The electrical conductivity of a semiconductor increases with rise in temperature because:

In a semiconductor , electrical conductivity depends on the number of free charge carriers (electrons and holes). As temperature rises, thermal energy increases , which causes more covalent bonds to break , liberating more electrons into the conduction band and creating holes in the valence band. This increase in intrinsic carrier concentration enhances conductivity. The band gap does decrease slightly with temperature, but not drastically enough to be the primary cause. The dominant mechanism is the thermal excitation of electrons across the band gap due to breaking of covalent bonds.