A simple non-equilibrium, statistical-physics toy model of thin-film growth

TL;DR

This paper introduces a simple non-equilibrium statistical physics model for thin-film growth, demonstrating phase transitions and condensate shapes that resemble real thin-film deposition processes like Stranski-Krastanov growth.

Contribution

It provides an analytically solvable 2D model and numerical phase diagrams for 3D, linking particle condensation behavior to thin-film growth phenomena.

Findings

Condensation occurs above a critical density in equilibrium.

The 2D model's predictions match 3D condensate shapes.

Deposition rate determines whether a single or multiple condensates form.

Abstract

We present a simple non-equilibrium model of mass condensation with Lennard-Jones interactions between particles and the substrate. We show that when some number of particles is deposited onto the surface and the system is left to equilibrate, particles condense into an island if the density of particles becomes higher than some critical density. We illustrate this with numerically obtained phase diagrams for three-dimensional systems. We also solve a two-dimensional counterpart of this model analytically and show that not only the phase diagram but also the shape of the cross-sections of three-dimensional condensates qualitatively matches the two-dimensional predictions. Lastly, we show that when particles are being deposited with a constant rate, the system has two phases: a single condensate for low deposition rates, and multiple condensates for fast deposition. The behaviour of our model is thus similar to that of thin film growth processes, and in particular to Stranski-Krastanov growth.