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Atomic force microscope analysis, with a resolution of ≲1.1 nm, shows that peak-to-peak surface roughness (Δhp-p) of amorphous silicon films thinner than ≈50 nm on silicon dioxide can be controlled to better than 5 nm. Low-pressure, chemically-vapor-deposited silicon films on silicon dioxide initially show an approximately linear increase in the surface roughness due to growing nuclei as the deposition progresses, followed by a decrease in the surface roughness as growth nuclei coalesce. A simple model based on random nucleation and nuclei growth displays similar trends. Films deposited on rougher substrates show more surface roughness. Surface treatment during the predeposition cleaning process does not significantly affect Δhp-p. As a means of producing smooth surfaces, films thinner than about 20 nm are first deposited more thickly than needed, and then etched back to the desired dimension; the use of a binary HNO3 and HF etching process improves roughness control. Boron-ion implanted and subsequently crystallized 45-nm-thick Si films show significant smoothing with Δhp-p≈2.2 nm. Thin amorphous silicon films deposited by source evaporation are attractive because they can be deposited at room temperature, and have smoother surfaces (Δhp-p≈2.5 nm) than comparable films produced by chemical vapor deposition.