Phase transitions, crystal growth

Phase-field simulation of two-dimensional material formation during epitaxial growth

P. E. L'vov^ab, A. I. Kochaev<sup>ac

a</sup> Ulyanovsk State University
^b Institute of Nanotechnologies of Microelectronics, Russian Academy of Sciences
^c National Engineering Physics Institute "MEPhI", Moscow

Abstract: In this study, we develop a phase-field model of the formation of two-dimensional (2D) materials during epitaxial growth. The model accounts for the anisotropy of boundary energy, thermal fluctuations, and the presence of continuous deposition and evaporation of atoms from the substrate surface. We investigate the formation of islands with hexagonal and triangular geometry proper to 2D materials, as well as the processes of their growth and coalescence up to the formation of a solid film. During the coalescence of two or more islands, we observed the formation of structure defects, which exhibit non-equilibrium character and gradually relax to an equilibrium shape. Some regularities of the dynamics of average size, surface number density, and size distribution function of islands are investigated.

Keywords: phase-field theory, 2D-materials, epitaxial growth, anisotropy of the boundary energy, faceting.

Received: 18.09.2025
Revised: 09.10.2025
Accepted: 11.10.2025

DOI: 10.61011/FTT.2025.10.61974.257-25

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