Why some elements of same group cannot be used for doping semiconductors? 15th group elements like As, Sb, P can be used for doping whereas N and Bi cannot be used for doping even though they too belong belong to 15th group. Why?
 A: For good doping you need two things: (1) get enough dopant in to be useful in changing carrier concentrations, and (2) having an energy level close to a band edge to generate electrons (holes) in the band, rather than making a mid-level recombination center. The below is assuming you are trying to dope Silicon.  Data is generally from Sze's excellent 'Physics of Semiconductor Devices' text.
Bismuth certainly has a donor level not much lower than As, satisfying (2). However, the solid solubility of Bi is roughly 3 orders of magnitude less than As, peaking at below $10^{18}/cm^3$.  This limits the utility of Bi in current device technology - you just can't get enough in.
Nitrogen has very low solubility in silicon.  I cannot find quickly any info on energy levels in the gap, but oxygen has several levels, all pretty much near gap.  I'd say nitrogen loses out on both (1) and (2).
A: Nitrogen is actually quite commonly used for doping silicon carbide. It doesn't work well in silicon for the reasons Jon Custer mentions, but silicon carbide with its different crystal structure and electronic properties allows nitrogen doping to work much better. Phosphorus can also be used, and I'm not too clear on the exact reasons one might be chosen over the other.
I believe (additional, beyond the stoichiometric amount) nitrogen is also a practical dopant in gallium nitride, though don't quote me on that--I work with SiC, not GaN.
I've never heard of using bismuth as a dopant in any semiconductor, though it probably can be used in some unusual ones. It's a very large atom, so I have doubts about how well it could be implanted into silicon carbide without destroying the crystal lattice--even the usual dopants for SiC cause a lot of crystal defects, and silicon carbide doesn't anneal out defects very well. Jon's answer already addresses why it can't be used in silicon.
