# Universality class change due to angle of deposition of thin-film growth by random particles aggregation

## TL;DR

This study investigates how the angle of particle deposition influences the universality class of thin-film growth, revealing a transition from random deposition to KPZ universality class through simulations and analytical modeling.

## Contribution

It demonstrates that non-perpendicular particle deposition can induce a universality class change in a random deposition model, supported by both Monte Carlo simulations and stochastic differential equations.

## Key findings

- Transition from RD to KPZ universality class with increasing deposition angle
- At 45°, the model exhibits KPZ-like scaling exponents
- Analytical stochastic equation supports simulation results

## Abstract

In this work we study numerically the effects of the angle of deposition of particles in the growth process of a thin-film generated by aggregation of particles added at random. The particles are aggregated in a random position of an initially flat surface and with a given angle distribution. This process gives rise to a rough interface after some time of deposition. We performed Monte Carlo simulations and, by changing the angle of deposition, we observed a transition from the random deposition (RD) universality class to the Kardar-Parisi-Zhang (KPZ) universality class. We measured the usual scaling exponents, namely, the roughness ($\alpha$), the growth ($\beta$) and the dynamic ($z$) exponents. Our results show that the particles added non-perpendicularly to the substrate, can change the universality class in a discrete atomistic random deposition model. When particles are deposited with an angle of $45^{\circ}$ in relation to the surface, the same values of the Ballistic Deposition model are observed in the Random Deposition model. We also propose an analytic approach, using a differential stochastic equation to analyze the growth process evolution, and our theoretical results corroborate the computer simulations.