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Predicted Polishing Behavior Of Plasma Assisted Chemical Etching (PACE) From A Unified Model Of The Temporal Evolution Of Etched Surfaces

We study the smoothing behavior of PACE using a differential equation which describes the temporal evolution of a solid surface subject to any etch (or deposition) process. The differential equation explicitly exhibits the evolution of any surface to be a product of a geometric factor, common to all such processes, and a rate factor that depends on the process physics. We take the rate factor to be a combination of isotropic and anisotropic processes. In general, it must be derived from first principles or deduced by comparing the topography predicted by the surface evolution equation with the observed etch topography for a particular physical hypothesis. An example of this is shown for the etched shape of microelectronic "deep isolation trenches" fabricated by a purely anisotropic process. Good agreement with observation is achieved when the rate coefficient is taken to have a local surface curvature or local electric field dependence. Finally, the surface evolution equation is used to explore the ability of PACE to smooth and polish an initially rough surface by obtaining the time dependence of the spatial Fourier coefficients of the surface shape from the differential equation. This analysis provides a vivid exposition of the PACE smoothing process. Both the anisotropic and isotropic etching regimes of PACE are considered.