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

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.

26 pages, 16 figures

References in corpus (4)

• Interaction driven real-space condensation
• Condensation in the inhomogeneous zero-range process: an interplay between interaction and diffusion disorder
• Numerical survey of the tunable condensate shape and scaling laws in pair-factorized steady states
• Phase separation transition of reconstituting k-mers in one dimension

Cited by in corpus (1)

• Dynamics of condensate formation in stochastic transport with pair-factorized steady states: Nucleation and coarsening time scales