Unstable Multilayer Growth: From Atomistic Models to 2D Continuum Step-Dynamics Treatments to 3D Continuum PDE’sMaozhi Li1 and J.W. Evans21Institute 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
Atomistic modeling has been immensely successful in elucidating epitaxial growth  (see Fig.1), but this approach can be computationally expensive. Consequently, efforts have been made to develop reliable coarse-grained continuum treatments which can be both more efficient and more instructive. However, there is some question as to the validity of current phenomenological 3D continuum evolution equations for far-from-equilibrium growth, and these do not yet have predictive reliability. Thus, a central open challenge is to rigorously obtain such equations from more detailed “finer level” models.
We have recently applied a 2D step-dynamics model to exactly analyze mound slope and shape selection during unstable multilayer homoepitaxial growth . We find that the predictions of existing phenomenological theories are in fact qualitatively incorrect. Furthermore, we have succeeded in coarse-graining the step-dynamics model to obtain exact continuum equations (see Fig.2), which differ from the phenomenological equations .
Such rigorous coarse-graining strategies potentially have immense potential for more complex heteroepitaxial growth systems of interest in this CMSN project. Here, atomistic modeling is often prohibitive, and most current modeling is based on phenomenological continuum formulations. We intend to develop procedures to validate these formulations, or to extend their regime of validity to incorporate various far-from-equilibrium kinetic processes.
 E. Cox, M. Li et al., Phys. Rev. B 71 (2005) 115414, and in preparation.
 Maozhi Li and J.W. Evans, Phys. Rev. Lett. 95 (2005) 256101.
[1-2] Work supported by NSF grant CHE-0414378.
STM Continuum Step-Dynamics Treatments to 3D Continuum PDE’s
Fig.1 STM versus KMC images (95 95 nm2) of mound morphologies in 3 ML Ag/Ag(100) films deposited at 150 K and 0.004 ML/s. Contours show step edges.
Fig.2 Comparison of predictions for selected mound shapes from a “step dynamics” model and our exact continuum theory. The mound valley (peak) is on the left (right).
Left (right) frame is for facile (inhibited) nucleation of top layer islands.
Maozhi Li and J.W. Evans, Phys. Rev. Lett. 95 (2005) 256101.