Kinetic roughening and porosity scaling in film growth with subsurface lateral aggregation

TL;DR

This paper investigates a model of film growth with subsurface lateral aggregation, revealing how porosity and surface roughness scale with aggregation probability, and confirming Kardar-Parisi-Zhang universality in surface roughening.

Contribution

It introduces a generalized growth model allowing subsurface attachment, deriving scaling laws for porosity and roughness, and confirming universality class through simulations.

Findings

Surface roughness follows KPZ scaling for nonzero aggregation probability.

Porosity scales as the cube root of aggregation probability.

Crossover times and height fluctuations follow specific power laws in aggregation probability.

Abstract

We study surface and bulk properties of porous films produced by a model in which particles incide perpendicularly to a substrate, interact with deposited neighbors in its trajectory, and aggregate laterally with probability of order $a$ at each position. The model generalizes ballistic-like models by allowing attachment to particles below the outer surface. For small values of $a$, a crossover from uncorrelated deposition (UD) to correlated growth is observed. Simulations are performed in 1+1 and 2+1 dimensions. Extrapolation of effective exponents and comparison of roughness distributions confirm Kardar-Parisi-Zhang roughening of the outer surface for $a>0$. A scaling approach for small $a$ predicts crossover times as $a^{-2/3}$ and local height fluctuations as $a^{-1/3}$ at the crossover, independently of substrate dimension. These relations are different from all previously studied models with crossovers from UD to correlated growth due to subsurface aggregation, which reduces scaling exponents. The same approach predicts the porosity and average pore height scaling as $a^{1/3}$ and $a^{-1/3}$, respectively, in good agreement with simulation results in 1+1 and 2+1 dimensions. These results may be useful to modeling samples with desired porosity and long pores.