Non-monotonic roughness evolution in film growth on weakly interacting substrates

Abstract

Thin film deposition on weakly interacting substrates exhibits a unique growth mode characterized by initially strong island formation and rapidly increasing roughness, which reaches a maximum and subsequently decreases as the film returns to a smooth morphology. Here we show this rough-to-smooth growth mode experimentally for two molecular systems with substantially different geometries, namely, the effectively spherical buckminsterfullerene (C$_{60}$) and the disk-like 1,4,5,8,9,11-hexaazatriphenylenehexacarbonitrile (HATCN). This growth mode is explained by a geometrical model that captures the basic mechanisms of multilayer island growth, island coalescence, and formation of a continuous film. Additionally, kinetic Monte Carlo simulations with minimal ingredients demonstrate that this mode generally occurs for weakly interacting substrates, providing quantitative estimates of parameters that characterize adsorbate-adsorbate and adsorbate-substrate interactions. Both the model and simulations accurately describe the experimental data and highlight the generic nature of the phenomenon, independently of the details of the interactions and the molecular flux, which opens up a path for controlling nanoscale film roughness.

Figures (4)

• Figure 1: (Color online) (a) Roughness $\sigma$ and (b) in-plane correlation length $l_{\parallel}$ evolutions of $\text{C}_{60}$ films. Thin full lines (blue; darker gray) with error bars are the experimentally extracted dependencies. Thick full lines (magenta; lighter gray) are KMC simulation results with $R=3\cdot10^3$, $E_b=2.5$, $E_s/E_b=1.33$. The dashed line in (a) is a fit to the geometric model (parameters $\alpha=0.28$, $C_L=5\%$, $L/d_0=2.0$, and $\beta d_0=0.115$). The inset in (a) shows the chemical structure of the $\text{C}_{60}$ molecule with carbon atoms represented as gray spheres. (c) AFM images of $\text{C}_{60}$ film at different thicknesses indicated in (a): (1) start of the growth; (2) roughness maximum; (3) smooth growth. The insets show exemplary line profiles through the maps taken at the positions indicated with white dashed lines. The horizontal axes are identical to those of the maps. (d) Heatmap height profiles from the KMC simulations under the same conditions.
• Figure 2: (a) Geometric model with islands growing with power laws for $d(\theta)$ and $h(\theta)$ in a capture zone of size $L \times L$. (b) Reduced roughness $\sigma/\theta_M$ vs. $\theta/\theta_M$ from Eq. \ref{['sigmascaling']} (full lines) and from the full geometric model (dashed lines) with $C_L=0.02$ for $\alpha=0.2$, $C_L=0.06$ for $\alpha=0.5$, and a reduced slope parameter for the pyramidal cover $\beta d_0=0.2$.
• Figure 3: KMC parameters $\{R,R_s,E_b\}$ from the set $\mathcal{S}$ (roughness maximum at coverages $5\leq\theta_M\leq 8$) fall onto an approximate line in the $E_\text{b}-\ln R_s$ plane. The different colored symbols differ in their $R$ value for the diffusion of film particles on film. The dotted lines are lines of constant $L=R_s^{1/4}\exp(-E_b/8)$, which is the approximate capture zone size (island distance) in ML units according to submonolayer scaling theory oliveirareis2013.
• Figure 4: Roughness $\sigma$ evolution for HATCN as a function of film thickness $\theta$. Thin full line (blue) with error bars is the experimentally extracted (from XRR) dependency. The dashed line is a fit to the geometric model with Gaussian distributed capture zone areas ($\alpha=0.35$, $L/d_0=2.48$, $C_L=5\%$, $\beta d_0=0.343$). The KMC parameters for the modified model (see S.VI. of the SM supplementary) are $R=10^5$, $E_b=5.0$, $E_s/E_b = 0.38$ and $E_{ES}=2.3$. The aspect ratio of the tetragonal unit cell is 1.58. The inset shows the chemical structure of the HATCN molecule with carbon atoms represented as gray spheres and nitrogen atoms as blue spheres.