Scaling of Si/SiO₂ interface roughness

The spatial scaling law of the Si/SiO₂ interface roughness was investigated with atomic force microscopy. Scaling behavior was observed on smaller scales, where the root-mean-square (RMS) roughness increased as a power of the scale of observation. When viewed as a fractal geometry, such a structure is characterized as a self-affine fractal. On larger scales, the roughness was no more dependent on the scale, showing the (macroscopic) RMS roughness in the conventional sense. The observed structure (self-affine fractal with a finite-length cut-off) is consistent with the prediction of the theory of kinetic roughening in a far-from-equilibrium growth, where the fluctuation on smaller scales evolves into roughness on larger scales. Statistical description of the Si/SiO₂ interface roughness was also given in terms of autocorrelation function and power spectral density. It was found that the autocorrelation function of the Si/SiO₂ interface roughness is well approximated by an exponential form rather than a Gaussian form. Numerical simulation was carried out to explain the kinetic roughening in the oxidation process with relation to the dependence on the oxide thickness.