Q.On which factors does the electrical conductivity of a pure semiconductor depend at a given temperature?

[!TLDR] At a fixed temperature, a pure semiconductor's conductivity depends on its charge-carrier density and their mobility, via $\sigma=nq\mu$ -- both of which trace back to the material's band gap and crystal quality. [!ANSWER] Carrier density $n$ (set by the band gap a …

Electrical conductivity of a solid is given by $\sigma=nq\mu$, where $n$ is the density of charge carriers, $q$ is the charge on each carrier, and $\mu$ is their mobility. For a PURE (intrinsic) semiconductor at a GIVEN, fixed temperature, this means the conductivity depends on: (1) the carrier density $n$ (in this case $n_e=n_h$), which itself is set by how many valence electrons have enough thermal energy to cross the material's particular band gap at that temperature -- a smaller band gap or a higher temperature produces more carriers; and (2) the mobility $\mu$ of those carriers, which depends on factors such as the carrier's effective mass, whether the crystal is crystalline or amorphous, the presence of structural defects, and the nature of any impurities present, all of which affect how easily a carrier can actually move through the lattice once it exists. So even …

Start from $\sigma=nq\mu$ and separately identify what determines n (band gap and temperature) and what determines mu (crystal …

Naming only temperature as the factor and forgetting that, even at one fixed temperature, crystal quality and mobility-affecting factors still …