We have studied the statistical properties of random surface roughness at the Si-SiO2 interface using high-resolution transmission electron microscopy (HRTEM). The spectral properties of the HRTEM roughness on normally prepared and intentionally roughened samples appears to be well characterized as a first-order autoregressive or Markovian process which corresponds to an exponential decay in the autocovariance function rather than the usual Gaussian approximation which has been widely used. Such an exponential decay is characterized by tails in the spectrum which are directly attributable to the discrete or steplike nature of the interface roughness which is restricted to occur on crystalline atomic sites. Using a simplified model, we have estimated the effect of projecting the two-dimensional interface roughness through the cross-section thickness to form the one-dimensional boundary studied here. For an isotropic medium, we find that the statistical character of the roughness is preserved during this transformation, but that the rms fluctuation of the roughness is attenuated so that the actual interface is rougher than indicated by the HRTEM technique. After correcting for such averaging, the parameters estimated from the HRTEM are more in agreement with the same parameters used to fit the surface-roughness-limited Hall mobility in metal-oxide-semiconductor field-effect transistor devices.
ASJC Scopus subject areas
- Condensed Matter Physics