Decoupling small-scale roughness and long-range features on deep reactive ion etched silicon surfaces

A methodology to decouple irregular small-scale roughness and regular long-range features on deep reactive ion etched (DRIE) silicon surfaces is presented. Height-height correlations of three different DRIE silicon surfaces are evaluated via atomic force microscopy height data and fit to an analytic, five-parameter model based on a phenomenological scaling function for the small-scale roughness and a Bessel function for the long-range features. The resulting roughness parameters are constant for all three surfaces at small lateral length scales, indicating self-affine roughness inherent to the DRIE process, but dependent on the etch process at large lateral length scales, increasing by a factor of five as the controlled portion of the DRIE process decreased. The results from the analysis are also compared to fracture strengths from recently introduced theta test samples with the same etch features as an example of the potential of the analysis in providing an unbiased assessment of the processing-structure-property relationships for DRIE silicon surfaces.