Session: 12-09-01: Instabilities in Solids and Structures

Paper Number: 149559

149559 - Meandering Instability in Vicinal Surfaces: A Comprehensive Analysis Beyond the Classical Bcf Model 

Epitaxial deposition is a widely used technology to grow thin films. A surface vicinal to a high-symmetry crystallographic plane is created by cutting the crystal at a small angle with respect to an atomic plane and thus creating steps, an obvious location site for the attachment of deposited adatoms. Through deposition of adatoms, these steps propagate uniformly and a process called step-flow growth occurs. Instead of a uniform growth generated by a constant velocity propagation of each step, two different instability mechanisms are  possible: step bunching, when the steps remain strait but tend to form close groups and step meandering when the steps are no longer straight and parallel to each other but become wavy.

We present here theoretical investigations of meandering steps on vicinal surfaces during epitaxial growth. Our results are based on the linear stability analysis of a recently proposed by the authors thermodynamically consistent step-flow model [2] - [3], which extends the classical BCF model [1] by accounting for the dynamics of adatom diffusion on terraces, attachment-detachment at steps, elastic configurational forces and generalizes the expression of the step chemical potential by incorporating the necessary coupling between the diffusion fields on adjacent terraces (the chemical effect). Having previously shown that these dynamical and chemical effects can explain the onset of step bunching without recourse to the inverse Ehrlich-Schwoebel barrier or other extraneous mechanisms in [2] and [3], the present work extends this analysis to meandering steps. Like in the straight-step context, the chemical and dynamical effects have a non-negligible influence on the stability of the system, leading to non-trivial behaviors like multimode instabilities or sharp bunching-to-meandering transitions.

Importantly, we have also demonstrated the possibility of multimode instabilities -- which is proscribed in the standard BCF model -- in the absence of heteroepitaxy or diffusion anisotropy for which it was previously reported. Finally, we have shown how a small variation of the adatom coverage could dramatically impact the instability regime, and have thus proposed a new explanation for seemingly contradictory experimental results where bunching and meandering have been observed despite almost identical conditions.

[1] “The growth of crystals and the equilibrium structure of their surfaces” (by W.K. Burton, N. Cabrera and F.C. Frank), Phil. Trans. R. Soc. A, 243, 1951, pp. 299–358.

[2] “Stability of Vicinal Surfaces: Beyond the Quasistatic Approximation”  (by L. Guin, M.Jabbour, L. Shaabani-Ardali, L. Benoit-Marechal and N. Triantafyllidis),  Physical Review Letters, 124, 2020, pp. 036101-1

[3] “Revisiting Step Instabilities on Crystal Surfaces. Part-II: General theory” (by L. Guin, L. Shaabani-Ardali, M. E. Jabbour and N. Triantafyllidis), J. Mech. Phys. Solids, 156, 2021, pp. 104582

Presenting Author: Nicolas Triantafyllidis Ecole Polytechnique

Presenting Author Biography: Prof. Nicolas Triantafyllidis has obtained a Ph.D. and an MS in Engineering (Solid Mechanics) and an MS in Applied Mathematics from Brown University by 1980. The same year he joined the faculty of the Aerospace Engineering Department at the University of Michigan in Ann Arbor, MI, USA starting as an Assistant Professor and reaching the rank of Full Professor in the Departments of Aerospace Engineering and Mechanical Engineering & Applied Mechanics. He is currently an emeritus Professor of the University of Michigan. In 2009 he moved to France to become CNRS Director of Research in the Solid Mechanics Laboratory (LMS) and a Professor of Mechanics at the Ecole Polytechnique, where he is currently a member of the Haut College.

Authors:

Lucas Benoit-Marechal Ecole Polytechnique
Michel Jabbour Ecole Polytechnique
Nicolas Triantafyllidis Ecole Polytechnique