At first place, let´s to change your assertion using the concepts: conductivity instead of resistivity in the following way:

"Taken a doped semiconductor at high impurity concentration such that the impurity states are extended in nature, as we lower the temperature, condutivity show weak temperature dependence i.e. very small decrease of condutivity with decrease in temperature. If the temperature is lowered further the condutivity becomes independent of temperature, why is it so?

Normally, if one reduce kT less number of carriers will move and hence condutivity should decrease !

This assertion is based in the Classical Model given by:

conductivity = charge x number of carriers x electron mobility.

where conductivity = 1 / resistivity (inverse)

But using a Quantum Model of energy bands we have that:

Metals are materials that have a half-filled conduction band or valence band of overlap of the conduction band. This allows electrons to walk freely through the metal. The semiconductor has a separation of these bands KT order. However, when a semiconductor is heavily doped band energy introduced by doping becomes too large superposing the semiconductor conduction band in intrinsic form, and this promotes the migration of valence band electrons into the conduction band so analogous to a metal (temperature independent) at very low temperature.

@Lucas Máximo Alves

I should rather ask, how does temperature induce insulator to metal transition for heavily doped semiconductors. Let me understand more. I have attached the schematic of the curve.

 Following paper may give u insight of metal to insulator transition

Dear Chetan,

Can you please send me the link or the paper in my email. I am not able to download it.

Regards,

Dinesh

heavily doped means more concentration of the charge carriers, which causes the increase in conductivity and hence becomes metallic like characteristics

Dear dinesh

http://onlinelibrary.wiley.com/doi/10.1002/zaac.201400042/abstract

@Yawar Abbas,

THAT IS TRUE FOR INCREASING CONCENTRATION, BUT I AM ASKING ABOUT SCENARIOS WHERE WE TAKE ONE SAMPLE (ONE CONCENTRATION) AND COOL IT DOWN. iN SUCH CASE WE SEE MIT TOO, WHY?

@Chetan Singh,

Can you please send the file to my email ID [email protected],

as it seems that our institute do not have access to this journal temporarily

Thanks.

Dear Dinesh, The conductivity of a semiconductor depends on the position of the Fermi level in the energy dyagram. At high doping the Fermi level is situated in the conduction band (for n-doping) and in valence band at p-doping. Such position of the Fermi level makes the number of carriers independent on temperature.

But at small doping the Fermi level is in the forbidden zone and its distance to the conduction zone plays a role of the activation energy. In this case the number of carriers exponentially depends on the reverse temperature.

At an intermediate level of doping at high temperature the Fermi level stays lower the bottom of the conduction band and at low temperature it enters the conduction zone with the mentioned by you result: thransition to metallic type of conductivity.

Dear Sir,

@Boris I. Sedunov

I think I have an answer my question now. However, it would be nice to have someone with sound knowledge would give me the answer.

you have mentioned, ''at low temperature it enters the conduction zone with the mentioned by you result: thransition to metallic type of conductivity." Why?

At high doping the energy levels of impurity atoms become attached to the bottom of the conductance band. So, these levels form some sort of attachment to the conductance zone. The Fermi level position is given by the electric neutrality of the semiconductor. It means: the number of ionized impurity atoms is equal to number of free moving electrons in the conductance zone. So, the Fermi level sticks to the impurity levels and changes not so much. It looks like the metallic type of conductivity.

Thanks for your question. I thought a lot about it 50 years ago. It is nice to refresh memories. Best regards,  Boris

If the doping is low and the donor band is separate from the conduction band, as temperature is lowered, Fermi level starts settling somewhere between the donor and conduction band. Due to this, the number of free carriers in the conduction band keeps going down. This is called freezing out of dopants. Once the doping is so high that the donor band merges with the conduction band, the free carriers cannot be frozen out because now there will always be states around the fermi level.

Yes, Geetak! That is just what I meant!