Extrinsic semiconductors exhibit intrinsic behavior at high temperatures primarily because thermal excitations significantly increase the number of electrons in the conduction band, overshadowing the contribution from doping. As temperature rises, the Fermi-Dirac statistics indicate that the thermal energy allows more electrons to be excited into the conduction band, leading to a predominance of intrinsic characteristics. The relevant criterion for this phenomenon is that the thermal energy (kT) must be much greater than the difference in Fermi levels between intrinsic and doped semiconductors. This results in the effective neglect of the additional doped carriers. Consequently, the semiconductor behaves as if it were intrinsic under these conditions.