Question

The electrical conductivity of pure semiconductor is increase exponentially with temperature

Answer 1

so what ?
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Answer 2

Let’s Consider the effect of increasing the temperature on the conductivity of semiconductors. 
                                      
Let's look at the factors that go into conductivity of a semiconductor and consider how each of these are affected:

sigma = ni q (me + mh)


First let's consider q. As with conductors, as temperature increases, the charge on each carrier will not change.
           

Now consider mobility. The effect of an increase in temperature on mobility is the same as it was for conductors. With the same reasoning, we see that the drift velocity will decrease causing the mobility to decrease. 
                  

Lastly, let's consider what will happen to ni for semiconductors as temperature increases. The electrons in the valance band will gain energy and go into the higher energy levels in the conduction band where they become charge carriers! So this term will increase. Not only will it increase, but it will increase exponentially! (Promoting electrons from the valance band into the conduction band is a thermally activated process.) 

ni = C e – (E – Eave)/kT  

ni = C e – Eg/2kT

So even though mobility decreases, the exponential increase in the number of charge carriers will dominate.

Conclusion:
The electrical conductivity of a semiconductor will increase exponentially with an increase in temperature!