Multi-Scale Regular-Fractal Topography Characterization and Modeling

Abstract

Regular-fractal topography on RF-switch MEMS surface is reported over different scale ranges. Surface topography is crucial in understanding underling physics associated with the surface contacts, switch working performance, and reliability. The complexity of these structures requires new techniques to characterize topography and then replicate the multi-scale regular-fractal structure for analysis. Topography on RF-switch contacting surfaces are scanned by atomic force microscopy (AFM) at different length scales (e.g. 1×1, 10×10 and 60×60 μm2). A sample allocation plan is designed to maximize the spatial representative of the AFM scanning patches with different resolutions and uniformly distributed sample patches. The scanning data are used for characterizing and model estimation. Hexagonal patterns are found on at coarser scales (e.g. 10×10 and 60×60 μm2). They were formed by the remnant (polymer) of etching process. Random irregularity is observed and the fractal structure at finer scales (e.g. 1×1 μm2) is identified. A regular-fractal model is proposed to decompose and characterize the regular and fractal structures with two model components: one for the regular geometric pattern and the other for fractal irregularity. The former uses a 2D cosine functions to characterize dominant modes in the regular (larger scale) patterns. The later summarizes random irregularity in finer scales with a statistical fractal model estimated from the data on the scattered sample patches. The model validation is made through the comparisons of topography and conventional roughness parameters between the results of simulation from the proposed model and that derived from AFM scanned data.

Finite element based contact analysis of radio frequency MEMs switch membrane surfaces

“…The newly emerged smaller contact spots can be observed close to the edge of existed larger contact zones. In Liu's work [44], it was shown that a fractal surface structure is statistically homogeneous or 'standing out' asperities spread more likely uniform and spatially separate. The asperity merge on pure fractal surfaces may tend to bring about fewer asperities together than on regular-fractal surfaces on that the merge bring about more closely clustered asperities on top of bumps, therefore forms many isolated smaller contacting islands all over.…”