We know that resistivity `rho=m/(e^2ngamma)` .
In a conductor, the value of n is large but almost constant with any change intemperature. However, with increasing temperature, the collision rate of electrons increase, and that causes `gamma` (mean time between collisions) to be smaller. That’s why resistivity increases with temperature in a conductor.
On the other hand, for a semiconductor, n is small but increases very fast, as the increased thermal agitation make more charge carriers available, and so resistivity decreases as temperature increases. Same as a conductor, the `gamma` value decreases as temperature goes up, but effect of increasing n is stronger then the decreasing in `gamma` , so the denominator in the formula is increasing, the whole formula has a decreasing value as temperature goes up, and it makes sense that resistivity decreases as temperature increases in a seminconductor.