Excessive number of high asperities for sputtered rough films

The roughness of solids is crucial for interactions between bodies at short separations due to capillary or van der Waals–Casimir forces and for contact mechanics. Specifically, it is critical for the fabrication and operation of microelectromechanical systems, for which functional materials are deposited using thin film coating technologies. Here, it is demonstrated that the materials deposited by magnetron sputtering or thermally evaporated on a cold Si substrate reveal a significantly larger number of high asperities than that predicted by the normal distribution. Such asperities define the distance between the solids in contact that is the key parameter for many problems. The effect is related to the nonequilibrium deposition conditions and is suppressed if the material is deposited on a hot substrate or annealed. The high asperity tails can be described by the extreme value distribution or in some cases by the exponential distribution.

Figure 1

(a) AFM image of Pt film with an area of $20\times 20\mu {\mathrm{m}}^2$ deposited on a Si substrate at room temperature (cold). The color bar shows the height scale. (b) A zoomed $2\times 2\mu {\mathrm{m}}^2$ area taken from the full image. (c) The same as (a) but the film is deposited on a hot substrate at $T=400{}^{\circ }\mathrm{C}$. (d) Magnified view of the film in (c).

Figure 2

(a) and (b) AFM image of Pt films with an area of $2\times 2\mu {\mathrm{m}}^2$ and a pixel size of $1.95\mathrm{nm}$ deposited on a cold and hot substrate, respectively. (c) and (d) The height-difference correlation function (circles) extracted from the images in (a) and (b). The solid black lines show the asymptotics corresponding to Eq. (2). The blue dashed line indicates the correlation length.

Figure 3

(a)–(d) $2\times 2\mu {\mathrm{m}}^2$ areas of the full images for Cu, W, ${\mathrm{SiO}}_2$, and Au, respectively, deposited at room temperature.

Figure 4

Probability density function for different materials deposited on a Si substrate at room temperature. The green dashed curve shows the normal distribution for the same rms roughness.

Figure 5

Probability density function for Pt and W deposited on hot Si substrates. The normal distribution (green dashed curve) describes well the observed distribution.

Figure 6

Number of pixels with a height $h$ larger than a given value $x$ for different materials. The data for high peaks are fitted with (4) or with the exponential distribution (for ${\mathrm{SiO}}_2$). For Pt and Cu the data are fitted piecewise by the extreme value distribution. The numbers at the breakpoints show the number of pixels for the corresponding $x$.