Using the Monte Carlo method with the Metropolis Algorithm, we show that steps on a vicinal surface can be pinned without impurities, adsorbates, or dislocations (Fig. 1)[1].

Fig. 1 Top view of a vicinal surface. The brighter, the higher, with 10 gradations. N_step=24. ε_int /ε = - 0.5. Driving force for growth: Δμ/ε = 0.1. k_BT/ε= 0.1. (a) Initial configuration, and (b) 3000 Monte Carlo Steps per site (MCS).

   The microscopic model of the vicinal surface is a restricted solid-on-solid (RSOS) model with point-contact-type step-step attraction (p-RSOS model)[1-3].   The Hamiltonian of the p-RSOS model is written as follows:

where h(i,j) represents the surface height at the site (i,j) on a square lattice, e represents a microscopic step energy, ε_int (ε_int<0) represents a microscopic step-step attractive energy, and δ(a,b) represents Kronecker delta.

   The step-step attraction causes a discontinuity in the surface tension at low temperatures[1-3].   This discontinuity leads to inhomogeneity on the vicinal surface[2].   Since the side surfaces of merged steps have few numbers of kinks, the dissolved steps grow faster than the merged steps.   The difference of growth speed between the dissolved steps and the merged steps cause the pinning of steps[1].

 References

 [1] N. Akutsu, Phys. Rev. E 86, (2012) 061604.  PRE Kaleidoscope Images: December 2012.

 [2] N. Akutsu, J. Phys.: Condens. Matter 23 (2011) 485004.

 [3] N. Akutsu, Appl. Surf. Sci. 256 (2009) 1205; J. Cryst. Growth, 318 (2011) 10.

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1. Smoothing of a macro-step induced by discontinuous surface tension