Predicted universality class of step bunching found on DC-heated Si(111) surfaces

Concerted experimental and numerical studies of step bunching on vicinal crystal surfaces resulting from step-down electromigration of partially charged adatoms, confirmed the theoretical prediction of scaling dependence of the minimal bunch distance $l_{\rm min}$ on the bunch size $N$: $l_{\rm min} \sim N^{-γ}$, with $γ= 2/3$. The value of the so called size-scaling exponent $γ$ was observed in experiments on vicinal surfaces of semiconducting, metallic, and dielectric materials. Careful theoretical investigations and numerical calculations predict a second value of $γ= 1/2$. However, this value is still not been reported from experiments. And we report here experimental observation of step bunching in the universality class relative to $γ= 1/2$. This is achieved by monitoring step flow during sublimation of Si(111)-vicinals heated by a direct step-down current at ~1200$^\circ$C. In the experiment we also measure other characteristic for the bunching quantities, such as the mean total number of steps in the bunch $N$ and the mean bunch width $W$. We then compare our findings with published experimental and numerical data to arrive at a theoretically consistent framework in terms of universality classes. The ultimate benefit of our study is not only to advance fundamental knowledge but also to provide further guidance for bottom-up synthesis of vicinal nanotemplates.

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