Surface Evolution of Polymer Films Grown by Vapor Deposition: Growth of Local and Global Slopes of Interfaces

Abstract

The kinetic roughening of polymer films grown by vapor deposition polymerization was analyzed using the widely accepted classification framework of "generic scaling ansatz" given for the structure factor. Over the past two decades, this method has played a pivotal role in classifying diverse forms of dynamic scaling and understanding the mechanisms driving interface roughening. The roughness exponents of the polymer films were consistently determined as α=1.25±0.09, αloc=0.73±0.02, and αs=0.99±0.06. However, the inability to unambiguously assign these roughness exponent values to a specific scaling subclass prompts the proposal of a practical alternative. This report illustrates how all potential dynamic scaling can be consistently identified and classified based on the relationship between two temporal scaling exponents measured in real space: the average local slope and the global slope of the interface. The intrinsic anomalous roughening class is conclusively assigned to polymer film growth characterized by anomalous "native (background slope-removed) local height fluctuations". Moreover, the new analysis reveals that interfaces exhibiting anomalous scaling, previously classified as intrinsic anomalous roughening, could potentially belong to the super-rough class, particularly when the spectral roughness exponent αs is equal to 1.

Keywords: atomic force microscopy; kinetic roughening; polymer film growth; surface roughness; vapor deposition polymerization.

Figure 1

Schematic diagram of CVD setup consisting of a sublimation furnace, pyrolysis furnace, deposition chamber, and pump station. With the bypass valve closed, both the gate valve and the system valve are opened to initiate polymer film growth on the substrate.

Figure 2

Representative AFM-scanned images of parylene-C films in the steady growth regime above film thickness d = 200 nm. A scan size of 3 × 3 μm² with 512-pixel resolution is maintained for each measurement.

Figure 3

(a) Saturation interface width versus correlation length in a log–log plot. The dashed line represents a linear best fit giving $\mathsf{\alpha }=1.25\pm 0.09.$ (b) Logarithmic plot of height difference correlation function versus radial distance $r$ at several representative film thicknesses. The dashed line, the guide for the eye, shows a linear slope of 0.73 corresponding to ${\alpha }_{loc}$. Inset displays the thickness dependence of the local (${\alpha }_{loc}$) and spectral (${\alpha }_s$) exponents in open circles and triangles, respectively. (c) Logarithmic plot of structure factor at several representative film thickness. The dashed line represents the linear slope of $-$4 corresponding to $-(2{\alpha }_s+2)$. Inset shows the log–log plot of the thickness dependence of $S(k_0,d)$ at $k_0=20 {\mathsf{\mu }\mathrm{m}}^{-1}$ indicated by the arrow. The error bars show the standard deviation from the average determined from at least four different locations on each film surface.

Figure 4

Types of dynamic scaling for growing interfaces mapped to the field of average local and global slope exponents. The condition that satisfies ${\kappa }_{loc}={\kappa }_G$ is indicated by a diagonal line passing through the first and third quadrants. Slope selection of the interface occurs when ${\kappa }_G=0$, which is indicated by the hatched line satisfying ${\kappa }_{loc}>0$ within the intrinsic anomalous roughening class.

Figure 5

(a) The average adjacent step height $\sqrt{H(r_0,t)}$ of underlying pit versus O₂ plasma treatment time. The inset shows representative trace of $H\left(r\right)$ at various O₂ plasma treatment times. The negative slope line corresponds to the local slope exponent ${\kappa }_{loc}=-1.08\pm 0.09$. (b) The average global slope $W/\xi$ versus duration of O₂ plasma treatment. A thin line with zero slope is a guide for the eye. A line with a negative slope is given by the least-square fit with an exponent ${\kappa }_G=-1.04\pm 0.03$. The error bars show the standard deviation from the mean value determined from at least four different locations on the surface of each film.

Figure 6

(a) The average local slope versus film thickness in the steady growth regime of parylene-C films above d~200 nm. The lattice spacing is given as $r_0=5.9$ nm. The dashed line is a guide for eye corresponding ${\kappa }_{loc}=0.14\pm 0.02$. (b) The averaged global slope (aspect ratio) of the interface versus the film thickness shows the formation of a slope-selected mound (${\kappa }_G~0$). The error bars show the standard deviation from the mean value determined from at least four different locations on the surface of each film.