How Does Temperature Affect the Conductivity of a SemiConductor? 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!
sigma = C e – Eg/2kT
We can graph this equation on log vs. 1/T axes to get a linear plot (as with all Arrhenius type equations):
