Mound slope and shape selection during unstable multilayer growth: Analysis of step-dynamics models including downward funneling

Step-dynamics models are developed for mound shape evolution during multilayer homoepitaxial growth in the presence of inhibited interlayer transport. Unconventionally, our models also incorporate downward funneling (DF) of atoms deposited at step edges. The extent of DF can be reduced continuously to zero where one recovers traditional step dynamics models. This allows direct comparison between the behavior of models with and without DF. We show that DF greatly enhances growth of the height of valleys at the mound bases to an extent compatible with slope selection. To elucidate the selected shapes of finite mounds, we consider a suitably defined net flux of adatom attachment at steps summed over a mound side between valley and peak. This quantity varies periodically but vanishes when further averaged over time, a condition which directly constrains the selected mound shapes. We also characterize the dependence of these shapes on the prescription of nucleation of new islands at the mound peak. Disciplines Biological and Chemical Physics | Mathematics Comments This article is from Physical Review B 73 (2006): 125434, doi: 10.1103/PhysRevB.73.125434. Posted with permission. This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/physastro_pubs/202 Mound slope and shape selection during unstable multilayer growth: Analysis of step-dynamics models including downward funneling Maozhi Li1 and J. W. Evans2 1Institute of Physical Research and Technology, and Ames Laboratory USDOE, Iowa State University, Ames, Iowa 50011, USA 2Department of Mathematics, and Ames Laboratory USDOE, Iowa State University, Ames Iowa 50011, USA Received 16 November 2005; published 28 March 2006 Step-dynamics models are developed for mound shape evolution during multilayer homoepitaxial growth in the presence of inhibited interlayer transport. Unconventionally, our models also incorporate downward funneling DF of atoms deposited at step edges. The extent of DF can be reduced continuously to zero where one recovers traditional step dynamics models. This allows direct comparison between the behavior of models with and without DF. We show that DF greatly enhances growth of the height of valleys at the mound bases to an extent compatible with slope selection. To elucidate the selected shapes of finite mounds, we consider a suitably defined net flux of adatom attachment at steps summed over a mound side between valley and peak. This quantity varies periodically but vanishes when further averaged over time, a condition which directly constrains the selected mound shapes. We also characterize the dependence of these shapes on the prescription of nucleation of new islands at the mound peak. DOI: 10.1103/PhysRevB.73.125434 PACS number s : 68.55. a, 81.10.Aj, 81.15.Aa, 68.35.Fx