Why the conductivity of metals increase with decrease in temperature, but conductivity of semiconductors increase with increase in temperature?
Why the conductivity of metals increase with decrease in temperature, but conductivity of semiconductors increase with increase in temperature?
The conductivity of metals is defined by
sigma=nqm
wheren= charge carrier density
q=charge of the carrier
m=mobility of the carrier
The electrons that are charge carriers in a conductor will gain energy and go into higher energy levels. However, these energy levels are all still in the valance band. So the number of charge carriers will not change for a conductor with an increase in temperature.
Now consider q. As temperature increases, the charge on each carrier will not change.
Finally, what happens to the mobility? Recall that mobility is the drift velocity divided by the electric field strength. Temperature won't affect the electric field strength. But it will decrease the drift velocity because as the temperature increases, the atomic vibrations will increase, which will cause more collisions of the electrons with the crystal lattice. Hence the drift velocity will decrease.
The relationship is not linear, however, if we consider the resistivity, which is the reciprocal of conductivity, we do get a linear relationship:
where rhoroomTemp is the room temperature resisitvity and alpha is the temperature coefficient of resistivity.
The electrical conductivity of a conductor will decrease with an increase in temperature
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