ + } \left( { - \left| {h_{0} } \right|} \right)} \right)$$ as well as the negative persistence probability for positive initial height $$\left( {P_{ - } \left( { + \left| {h_{0} } \right|} \right)} \right)$$ shows power-law decay with time if $$\left| {h_{0} } \right|$$ is larger than the saturated interface width $$\left( {W_{\text{sat}} } \right)$$ of the model. The persistence exponent decreases when $$\left| {h_{0} } \right|$$ increases. The (2 + 1)-dimensional DT model is studied for comparison. We also find a relation that shows how the persistence probability scales with the initial height, the system size and the discrete sampling time. The relation works for models with and without up–down symmetry.