Dynamic scaling of roughness at the early stage of tungsten film growth

The roughening of sputter-deposited tungsten films is studied in situ and in real time using grazing incidence x-ray scattering. It is shown that the power spectral density functions characterizing the external film surface roughness and the film-substrate roughness conformity can be uniquely extracted from a single scattering diagram when measured at a grazing incidence angle exceeding the critical angle of total external reflection. The temporal evolution of the roughness spectrum is demonstrated to obey a universal scaling form leading to a roughness exponent $\alpha =0.18\pm 0.02$ and to an extremely small growth exponent $\beta =0.06\pm 0.01$. In accordance with the scaling theory, these values of the scaling exponents provide a collapse into a single master curve of the “renormalized” power spectral density functions for film thicknesses ranging between 2 and $25\mathrm{nm}$.

Figure 1

XRS diagrams (circles) measured in situ and in real time at progressive tungsten film thickness: (1) $1.90\mathrm{nm}$, (2) $3.83\mathrm{nm}$, (3) $7.55\mathrm{nm}$, (4) $15.75\mathrm{nm}$, and (5) $24.6\mathrm{nm}$. The data (except curve 1) are shifted vertically by factors of 30 for clarity. The solid curves were calculated using the PSD functions extracted from the experimental data.

Figure 2

The functions ${\mathrm{PSD}}_{ff}$ and ${\mathrm{PSD}}_{sf}$ (solid and dashed lines, respectively) of the (1) thinnest and (2) thickest films grown. The symbols represent the function ${\mathrm{PSD}}_{ff}$ extracted from XRS diagram directly. Curve 3 shows the PSD function of the substrate.

Figure 3

Illustration of the data collapse obtained with eight PSD functions representing the external tungsten film surface for layer thickness ranging from $1.9\text{to}24.6\mathrm{nm}$. Inset: Thickness dependence of the rms roughness of the external film surface superimposed to a power law with growth exponent $\beta =\alpha ∕z=0.06$.

Figure 4

Replication factor versus spatial frequency for different thicknesses of tungsten film: $h$ are (1) $3.83\mathrm{nm}$, (2) $7.55\mathrm{nm}$, (3) $15.75\mathrm{nm}$, and (4) $24.6\mathrm{nm}$. Inset: Replication factor versus film thickness at the fixed spatial frequency $p=0.02{\mathrm{nm}}^{-1}$.