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How would one get or make STM tips with the following characteristics:-apex has 1 nm radius of curvature (or less)-opening angle (or cone angle) in the 5 nm above the apex is less than 60 degrees (full angle)-tip material is stable in air -can achieve atomic resolution
The two main types of STM tips seem to be W and Pt-Ir. W oxidizes in air, Pt-Ir does not (are you doing STM in air or UHV?). I've seen where people used W tips etched in HF just prior to scanning and they lasted a little while before oxidizing.
Usually W tips are electrochemically etched, usually Pt-Ir tips are cut/torn (although they can also be etched).
I would think that using electrochemical etching (where you control the voltage/current and can move the sample in/out of the solution) you could control the tip characteristics as required.
You may want to check out Bob Wolkow's method for making tips
[M. Rezeq, J. Pitters and R.A. Wolkow, J. Chem. Phys. 124 (2006), p.
204716]. He reports the process working with tungsten.