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

Abstract

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 $\ensuremath{\alpha}=0.18\ifmmode\pm\else\textpm\fi{}0.02$ and to an extremely small growth exponent $\ensuremath{\beta}=0.06\ifmmode\pm\else\textpm\fi{}0.01$. 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 $25\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$.