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The patterning of silicon and silicon oxide nanocones onto the surfaces of devices introduces interesting phenomena such as anti-reflection and super-transmissivity. While silicon nanocone formation is well-documented, current techniques to fabricate silicon oxide nanocones either involve complex fabrication procedures, non-deterministic placement, or poor uniformity. Here, we introduce a single-mask dry etching procedure for the fabrication of sharp silicon oxide nanocones with smooth sidewalls and deterministic distribution using electron beam lithography. Silicon oxide films deposited using plasma-enhanced chemical vapor deposition are etched using a thin alumina hard mask of selectivity > 88, enabling high aspect ratio nanocones with smooth sidewalls and arbitrary distribution across the target substrate. We further introduce a novel multi-step dry etching technique to achieve ultra-sharp amorphous silicon oxide nanocones with tip diameters of ~10 nm. The processes presented in this work may have applications in the fabrication of amorphous nanocone arrays onto arbitrary substrates or as nanoscale probes.