Specific resistance of semiconductors Why does the specific resistance of a semiconductor decrease with an increase in temperature, as an increase in temperature should cause the specific resistance to increase?
 A: The electrical resistance in a material is a property determined by
electrical charges in motion.   So, there are two sources of 
temperture dependence: the charges can change (basically, become more or
less numerous), or the motion can change.   
Electrical resistance in metals
is almost entirely due to scattering (thermal interaction with the
motion of the charge carriers), because the number of charge carriers
is just the population of electrons in the conduction band.  
So, for conduction in a metal, where charge carriers are constant in number,

increase in temperature should cause the specific resistance to increase
  is correct.   In the Drude approximation, a metal's resistance rises
  proportionally to absolute (Kelvin) temperature.


Semiconductors, on the other hand, have no charge carriers except a few
that are CREATED by thermal excitation.   So, under any conditions
where the temperature  has a larger effect on charge-carrier-density than
3000 parts per million per degree K, we expect the temperature
dependence of resistance to change sign.   In semiconductors, it does.
In some materials (semimetals, like graphite at room temperature) the
two effects just balance; we don't call those materials semiconductors
or metals.
A: The relaxation time  t , as well as to some extent the charged carrier density, n, changes with temperature in a semiconductor. The density for a semiconductor at any arbitrary temperature,T can be given as 
$n(T) = n'e^{-\frac{E}{k_{B}T}}$
In the above equation E is the energy gap between the upper portion of the valence band and lower portion of conduction band. $k_{B}$ is Boltzmann's constant 
Equation suggests that the density of the charged carrier increases with temperature hence conductivity increases so finally resistivity decreases 
Why the last part? 
Here is the equation I hope you know this 
Conductivity = $\dfrac{(n q^{2}t)}{m}$
