Combining TEM, AFM, and Profilometry for Quantitative Topography Characterization Across All Scales

Abstract

Surface roughness affects the functional properties of surfaces, including adhesion, friction, hydrophobicity, biological response, and electrical and thermal transport properties. However, experimental investigations to quantify these links are often inconclusive because surfaces are fractal-like, and the values of measured roughness parameters depend on measurement size. Here, we demonstrate the characterization of topography of an ultrananocrystalline diamond (UNCD) surface at the angstrom scale using transmission electron microscopy (TEM), as well as its combination with conventional techniques to achieve a comprehensive surface description spanning 8 orders of magnitude in size. We performed more than 100 individual measurements of the nanodiamond film using both TEM and conventional techniques (stylus profilometry and atomic force microscopy). While individual measurements of root-mean-square (RMS) height, RMS slope, and RMS curvature vary by orders of magnitude, we combine the various techniques using the power spectral density and use this to compute scale-independent parameters. This analysis reveals that "smooth" UNCD surfaces have an RMS slope greater than 1, even larger than the slope of the Austrian Alps when measured on the scale of a human step. This approach of comprehensive multiscale roughness characterization, measured with angstrom-scale detail, will enable the systematic evaluation and optimization of other technologically relevant surfaces, as well as systematic testing of the many analytical and numerical models for the behavior of rough surfaces.

The emergence of small-scale self-affine surface roughness from deformation

“…Rough surfaces are often fractals with statistical self-affine scaling 12,13 observed from the atomic to the tectonic. 2,14,15 There is presently no unifying explanation for the origins of this self-affinity, but the influence of microstructural heterogeneity on material deformation is widely cited as a possible mechanism. 5,[16][17][18][19][20] The fact that scale-invariant roughness is observed from microscopic to geological scales hints that a common mechanism is active across vastly different length scales.…”

Characterization of small-scale surface topography using transmission electron microscopy

“…Therefore, the TEM data can be paired with atomic force microscopy data (e.g., Ref. [21]), which will more accurately characterize the largerscale topography. Overall, for the vast majority of real-world materials, the described methods will enable the accurate measurement of roughness statistics with no significant effect of sample thickness.…”

“…From this the Hurst exponent of the surface can be calculated (as described in Ref. [21]) as H=0.93 ± 0.04, 0.92 ± 0.06, and 0.98 ± 0.08, respectively. (Note that the wedge samples are the same ones that were characterized in Ref.…”

“…[21], which used the wedgedeposition method, exactly as it is described in the present article. As noted in that prior article [21], the precise value of Hurst exponent that is measured depends on the range of wavevectors over which the fitting is done.) The measured Hurst exponents between the different sample preparations are identical within experimental uncertainty.…”

“…Here, an averaged PSD has been stitched together from the individually measured PSDs computed from each image (using the techniques described in Ref. [21]). The PSDs demonstrate that the material can be characterized at size scales below 10 nm (above = 6 ×10 8 m -1 ); these scales are inaccessible using conventional techniques.…”