Here in semiconductors, the carrier density n is tuned.
Temperature effect
In metals, conductivity decreases with increasing temperature. This is generally caused by the reduced relaxation time τ because of the increasing lattice vibrations.
However, in semiconductors, the conductivity will be overwhelmed by the huge increase in carrier density (generally, n(T)≈Nexp(−E/KT)).
Density
Density of the occupying electrons ρ is the density of states D(E) times state occupancy f(E).
ρ(E)=dn(E)/dE=D(E)f(E)
Direct and indirect bandgap
To direct bandgap semiconductor can emit photon directly, indirect semiconductors must have phonon involve.
Number of holes/vacancies
n=∫Eg∞f(E)D(E)dEandp=∫0Eg[1−f(E)]D(E)dE
with Fermi-Dirac distribution function f(E)=1/(1+expkTE−μ) and D(E)=DeE−Eg from electron gas model.