Why can't we dope the intrinsic semiconductors with sixth or second group elements? Suppose we want to make an n-type  silicon semiconductor why do we use arsenic or phosporous as an impurity? Why cant we use selinium or terellium?
Infact my doubt is when we use sixth group element it can donate two free electrons so that we can have higher carrier concentration even with lesser doping concentration . Why it is not done so?
 A: On theoretical grounds, there is the issue of dopant "depth". You can look online for a table of ionization energies of dopants in Si, for example here: Dopant Energy Levels.
In terms of this table, what you want is the highest energy level (for donor) or lowest energy level (for acceptor). The ionization energies listed are relative to the band where the electron goes to/comes from. "Shallow dopants" have a small ionization energy which is important for a couple of reasons.


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*A small ionization energy makes it very easy for the electron to leave the dopant, in fact it is often said that shallow dopants are guaranteed to be thermally ionized under normal conditions. The probability of ionization depends on the location of dopant energy level in respect to the Fermi level (filling), however the Fermi level is almost always within the band gap.
Phosphorus is a classic shallow dopant in silicon, only having 0.045 eV ionization energy.
You can see with selenium however that there are two ionization levels, indicating that, yes, it should be able to donate two electrons. The first, 0.25 eV, could provide some doping, but the second ionization, 0.4 eV, is unlikely occur if there are already too many conduction electrons -- if the Fermi level is already sitting too high in the band gap. This means we cannot use Se to obtain high doping levels.

*Another closely related factor with dopant depth is that deep dopants act as more powerful scattering sites. Although it's not a perfect relationship, the ionization energy can be thought of as the depth of the potential well that binds the electron. Once the electron leaves the dopant it leaves behind that potential well like a gaping hole. Moreover the deep dopants can also act as recombination centers, literally sucking out the minority carriers that need in devices like bipolar transistors.
To make an analogy, imagine you (electron in conduction band) are driving along a road (potential landscape). Shallow dopants are like little pot holes here and there, whereas deep dopants are like giant pits where there you can probably get out, but there is the chance that you will fall through all the way down into the sewer (valence band). :)
In practice, other issues may intervene such as the practicality of dissolving the dopant nicely into the silicon melt, or tendencies of the dopants to clump together into inert clusters or to initiate crystal faults during crystal growth. Dopants have very different diffusion rates, which must be balanced together in diffusion doping. Also, scattering is not strictly proportional to ionization energy. I suppose one of these practical reasons is why manufacturers never use lithium, for example.
See also http://ecee.colorado.edu/~bart/book/extrinsi.htm
