Analyzing of the Evolution and the Scaling Properties of a Sinusoidal Mound
Abstract
The evolution of an initial surface (below its roughening temperature) bounded by a sinusoidal function and consisting of concentric circular steps in two dimensions has been investigated in the Diffusion Limited (DL) regime. Assuming that there were entropic interactions between steps and the local mass transfer took place due to the surface diffusion, the solution of the diffusion equation has been obtained by using polar coordinates in two dimensions. The results obtained in this investigation with analyzing the surface height’s evolution as a function of time are as follows: The surface’s height approximately decreases as τ^α (α≈0.35) and α is independent of the amplitude and the wavelength of the initial surface. The variations in the heights of the surfaces which have different amplitudes (A_01,A_02 ) and wavelengths (λ_1,λ_2 ) scale as (A_01⁄A_02 ) (λ_1⁄λ_2 )^3.
Keywords
Mass transfer, Surface structure, Surface processes, Diffusion limited regime
References
- [1] Rettori A., Villain J., Flattening of Grooves on a Crystal Surface: A Method of Investigation of Surface Roughness, J. Phys. France, 49 (1988) 257–267.
- [2] Uwaha M., Relaxation of Crystal Shapes Caused by Step Motion, J. Phys. Soc. Jpn., 57 (1988) 1681–1686.
- [3] Ozdemir M., Zangwill A., Morphological Equilibration of a Corrugated Crystalline Surface, Phys. Rev. B, 42 (1990) 5013.
- [4] Umbach C.C., Keeffe M.E., Blakely J.M., Scanning Tunneling Microscopy of One Dimensional Periodic Corrugated Silicon Surfaces, J. Vac. Sci. Technol. A, 9 (1991) 1014.
- [5] Israeli N., Kandel D., Profile of a Decaying Crystalline Cone, Phys. Rev. B, 60 (1999) 5946.
- [6] Ichimiya A., Hayashi K., Williams E.D., Einstein T.L., Uwaha M., Watanabe K., Decay of Silicon Mounds: Scaling Laws and Description with Continuum Step Parameters, Appl. Surf. Sci., 175– 176 (2001) 33–35.
- [7] Li M., Wendelken J.F., Liu B., Wang E.G., Zhang Z., Decay Characteristics of Surface Mounds with Contrasting Interlayer Mass Transport Channels, Phys. Rev. Lett., 86 (2001) 2345.
- [8] Kodambaka S., Petrova V., Vailionis A., Petrov I., Greene J.E., In Situ High-Temperature Scanning Tunneling Microscopy Studies of Two-Dimensional TiN Island Coarsening Kinetics on TiN (001), Surf. Sci., 526 (2003) 85–96.
- [9] Kodambaka S., Israeli N., Bareno J., Swiech W., Ohmori K., Petrov I., Greene J.E., Low Energy Electron Microscopy Studies of Interlayer Mass Transport Kinetics on TiN (111), Surf. Sci., 560 (2004) 53–62.
- [10] Kellogg G.L., Bartelt N.C., Surface-Diffusion-Limited Island Decay on Rh(001), Surf. Sci., 577 (2005) 151-157.