Scaling of Roughness and Porosity in Thin Film Deposition with Mixed Transport Mechanisms and Adsorption Barriers

Abstract

Thin film deposition with particle transport mixing collimated and diffusive components and with barriers for adsorption are studied using numerical simulations and scaling approaches. Biased random walks on lattices are used to model the particle flux and the analogy with advective-diffusive transport is used to define a Peclet number P that represents the effect of the bias towards the substrate. An aggregation probability that relates the rates of adsorption and of the dominant transport mechanism plays the role of a Damkohler number D, where D 1 is set to describe moderate to low adsorption rates. Very porous deposits with sparse branches are obtained with P 1, whereas low porosity deposits with large height fluctuations at short scales are obtained with P 1. For P 1 in which the field bias is intense, an initial random deposition is followed by Kardar- Parisi-Zhang (KPZ) roughening. As the transport is displaced from those limiting conditions, the interplay of the transport and adsorption mechanisms establishes a condition to produce films with the smoothest surfaces for a constant deposited mass: with low adsorption barriers, a balance of random and collimated flux is required, whereas for high barriers the smoothest surfaces are obtained with P ∼ D1/2. For intense bias, the roughness is shown to be a power law of P/D, whose exponent depends on the growth exponent β of the KPZ class, and the porosity has a superuniversal scaling as (P/D)−1/3. We also study a generalized ballistic deposition model with slippery particle aggregation that shows the universality of these relations in growth with dominant collimated flux, particle adsorption at any point of the deposit, and negligible adsorbate diffusion, in contrast with the models where aggregation is restricted to the outer surface.