Honestly, i do not actually know if this is possible, certainly not by me, or perhaps it has been invented and done or tried and failed before, i do not know, but here goes anyway, at the risk of looking stupid. i do not want to hold a concept idea back being afraid to look stupid while it might actually serve mankind one day.

Atomic sieve - Concept.

Prepare a lattice made from 9 similar atoms of the same element or kind, arranged 3x3x3, now punch out the single center atom from the 9, to create a central, one atom thick, open hole, a atomic sieve that only allows a single atom thick through the other 8 atoms forming a [solid] outer rim. [ Could use more atoms for more strength of course].

If we made the atomic sieve out of a magnetic material, like a metal, and we punched out the single, one metallic atom [impurity], it could fall down onto the pure silicon's crucibles top layer, and contaminate the pure silicon below, but, this would allow us to use a Anode or magnetic needle, to stick through the center of the one atom thick sieve, and electro magnetically pick back up the single metallic atom, now fused with the silicon, and allow us to lift the most thin, pure silicon string imaginable.

The single metal atom found on the upper most top of the silicon string will be discarded anyway. A extremely slow twist, or turning could be introduced to the electro Magnetic Anode, the needle lifter, way more steady and precise than a human hand ever could.

Someone in the comments will surely explain to me how utterly ridiculous the concept is and why.