Temperature Dependence of Semiconductor Conductivity

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nematollahi

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Hi every one
I want some one explain me this event in semiconductors:

Suppose we have a semiconductor with some impurity. By increasing the temperatures, an increase in majority(that is negligible with respect to the total number of them) and minority carriers will be seen. The difference between the concentrations of majority and minority carriers remains constant.
This difference vanishes at very high temperatures

My question is about the last term. If both carriers increase,why the difference will be vanish?By increasing temperature the electron-hole pair will be produced and the number of added carriers of two type are equal.
 

In a semiconductor all the carriers have exponential dependence of temperature .
At mid range temperatures ,
the concentration of extrinsic carriers dominate and are larger than intrinsic carriers by factor of (10^x,x=1,2,3...)
however at high temperatures intrinsic carriers dominate.
now as per your question "If both carriers increase,why the difference will be vanish?"
the difference doesn't vanish as electron-hole pairs are generated it's only that the difference becomes negligible in comparison with the large amount of carriers present(like adding 0.1 to 100) ,the extrinsic features of the semiconductor no longer matter.
The other way of saying it is that the ,ratio of the difference to the intrinsic carrier concentration vanishes.
 

Another way to think of this is in terms of the Fermi energy. If the Fermi energy of the electrons in a semiconductor is in between a conduction and a valence band at room temperature, the electrons will not have sufficient potential to go to the conduction band (except for the statistical few that cross ie dark current). As the temperature of the semiconductor increases, the Fermi energy increases (dark current increases) and at a high enough temperature it will reside in the conduction band. Once the fermi energy is in the conduction band, all electrons have enough thermal energy to go to the conduction band and therefore there no longer exists a band gap or any semblance of electron-hole pairs: it is now a bad conductor.
 

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